Related Links:
Phase II Studies Explained Page
Introduction
Calculations
Sample Size Tables
References
Introduction
Technical Considerations
Example
This page provides explanations, calculations, and sample size tables for Phase II trials, where the sample size needed is determined by Simon's procedure.
Only Simon's two stage procedure will be discussed in this page. Readers are referred to the Phase II Studies Explained Page
for Phase II studies generally and for comparison with other procedures available.
Simon's is a two stage procedure.
- The first stage requires a small sample size (n1), and sets a bench mark number of successes (r1) above which the
trial enters the second stage. If that bench mark (r1) is not surpassed at the end of stage 1 (n1), then the trial ends
with the treatment considered inadequate and abandoned (rejection).
- In the second stage, the total sample size, including those already
collected in stage 1, is defined (nTot), and a second and final bench mark for the total number of
successes, including those already collected in stage 1, is defined (rTot). once
the number of successes surpassed rTot, the trial can terminate and the treatment
considered worthy of further evaluation at the Phase III or control trial level (acceptance).
If rTot is not surpassed after nTot cases, then the trial terminates, and the
treatment considered inadequate and abandoned (rejection).
- Please note: In Simon's procedure, acceptance and rejection refers to whether the treatment being tested is successful enough for further evaluation, but not the acceptance or rejection of the null hypothesis
Simon's procedure therefore has advantages over Fleming's Procedures as in the Sample Size for Phase II Study (Fleming's Procedure) Page
and Gehan's Procedure as in the Sample Size for Phase II Study (Gehan's Procedure) Page
, in that the sample size is not fixed, and the
trial can terminate early if the results are obvious. It is particularly effective in rejecting new treatments with
below expectation proportion of successes.
Parameters : The following parameters are required
- The success rate below which the treatment is considered inadequate and rejected (π0)
- The success rate above which the treatment is accepted as worthy of further evaluatuion (π1)
- Probability of Type I Error (α), the probability of error for rejecting the null hypothesis, that of wrongly accepting the treatment as worthy of further evaluation. In most cases α of 0.1 or 0.05 is used
- Power (1-β) where β is the Probability of Type II Error. Power is therefore the probability of accepting the treatment as worthy of further evaluation, and in most cases power of 0.8 or 0.9 is used
Results : The programs produces the following results
- The maximum sample size for stage 1 (n1)
- The number of success required in stage 1, above which stage 2 is entered, and at or below which after n1 cases results in
terminating the trial with rejection of the treatment
- The total maximum sample size (nTot), inclusive of both stages
- The total number of success required (rTot), inclusive of both stages, above which resulting in terminating the trial with
acceptance of the treatment for further evaluation, and at or below which after nTot cases results in rejection of the treatment
- The average expected number of cases (EN) for a decision
- The probability of early termination of the study (PET) if the true success rate is below requirements
Models : Simon's Procedure produces two alternative results, based on different statistical assumptions.
- The Optimal model has a smaller sample size for stage 1 and is more likely to terminate early (PET) if the true success rate
is below requirement (<π0), so is preferred for early screening of new treatments to exclude those without potentials from expensive further study.
- The minimax model requires a smaller overall sample size (EN), so is preferred if the researcher
is optimistic about the treatment being tested, hoping to require a smaller overall sample size to validate the acceptance of the treatment for further trials
References
Simon R (1989) Optimal two-stage designs for phase II clinical trials.
Control Clin Trials 10:1-10
Machin D, Campbell M, Fayers, P, Pinol A (1997) Sample Size Tables for
Clinical Studies. Second Ed. Blackwell Science IBSN 0-86542-870-0 p. 256-257
Algorithm
I created the Javascript program on this page to calculate the sample sizes for Simon's procedure. I followed the formulae as described in Machin's text book (see references). In checking my results against the table in the text book (Table 10.5 page 285), I found that I was able to replicate all the contents of the table in the Optimal model, but in nearly a third of the calculations for the Minimax model, the results of my calculations differed from that in the text book. After examining the formulae in detail, and some trial and errors I think I have found out the reason and the solution.
The formula for calculating the number to use when starting interation (the starting point), produced by formula 10.2 (page 257) produces the correct result in the majority of situations, but is too large when the precision required is too high (higher power or lower α) when the rejection rate (π0) is close to 0.5, or when the gap between acceptance and rejection rates (π1-π0) is narrow. In these situation the starting point number need to be smaller.
After some trial and error, I reduce the starting number by 10, then iterate the whole algorithm, increasing the starting number with each iteration, until the starting point calculated by formula 10.2 is reached, choosing the results where the total sample size (nTot) for the Minimax model is the smallest. By doing this, I was able to replicate exactly all the numbers in table 10.5 of the text book.
My conclusions are that the algorithm in StatsToDo produces the correct answer within the tested ranges. These are
- π0 in a range between 0.05 (5%) and 0.8 (80%)
- π1π0>=0.1 (10%)
- α >= 0.01
- power <= 0.9
Users should however note that, although the reference values can be replicated, the original formulation has been altered to achieve this. Inexperienced user should therefore seek advice before using the results.
The algorithm I used, translated into R code, is presented in the R code section on this page. The coding is deliberately long handed to make it simple for others to follow. This algorithm is able to reproduce all the numbers in table 10.5 of the text book by Machins. For those who are interested, feedback, criticism, correction, and advice are very much welcomed.
Limitations
The algorithm in this web page is written in Javascript and has the following limitations
- To calculate the best Optimal results, the program is iterated forewards by 30 (finish = start + 30). If this sample size value exceeds 120, the program will be aborted as it would take too long to run.
- To calculate the Minimax model with the least total sample size, the starting value is reduce by 10, then iterate forwards until it reaches the original starting number. The iteration with the minuimum total sample size for Minimax model is then selected as the result. This is sufficient for most cases, but may still produce suboptimal values (Total sample size larger than necessary) if α is low (α<0.01), power is large (pw>=0.9), π0 is close to 0.5 and the difference (π1-π0) less than 0.1
- For special cases where the range of search need to be wider than that set in the web page program, the user will need to download the R orogram, adjust the range of search (start and finish) manually, and run the program in R.
A better program
R has a package to perform Simon's procedure, but unfortunately it will not download on my version of R so I am unable to test or use it. For those who is able to download the package, the instructions are in https://www.rdocumentation.org/packages/clinfun/versions/1.0.15/topics/ph2simon
A particular cancer, with the current available treatment, has a five year survival rate of 10%.
A new drug is developed which looks promising, and we wish to conduct a Phase II trial. We decided that
if the new drug can improve survival to 40% in a phase II trial, then it is worth the expense
of develop this drug and test it in a large phase III trial (acceptance of the treatment). However, if the
survival rate is no better than 40%, then the new drug should be rejected from
further development (rejection of the treatment). We decided to use α of 0.05, and power of 0.8 in such a study.
| Optimal | Minimax |
r1 | 0 | 1 |
n1 | 4 | 8 |
rTot | 3 | 3 |
nTot | 15 | 13 |
EN | 8 | 9 |
PET | 0.66 | 0.81 |
The parameters are therefore α=0.05, (1-β)=0.8, π0 = 0.1, and π1=0.4. The results
are as in the table to the right.
The following are the possible scenarios after, the minimax model is used to demonstrate
- Stage 1. n1 = 8, r1 = 1
- If no more than 1 case survived (success<=1) in the first 8 cases,
the treatment is abandoned (treatment rejection) at the end of stage 1. End of study
- With the second survival (success>1) anytime within the first 8 cases, the trial enters the second stage
- Stage 2. nTot = 13, rTot = 3
- Including the data from stage 1, if there are 3 or less survivals (successes<=3) at the end of 13 cases,
the treatment is abandoned (treatment rejection) as not worthy of further development. End of study.
- On the 4th survival (>3 successes, 2 in stage 2 plus the 2 from stage 1) any time before 13 cases are studied,
the treatment is declared worthy of further development, go onto Phase III trial, etc, (treatment acceptance). End of study.
- We expect that, if the true success rate is 40% or more, we need an average of 9 (EN=9) cases to decide accepting the treatment.
If the true success rate is less than 40%, we have 81% chance (PET=0.81) of rejecting the treatment
α=0.1 pw=0.8
α=0.05 pw=0.8
α=0.01 pw=0.8
α=0.1 pw=0.9
α=0.05 pw=0.9
α=0.01 pw=0.9
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.8 | 0.05 | 0.15 | 1 | 20 | 4 | 56 | 29.5 | 0.74 | 1 | 29 | 4 | 44 | 35.4 | 0.57 |
0.1 | 0.8 | 0.05 | 0.2 | 0 | 9 | 2 | 24 | 14.5 | 0.63 | 0 | 12 | 2 | 21 | 16.1 | 0.54 |
0.1 | 0.8 | 0.05 | 0.25 | 0 | 6 | 2 | 23 | 10.5 | 0.74 | 0 | 12 | 2 | 16 | 13.8 | 0.54 |
0.1 | 0.8 | 0.05 | 0.3 | 0 | 5 | 1 | 12 | 6.6 | 0.77 | 0 | 8 | 1 | 9 | 8.3 | 0.66 |
0.1 | 0.8 | 0.05 | 0.35 | 0 | 4 | 1 | 11 | 5.3 | 0.81 | 0 | 6 | 1 | 8 | 6.5 | 0.74 |
0.1 | 0.8 | 0.05 | 0.4 | 0 | 4 | 1 | 8 | 4.7 | 0.81 | 0 | 5 | 1 | 7 | 5.5 | 0.77 |
0.1 | 0.8 | 0.05 | 0.45 | 0 | 3 | 1 | 8 | 3.7 | 0.86 | 0 | 4 | 1 | 6 | 4.4 | 0.81 |
0.1 | 0.8 | 0.05 | 0.5 | 0 | 3 | 1 | 6 | 3.4 | 0.86 | 0 | 3 | 1 | 6 | 3.4 | 0.86 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.8 | 0.1 | 0.2 | 2 | 24 | 9 | 65 | 41.9 | 0.56 | 2 | 29 | 8 | 56 | 44.3 | 0.43 |
0.1 | 0.8 | 0.1 | 0.25 | 1 | 13 | 5 | 34 | 21 | 0.62 | 1 | 16 | 5 | 31 | 23.3 | 0.51 |
0.1 | 0.8 | 0.1 | 0.3 | 0 | 7 | 3 | 18 | 12.7 | 0.48 | 0 | 7 | 3 | 18 | 12.7 | 0.48 |
0.1 | 0.8 | 0.1 | 0.35 | 1 | 8 | 2 | 13 | 8.9 | 0.81 | 1 | 9 | 2 | 12 | 9.7 | 0.77 |
0.1 | 0.8 | 0.1 | 0.4 | 0 | 4 | 2 | 11 | 6.4 | 0.66 | 0 | 5 | 2 | 10 | 7 | 0.59 |
0.1 | 0.8 | 0.1 | 0.45 | 0 | 3 | 2 | 11 | 5.2 | 0.73 | 0 | 4 | 2 | 9 | 5.7 | 0.66 |
0.1 | 0.8 | 0.1 | 0.5 | 0 | 3 | 1 | 6 | 3.8 | 0.73 | 0 | 4 | 1 | 5 | 4.3 | 0.66 |
0.1 | 0.8 | 0.1 | 0.55 | 0 | 3 | 1 | 5 | 3.5 | 0.73 | 0 | 3 | 1 | 5 | 3.5 | 0.73 |
0.1 | 0.8 | 0.1 | 0.6 | 0 | 2 | 1 | 5 | 2.6 | 0.81 | 0 | 3 | 1 | 4 | 3.3 | 0.73 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.8 | 0.15 | 0.25 | 4 | 29 | 16 | 84 | 53.4 | 0.56 | 6 | 46 | 15 | 75 | 61.8 | 0.45 |
0.1 | 0.8 | 0.15 | 0.3 | 3 | 19 | 8 | 39 | 25.3 | 0.68 | 2 | 18 | 8 | 37 | 27.9 | 0.48 |
0.1 | 0.8 | 0.15 | 0.35 | 1 | 9 | 5 | 23 | 14.6 | 0.6 | 1 | 10 | 5 | 22 | 15.5 | 0.54 |
0.1 | 0.8 | 0.15 | 0.4 | 1 | 7 | 4 | 18 | 10.1 | 0.72 | 1 | 9 | 4 | 16 | 11.8 | 0.6 |
0.1 | 0.8 | 0.15 | 0.45 | 1 | 6 | 3 | 13 | 7.6 | 0.78 | 0 | 4 | 3 | 12 | 7.8 | 0.52 |
0.1 | 0.8 | 0.15 | 0.5 | 0 | 4 | 2 | 8 | 5.9 | 0.52 | 0 | 4 | 2 | 8 | 5.9 | 0.52 |
0.1 | 0.8 | 0.15 | 0.55 | 0 | 3 | 2 | 7 | 4.5 | 0.61 | 0 | 3 | 2 | 7 | 4.5 | 0.61 |
0.1 | 0.8 | 0.15 | 0.6 | 0 | 2 | 2 | 8 | 3.7 | 0.72 | 0 | 3 | 2 | 6 | 4.2 | 0.61 |
0.1 | 0.8 | 0.15 | 0.65 | 0 | 2 | 1 | 4 | 2.6 | 0.72 | 0 | 2 | 1 | 4 | 2.6 | 0.72 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.8 | 0.2 | 0.3 | 8 | 39 | 24 | 99 | 61.5 | 0.62 | 8 | 45 | 21 | 84 | 66.8 | 0.44 |
0.1 | 0.8 | 0.2 | 0.35 | 2 | 13 | 12 | 46 | 29.4 | 0.5 | 2 | 13 | 12 | 46 | 29.4 | 0.5 |
0.1 | 0.8 | 0.2 | 0.4 | 2 | 12 | 7 | 25 | 17.7 | 0.56 | 2 | 14 | 7 | 24 | 19.5 | 0.45 |
0.1 | 0.8 | 0.2 | 0.45 | 1 | 7 | 5 | 17 | 11.2 | 0.58 | 1 | 10 | 5 | 16 | 13.7 | 0.38 |
0.1 | 0.8 | 0.2 | 0.5 | 1 | 6 | 4 | 13 | 8.4 | 0.66 | 1 | 8 | 4 | 12 | 10 | 0.5 |
0.1 | 0.8 | 0.2 | 0.55 | 1 | 5 | 3 | 10 | 6.3 | 0.74 | 0 | 4 | 3 | 9 | 7 | 0.41 |
0.1 | 0.8 | 0.2 | 0.6 | 0 | 3 | 2 | 6 | 4.5 | 0.51 | 0 | 3 | 2 | 6 | 4.5 | 0.51 |
0.1 | 0.8 | 0.2 | 0.65 | 0 | 2 | 2 | 6 | 3.4 | 0.64 | 0 | 2 | 2 | 6 | 3.4 | 0.64 |
0.1 | 0.8 | 0.2 | 0.7 | 0 | 2 | 2 | 5 | 3.1 | 0.64 | 0 | 2 | 2 | 5 | 3.1 | 0.64 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.8 | 0.25 | 0.35 | 11 | 43 | 33 | 112 | 69.6 | 0.61 | 12 | 52 | 29 | 96 | 76.3 | 0.45 |
0.1 | 0.8 | 0.25 | 0.4 | 7 | 25 | 16 | 52 | 32.4 | 0.73 | 5 | 24 | 15 | 46 | 36.7 | 0.42 |
0.1 | 0.8 | 0.25 | 0.45 | 4 | 15 | 9 | 27 | 18.8 | 0.69 | 3 | 15 | 9 | 26 | 20.9 | 0.46 |
0.1 | 0.8 | 0.25 | 0.5 | 2 | 8 | 7 | 21 | 12.2 | 0.68 | 2 | 9 | 6 | 17 | 12.2 | 0.6 |
0.1 | 0.8 | 0.25 | 0.55 | 1 | 5 | 5 | 14 | 8.3 | 0.63 | 1 | 6 | 5 | 13 | 9.3 | 0.53 |
0.1 | 0.8 | 0.25 | 0.6 | 1 | 5 | 4 | 10 | 6.8 | 0.63 | 1 | 5 | 4 | 10 | 6.8 | 0.63 |
0.1 | 0.8 | 0.25 | 0.65 | 0 | 2 | 3 | 8 | 4.6 | 0.56 | 0 | 2 | 3 | 8 | 4.6 | 0.56 |
0.1 | 0.8 | 0.25 | 0.7 | 0 | 2 | 2 | 5 | 3.3 | 0.56 | 0 | 2 | 2 | 5 | 3.3 | 0.56 |
0.1 | 0.8 | 0.25 | 0.75 | 0 | 2 | 2 | 5 | 3.3 | 0.56 | 0 | 2 | 2 | 5 | 3.3 | 0.56 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.8 | 0.3 | 0.4 | 12 | 40 | 42 | 122 | 74.7 | 0.58 | 20 | 67 | 36 | 102 | 82.8 | 0.55 |
0.1 | 0.8 | 0.3 | 0.45 | 6 | 20 | 20 | 55 | 33.7 | 0.61 | 6 | 23 | 18 | 48 | 37 | 0.44 |
0.1 | 0.8 | 0.3 | 0.5 | 5 | 15 | 12 | 32 | 19.7 | 0.72 | 3 | 12 | 11 | 28 | 20.1 | 0.49 |
0.1 | 0.8 | 0.3 | 0.55 | 2 | 8 | 8 | 20 | 13.4 | 0.55 | 2 | 8 | 8 | 20 | 13.4 | 0.55 |
0.1 | 0.8 | 0.3 | 0.6 | 1 | 5 | 6 | 14 | 9.2 | 0.53 | 1 | 5 | 6 | 14 | 9.2 | 0.53 |
0.1 | 0.8 | 0.3 | 0.65 | 2 | 6 | 4 | 9 | 6.8 | 0.74 | 2 | 6 | 4 | 9 | 6.8 | 0.74 |
0.1 | 0.8 | 0.3 | 0.7 | 2 | 5 | 3 | 7 | 5.3 | 0.84 | 2 | 5 | 3 | 7 | 5.3 | 0.84 |
0.1 | 0.8 | 0.3 | 0.75 | 1 | 3 | 3 | 7 | 3.9 | 0.78 | 0 | 2 | 3 | 6 | 4 | 0.49 |
0.1 | 0.8 | 0.3 | 0.8 | 0 | 2 | 2 | 4 | 3 | 0.49 | 0 | 2 | 2 | 4 | 3 | 0.49 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.8 | 0.35 | 0.45 | 19 | 52 | 52 | 132 | 79.9 | 0.65 | 18 | 55 | 44 | 109 | 86.2 | 0.42 |
0.1 | 0.8 | 0.35 | 0.5 | 7 | 20 | 24 | 58 | 35.2 | 0.6 | 10 | 31 | 21 | 49 | 40.8 | 0.46 |
0.1 | 0.8 | 0.35 | 0.55 | 4 | 12 | 14 | 32 | 20.3 | 0.58 | 4 | 12 | 14 | 32 | 20.3 | 0.58 |
0.1 | 0.8 | 0.35 | 0.6 | 4 | 10 | 10 | 23 | 13.2 | 0.75 | 4 | 13 | 8 | 17 | 15 | 0.5 |
0.1 | 0.8 | 0.35 | 0.65 | 1 | 4 | 7 | 15 | 8.8 | 0.56 | 2 | 7 | 7 | 14 | 10.3 | 0.53 |
0.1 | 0.8 | 0.35 | 0.7 | 0 | 2 | 5 | 10 | 6.6 | 0.42 | 0 | 2 | 5 | 10 | 6.6 | 0.42 |
0.1 | 0.8 | 0.35 | 0.75 | 1 | 3 | 5 | 10 | 5 | 0.72 | 0 | 2 | 4 | 8 | 5.5 | 0.42 |
0.1 | 0.8 | 0.35 | 0.8 | 1 | 3 | 3 | 6 | 3.8 | 0.72 | 1 | 3 | 3 | 6 | 3.8 | 0.72 |
0.1 | 0.8 | 0.35 | 0.85 | 0 | 1 | 3 | 6 | 2.8 | 0.65 | 0 | 1 | 3 | 6 | 2.8 | 0.65 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.8 | 0.4 | 0.5 | 23 | 55 | 60 | 135 | 82 | 0.66 | 27 | 71 | 51 | 112 | 94.9 | 0.42 |
0.1 | 0.8 | 0.4 | 0.55 | 9 | 22 | 28 | 60 | 36.3 | 0.62 | 11 | 30 | 24 | 50 | 41.4 | 0.43 |
0.1 | 0.8 | 0.4 | 0.6 | 5 | 12 | 18 | 38 | 20.7 | 0.67 | 6 | 16 | 14 | 28 | 21.7 | 0.53 |
0.1 | 0.8 | 0.4 | 0.65 | 5 | 11 | 10 | 20 | 13.2 | 0.75 | 3 | 9 | 10 | 19 | 14.2 | 0.48 |
0.1 | 0.8 | 0.4 | 0.7 | 2 | 5 | 8 | 16 | 8.5 | 0.68 | 2 | 6 | 7 | 13 | 9.2 | 0.54 |
0.1 | 0.8 | 0.4 | 0.75 | 2 | 5 | 5 | 9 | 6.3 | 0.68 | 2 | 5 | 5 | 9 | 6.3 | 0.68 |
0.1 | 0.8 | 0.4 | 0.8 | 1 | 3 | 4 | 7 | 4.4 | 0.65 | 1 | 3 | 4 | 7 | 4.4 | 0.65 |
0.1 | 0.8 | 0.4 | 0.85 | 0 | 1 | 4 | 7 | 3.4 | 0.6 | 1 | 3 | 3 | 5 | 3.7 | 0.65 |
0.1 | 0.8 | 0.4 | 0.9 | 0 | 1 | 3 | 5 | 2.6 | 0.6 | 0 | 1 | 3 | 5 | 2.6 | 0.6 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.8 | 0.45 | 0.55 | 22 | 48 | 66 | 133 | 81.6 | 0.6 | 27 | 61 | 58 | 115 | 87.6 | 0.51 |
0.1 | 0.8 | 0.45 | 0.6 | 9 | 20 | 31 | 60 | 36.3 | 0.59 | 11 | 26 | 27 | 51 | 39.2 | 0.47 |
0.1 | 0.8 | 0.45 | 0.65 | 8 | 16 | 18 | 34 | 20.6 | 0.74 | 5 | 12 | 17 | 31 | 21 | 0.53 |
0.1 | 0.8 | 0.45 | 0.7 | 5 | 10 | 11 | 20 | 12.6 | 0.74 | 3 | 8 | 11 | 19 | 13.8 | 0.48 |
0.1 | 0.8 | 0.45 | 0.75 | 2 | 5 | 7 | 12 | 7.8 | 0.59 | 2 | 5 | 7 | 12 | 7.8 | 0.59 |
0.1 | 0.8 | 0.45 | 0.8 | 1 | 3 | 6 | 10 | 6 | 0.57 | 1 | 3 | 6 | 10 | 6 | 0.57 |
0.1 | 0.8 | 0.45 | 0.85 | 2 | 4 | 5 | 8 | 5 | 0.76 | 2 | 4 | 5 | 8 | 5 | 0.76 |
0.1 | 0.8 | 0.45 | 0.9 | 1 | 2 | 4 | 7 | 3 | 0.8 | 0 | 1 | 4 | 6 | 3.3 | 0.55 |
0.1 | 0.8 | 0.45 | 0.95 | 0 | 1 | 2 | 3 | 1.9 | 0.55 | 0 | 1 | 2 | 3 | 1.9 | 0.55 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.8 | 0.5 | 0.6 | 32 | 61 | 71 | 130 | 82 | 0.7 | 52 | 96 | 63 | 114 | 99.2 | 0.82 |
0.1 | 0.8 | 0.5 | 0.65 | 12 | 23 | 34 | 60 | 35.5 | 0.66 | 10 | 22 | 29 | 50 | 38.4 | 0.42 |
0.1 | 0.8 | 0.5 | 0.7 | 6 | 12 | 19 | 32 | 19.7 | 0.61 | 7 | 15 | 17 | 28 | 21.5 | 0.5 |
0.1 | 0.8 | 0.5 | 0.75 | 5 | 9 | 13 | 22 | 12.3 | 0.75 | 3 | 7 | 12 | 19 | 13 | 0.5 |
0.1 | 0.8 | 0.5 | 0.8 | 4 | 7 | 8 | 13 | 8.4 | 0.77 | 4 | 7 | 8 | 13 | 8.4 | 0.77 |
0.1 | 0.8 | 0.5 | 0.85 | 2 | 4 | 6 | 9 | 5.6 | 0.69 | 2 | 4 | 6 | 9 | 5.6 | 0.69 |
0.1 | 0.8 | 0.5 | 0.9 | 0 | 1 | 4 | 6 | 3.5 | 0.5 | 0 | 1 | 4 | 6 | 3.5 | 0.5 |
0.1 | 0.8 | 0.5 | 0.95 | 0 | 1 | 3 | 4 | 2.5 | 0.5 | 0 | 1 | 3 | 4 | 2.5 | 0.5 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.8 | 0.55 | 0.65 | 26 | 47 | 72 | 120 | 78.1 | 0.57 | 35 | 64 | 66 | 109 | 85.2 | 0.53 |
0.1 | 0.8 | 0.55 | 0.7 | 11 | 20 | 33 | 53 | 33.7 | 0.59 | 13 | 25 | 31 | 49 | 38 | 0.46 |
0.1 | 0.8 | 0.55 | 0.75 | 6 | 11 | 20 | 31 | 18.9 | 0.6 | 6 | 12 | 17 | 26 | 19.4 | 0.47 |
0.1 | 0.8 | 0.55 | 0.8 | 4 | 7 | 13 | 20 | 11.1 | 0.68 | 3 | 6 | 12 | 18 | 11.3 | 0.56 |
0.1 | 0.8 | 0.55 | 0.85 | 3 | 5 | 8 | 12 | 6.8 | 0.74 | 1 | 3 | 7 | 10 | 7 | 0.43 |
0.1 | 0.8 | 0.55 | 0.9 | 2 | 4 | 6 | 8 | 5.6 | 0.61 | 2 | 4 | 6 | 8 | 5.6 | 0.61 |
0.1 | 0.8 | 0.55 | 0.95 | 1 | 2 | 3 | 4 | 2.6 | 0.7 | 1 | 2 | 3 | 4 | 2.6 | 0.7 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.8 | 0.6 | 0.7 | 28 | 46 | 76 | 117 | 74.2 | 0.6 | 48 | 79 | 67 | 102 | 88.3 | 0.6 |
0.1 | 0.8 | 0.6 | 0.75 | 10 | 17 | 33 | 49 | 31.3 | 0.55 | 14 | 24 | 30 | 44 | 33.8 | 0.51 |
0.1 | 0.8 | 0.6 | 0.8 | 7 | 11 | 21 | 31 | 16.9 | 0.7 | 6 | 11 | 17 | 24 | 17.9 | 0.47 |
0.1 | 0.8 | 0.6 | 0.85 | 3 | 5 | 14 | 20 | 10.1 | 0.66 | 4 | 7 | 11 | 15 | 10.4 | 0.58 |
0.1 | 0.8 | 0.6 | 0.9 | 4 | 6 | 8 | 11 | 7.2 | 0.77 | 4 | 6 | 8 | 11 | 7.2 | 0.77 |
0.1 | 0.8 | 0.6 | 0.95 | 2 | 3 | 6 | 8 | 4.1 | 0.78 | 3 | 4 | 5 | 7 | 4.4 | 0.87 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.8 | 0.65 | 0.75 | 29 | 44 | 75 | 107 | 68.8 | 0.61 | 43 | 64 | 69 | 98 | 74.6 | 0.69 |
0.1 | 0.8 | 0.65 | 0.8 | 13 | 19 | 37 | 52 | 28.8 | 0.7 | 12 | 19 | 30 | 41 | 29.6 | 0.52 |
0.1 | 0.8 | 0.65 | 0.85 | 5 | 8 | 18 | 24 | 14.8 | 0.57 | 5 | 8 | 18 | 24 | 14.8 | 0.57 |
0.1 | 0.8 | 0.65 | 0.9 | 4 | 6 | 10 | 13 | 8.2 | 0.68 | 4 | 6 | 10 | 13 | 8.2 | 0.68 |
0.1 | 0.8 | 0.65 | 0.95 | 2 | 3 | 7 | 9 | 4.6 | 0.73 | 2 | 3 | 7 | 9 | 4.6 | 0.73 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.8 | 0.7 | 0.8 | 27 | 38 | 72 | 96 | 60.2 | 0.62 | 29 | 42 | 65 | 86 | 63.8 | 0.5 |
0.1 | 0.8 | 0.7 | 0.85 | 10 | 14 | 33 | 43 | 24.3 | 0.64 | 9 | 13 | 31 | 40 | 24.4 | 0.58 |
0.1 | 0.8 | 0.7 | 0.9 | 4 | 6 | 16 | 20 | 11.9 | 0.58 | 4 | 6 | 16 | 20 | 11.9 | 0.58 |
0.1 | 0.8 | 0.7 | 0.95 | 2 | 3 | 9 | 11 | 5.7 | 0.66 | 2 | 3 | 9 | 11 | 5.7 | 0.66 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.8 | 0.75 | 0.85 | 25 | 33 | 65 | 81 | 51.9 | 0.61 | 34 | 46 | 59 | 73 | 59.8 | 0.49 |
0.1 | 0.8 | 0.75 | 0.9 | 10 | 13 | 28 | 34 | 20 | 0.67 | 7 | 10 | 25 | 30 | 20.5 | 0.47 |
0.1 | 0.8 | 0.75 | 0.95 | 2 | 3 | 15 | 18 | 9.3 | 0.58 | 0 | 1 | 12 | 14 | 10.8 | 0.25 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.8 | 0.8 | 0.9 | 23 | 28 | 56 | 66 | 40 | 0.69 | 28 | 34 | 52 | 61 | 42.1 | 0.7 |
0.1 | 0.8 | 0.8 | 0.95 | 9 | 11 | 21 | 24 | 15.2 | 0.68 | 12 | 14 | 20 | 23 | 15.8 | 0.8 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.8 | 0.85 | 0.95 | 12 | 14 | 43 | 48 | 26.1 | 0.64 | 23 | 26 | 37 | 41 | 29.4 | 0.77 |
α=0.1, Power = 0.8 π0 = proportion of success at or below which treatment is abandoned π1 = proportion of success at or above which treatment will be accepted for further development and trials r1 = number of successes above which stage 2 can be entered, and at or below which the trial terminates after n1 cases, and the treatment rejected n1 = maximum sample size in stage 1 rTot = the total number of successes (stage 1 and 2 combined) above which the study can be terminated and the treatment accepted for further development and trials, and at or below which after nTot cases the treatment is rejected. nTot = the total maximum sample size (stage 1 and 2 combined) EN = expected sample size, an estimated average sample size that will be used before the trial terminates. This is a measure of efficiency in detecting PET = probability of early termination (when treatment is abandoned), a measure of efficiency in rejecting ineffective treatments.
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.8 | 0.05 | 0.15 | 1 | 23 | 5 | 56 | 33.6 | 0.68 | 1 | 30 | 5 | 52 | 39.8 | 0.55 |
0.05 | 0.8 | 0.05 | 0.2 | 0 | 10 | 3 | 29 | 17.6 | 0.6 | 0 | 13 | 3 | 27 | 19.8 | 0.51 |
0.05 | 0.8 | 0.05 | 0.25 | 0 | 9 | 2 | 17 | 12 | 0.63 | 0 | 12 | 2 | 16 | 13.8 | 0.54 |
0.05 | 0.8 | 0.05 | 0.3 | 0 | 5 | 2 | 18 | 7.9 | 0.77 | 0 | 7 | 2 | 14 | 9.1 | 0.7 |
0.05 | 0.8 | 0.05 | 0.35 | 0 | 4 | 2 | 16 | 6.2 | 0.81 | 0 | 6 | 2 | 12 | 7.6 | 0.74 |
0.05 | 0.8 | 0.05 | 0.4 | 0 | 4 | 1 | 8 | 4.7 | 0.81 | 0 | 5 | 1 | 7 | 5.5 | 0.77 |
0.05 | 0.8 | 0.05 | 0.45 | 0 | 3 | 1 | 8 | 3.7 | 0.86 | 0 | 4 | 1 | 6 | 4.4 | 0.81 |
0.05 | 0.8 | 0.05 | 0.5 | 0 | 3 | 1 | 6 | 3.4 | 0.86 | 0 | 4 | 1 | 5 | 4.2 | 0.81 |
0.05 | 0.8 | 0.05 | 0.55 | 0 | 3 | 1 | 5 | 3.3 | 0.86 | 0 | 3 | 1 | 5 | 3.3 | 0.86 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.8 | 0.1 | 0.2 | 3 | 30 | 13 | 89 | 50.8 | 0.65 | 4 | 45 | 12 | 78 | 60.6 | 0.53 |
0.05 | 0.8 | 0.1 | 0.25 | 2 | 18 | 7 | 43 | 24.7 | 0.73 | 2 | 22 | 7 | 40 | 28.8 | 0.62 |
0.05 | 0.8 | 0.1 | 0.3 | 1 | 10 | 5 | 29 | 15 | 0.74 | 1 | 15 | 5 | 25 | 19.5 | 0.55 |
0.05 | 0.8 | 0.1 | 0.35 | 1 | 8 | 4 | 22 | 10.6 | 0.81 | 1 | 11 | 4 | 18 | 13.1 | 0.7 |
0.05 | 0.8 | 0.1 | 0.4 | 0 | 4 | 3 | 15 | 7.8 | 0.66 | 1 | 8 | 3 | 13 | 8.9 | 0.81 |
0.05 | 0.8 | 0.1 | 0.45 | 0 | 4 | 2 | 9 | 5.7 | 0.66 | 0 | 4 | 2 | 9 | 5.7 | 0.66 |
0.05 | 0.8 | 0.1 | 0.5 | 0 | 3 | 2 | 9 | 4.6 | 0.73 | 0 | 4 | 2 | 8 | 5.4 | 0.66 |
0.05 | 0.8 | 0.1 | 0.55 | 0 | 3 | 2 | 7 | 4.1 | 0.73 | 0 | 3 | 2 | 7 | 4.1 | 0.73 |
0.05 | 0.8 | 0.1 | 0.6 | 0 | 2 | 2 | 8 | 3.1 | 0.81 | 0 | 3 | 2 | 6 | 3.8 | 0.73 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.8 | 0.15 | 0.25 | 6 | 38 | 23 | 116 | 64.6 | 0.66 | 8 | 55 | 20 | 97 | 73.7 | 0.56 |
0.05 | 0.8 | 0.15 | 0.3 | 3 | 19 | 12 | 55 | 30.4 | 0.68 | 3 | 23 | 11 | 48 | 34.5 | 0.54 |
0.05 | 0.8 | 0.15 | 0.35 | 1 | 9 | 8 | 34 | 19 | 0.6 | 2 | 15 | 7 | 28 | 20.1 | 0.6 |
0.05 | 0.8 | 0.15 | 0.4 | 1 | 7 | 6 | 25 | 12.1 | 0.72 | 1 | 9 | 5 | 19 | 13 | 0.6 |
0.05 | 0.8 | 0.15 | 0.45 | 1 | 6 | 5 | 19 | 8.9 | 0.78 | 0 | 5 | 4 | 14 | 10 | 0.44 |
0.05 | 0.8 | 0.15 | 0.5 | 1 | 5 | 4 | 16 | 6.8 | 0.84 | 0 | 4 | 3 | 10 | 6.9 | 0.52 |
0.05 | 0.8 | 0.15 | 0.55 | 0 | 3 | 3 | 10 | 5.7 | 0.61 | 0 | 4 | 3 | 9 | 6.4 | 0.52 |
0.05 | 0.8 | 0.15 | 0.6 | 0 | 3 | 2 | 6 | 4.2 | 0.61 | 0 | 3 | 2 | 6 | 4.2 | 0.61 |
0.05 | 0.8 | 0.15 | 0.65 | 0 | 2 | 2 | 6 | 3.1 | 0.72 | 0 | 2 | 2 | 6 | 3.1 | 0.72 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.8 | 0.2 | 0.3 | 10 | 46 | 35 | 141 | 75.1 | 0.69 | 13 | 66 | 30 | 116 | 88.6 | 0.55 |
0.05 | 0.8 | 0.2 | 0.35 | 5 | 22 | 19 | 72 | 35.4 | 0.73 | 6 | 31 | 15 | 53 | 40.4 | 0.57 |
0.05 | 0.8 | 0.2 | 0.4 | 3 | 13 | 12 | 43 | 20.6 | 0.75 | 4 | 18 | 10 | 33 | 22.3 | 0.72 |
0.05 | 0.8 | 0.2 | 0.45 | 2 | 10 | 7 | 22 | 13.9 | 0.68 | 2 | 13 | 7 | 21 | 17 | 0.5 |
0.05 | 0.8 | 0.2 | 0.5 | 2 | 8 | 6 | 18 | 10 | 0.8 | 2 | 9 | 6 | 17 | 11.1 | 0.74 |
0.05 | 0.8 | 0.2 | 0.55 | 1 | 5 | 5 | 14 | 7.4 | 0.74 | 1 | 6 | 4 | 11 | 7.7 | 0.66 |
0.05 | 0.8 | 0.2 | 0.6 | 1 | 4 | 4 | 12 | 5.4 | 0.82 | 1 | 5 | 4 | 10 | 6.3 | 0.74 |
0.05 | 0.8 | 0.2 | 0.65 | 0 | 2 | 3 | 8 | 4.2 | 0.64 | 1 | 5 | 3 | 7 | 5.5 | 0.74 |
0.05 | 0.8 | 0.2 | 0.7 | 0 | 2 | 3 | 7 | 3.8 | 0.64 | 0 | 2 | 3 | 7 | 3.8 | 0.64 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.8 | 0.25 | 0.35 | 15 | 56 | 45 | 149 | 85.3 | 0.69 | 20 | 80 | 40 | 129 | 101.6 | 0.56 |
0.05 | 0.8 | 0.25 | 0.4 | 5 | 20 | 23 | 71 | 39.5 | 0.62 | 16 | 51 | 20 | 60 | 52 | 0.89 |
0.05 | 0.8 | 0.25 | 0.45 | 5 | 17 | 14 | 41 | 22.6 | 0.77 | 4 | 17 | 13 | 36 | 25.1 | 0.57 |
0.05 | 0.8 | 0.25 | 0.5 | 2 | 9 | 9 | 24 | 15 | 0.6 | 2 | 9 | 9 | 24 | 15 | 0.6 |
0.05 | 0.8 | 0.25 | 0.55 | 2 | 7 | 8 | 21 | 10.4 | 0.76 | 2 | 9 | 7 | 17 | 12.2 | 0.6 |
0.05 | 0.8 | 0.25 | 0.6 | 1 | 5 | 5 | 12 | 7.6 | 0.63 | 1 | 5 | 5 | 12 | 7.6 | 0.63 |
0.05 | 0.8 | 0.25 | 0.65 | 1 | 4 | 5 | 12 | 6.1 | 0.74 | 0 | 3 | 4 | 9 | 6.5 | 0.42 |
0.05 | 0.8 | 0.25 | 0.7 | 0 | 2 | 4 | 9 | 5.1 | 0.56 | 0 | 3 | 4 | 8 | 5.9 | 0.42 |
0.05 | 0.8 | 0.25 | 0.75 | 1 | 3 | 3 | 7 | 3.6 | 0.84 | 0 | 2 | 3 | 6 | 3.8 | 0.56 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.8 | 0.3 | 0.4 | 19 | 59 | 59 | 168 | 91.7 | 0.7 | 36 | 107 | 51 | 142 | 113.2 | 0.82 |
0.05 | 0.8 | 0.3 | 0.45 | 9 | 27 | 30 | 81 | 41.7 | 0.73 | 16 | 46 | 25 | 65 | 49.6 | 0.81 |
0.05 | 0.8 | 0.3 | 0.5 | 5 | 15 | 18 | 46 | 23.6 | 0.72 | 6 | 19 | 16 | 39 | 25.7 | 0.67 |
0.05 | 0.8 | 0.3 | 0.55 | 3 | 9 | 14 | 35 | 16 | 0.73 | 2 | 9 | 11 | 25 | 17.6 | 0.46 |
0.05 | 0.8 | 0.3 | 0.6 | 3 | 8 | 10 | 24 | 11.1 | 0.81 | 2 | 10 | 8 | 17 | 14.3 | 0.38 |
0.05 | 0.8 | 0.3 | 0.65 | 1 | 4 | 7 | 15 | 7.8 | 0.65 | 2 | 7 | 7 | 14 | 9.5 | 0.65 |
0.05 | 0.8 | 0.3 | 0.7 | 0 | 2 | 5 | 10 | 6.1 | 0.49 | 0 | 2 | 5 | 10 | 6.1 | 0.49 |
0.05 | 0.8 | 0.3 | 0.75 | 1 | 3 | 5 | 10 | 4.5 | 0.78 | 2 | 5 | 4 | 8 | 5.5 | 0.84 |
0.05 | 0.8 | 0.3 | 0.8 | 1 | 3 | 4 | 7 | 3.9 | 0.78 | 2 | 4 | 3 | 6 | 4.2 | 0.92 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.8 | 0.35 | 0.45 | 23 | 62 | 71 | 176 | 97.6 | 0.69 | 38 | 113 | 61 | 148 | 133.2 | 0.42 |
0.05 | 0.8 | 0.35 | 0.5 | 10 | 27 | 33 | 77 | 43.5 | 0.67 | 22 | 55 | 29 | 66 | 57 | 0.82 |
0.05 | 0.8 | 0.35 | 0.55 | 5 | 14 | 20 | 44 | 24.8 | 0.64 | 8 | 21 | 18 | 39 | 26.3 | 0.71 |
0.05 | 0.8 | 0.35 | 0.6 | 3 | 9 | 13 | 27 | 16 | 0.61 | 6 | 18 | 13 | 26 | 21.6 | 0.55 |
0.05 | 0.8 | 0.35 | 0.65 | 2 | 6 | 10 | 20 | 10.9 | 0.65 | 8 | 16 | 9 | 18 | 16.1 | 0.93 |
0.05 | 0.8 | 0.35 | 0.7 | 2 | 5 | 8 | 16 | 7.6 | 0.76 | 2 | 6 | 7 | 13 | 8.5 | 0.65 |
0.05 | 0.8 | 0.35 | 0.75 | 1 | 3 | 7 | 13 | 5.8 | 0.72 | 2 | 5 | 5 | 9 | 5.9 | 0.76 |
0.05 | 0.8 | 0.35 | 0.8 | 1 | 3 | 4 | 7 | 4.1 | 0.72 | 1 | 3 | 4 | 7 | 4.1 | 0.72 |
0.05 | 0.8 | 0.35 | 0.85 | 0 | 1 | 4 | 7 | 3.1 | 0.65 | 0 | 1 | 4 | 7 | 3.1 | 0.65 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.8 | 0.4 | 0.5 | 25 | 60 | 80 | 176 | 99.9 | 0.66 | 53 | 121 | 71 | 154 | 126.7 | 0.83 |
0.05 | 0.8 | 0.4 | 0.55 | 11 | 26 | 40 | 84 | 44.9 | 0.67 | 28 | 59 | 34 | 70 | 60.1 | 0.9 |
0.05 | 0.8 | 0.4 | 0.6 | 7 | 16 | 23 | 46 | 24.5 | 0.72 | 17 | 34 | 20 | 39 | 34.4 | 0.91 |
0.05 | 0.8 | 0.4 | 0.65 | 5 | 11 | 16 | 31 | 15.9 | 0.75 | 5 | 12 | 14 | 26 | 16.7 | 0.67 |
0.05 | 0.8 | 0.4 | 0.7 | 3 | 7 | 11 | 20 | 10.8 | 0.71 | 6 | 12 | 10 | 18 | 12.9 | 0.84 |
0.05 | 0.8 | 0.4 | 0.75 | 2 | 5 | 8 | 14 | 7.9 | 0.68 | 2 | 5 | 8 | 14 | 7.9 | 0.68 |
0.05 | 0.8 | 0.4 | 0.8 | 1 | 3 | 6 | 10 | 5.5 | 0.65 | 1 | 3 | 6 | 10 | 5.5 | 0.65 |
0.05 | 0.8 | 0.4 | 0.85 | 0 | 1 | 6 | 10 | 4.6 | 0.6 | 2 | 4 | 5 | 8 | 4.7 | 0.82 |
0.05 | 0.8 | 0.4 | 0.9 | 0 | 1 | 4 | 6 | 3 | 0.6 | 0 | 1 | 4 | 6 | 3 | 0.6 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.8 | 0.45 | 0.55 | 31 | 66 | 88 | 174 | 101.3 | 0.67 | 47 | 106 | 79 | 154 | 130.7 | 0.49 |
0.05 | 0.8 | 0.45 | 0.6 | 12 | 26 | 41 | 77 | 45.1 | 0.63 | 19 | 42 | 38 | 70 | 53.9 | 0.58 |
0.05 | 0.8 | 0.45 | 0.65 | 7 | 15 | 24 | 43 | 24.7 | 0.65 | 16 | 30 | 22 | 39 | 31.2 | 0.86 |
0.05 | 0.8 | 0.45 | 0.7 | 5 | 10 | 19 | 33 | 16 | 0.74 | 5 | 12 | 15 | 25 | 18.1 | 0.53 |
0.05 | 0.8 | 0.45 | 0.75 | 2 | 5 | 11 | 18 | 10.3 | 0.59 | 2 | 6 | 10 | 16 | 11.6 | 0.44 |
0.05 | 0.8 | 0.45 | 0.8 | 1 | 3 | 9 | 14 | 7.7 | 0.57 | 1 | 3 | 9 | 14 | 7.7 | 0.57 |
0.05 | 0.8 | 0.45 | 0.85 | 2 | 4 | 6 | 9 | 5.2 | 0.76 | 2 | 4 | 6 | 9 | 5.2 | 0.76 |
0.05 | 0.8 | 0.45 | 0.9 | 1 | 2 | 7 | 11 | 3.8 | 0.8 | 1 | 3 | 5 | 7 | 4.7 | 0.57 |
0.05 | 0.8 | 0.45 | 0.95 | 0 | 1 | 3 | 4 | 2.4 | 0.55 | 0 | 1 | 3 | 4 | 2.4 | 0.55 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.8 | 0.5 | 0.6 | 30 | 58 | 101 | 182 | 101 | 0.65 | 68 | 125 | 87 | 155 | 129.2 | 0.86 |
0.05 | 0.8 | 0.5 | 0.65 | 15 | 28 | 48 | 83 | 43.7 | 0.71 | 39 | 66 | 40 | 68 | 66.1 | 0.95 |
0.05 | 0.8 | 0.5 | 0.7 | 8 | 15 | 26 | 43 | 23.5 | 0.7 | 12 | 23 | 23 | 37 | 27.7 | 0.66 |
0.05 | 0.8 | 0.5 | 0.75 | 6 | 11 | 16 | 25 | 14.8 | 0.73 | 7 | 14 | 15 | 23 | 17.6 | 0.6 |
0.05 | 0.8 | 0.5 | 0.8 | 4 | 7 | 13 | 20 | 9.9 | 0.77 | 3 | 6 | 12 | 18 | 10.1 | 0.66 |
0.05 | 0.8 | 0.5 | 0.85 | 2 | 4 | 9 | 13 | 6.8 | 0.69 | 7 | 10 | 8 | 12 | 10.1 | 0.95 |
0.05 | 0.8 | 0.5 | 0.9 | 1 | 2 | 9 | 14 | 5 | 0.75 | 2 | 4 | 6 | 8 | 5.3 | 0.69 |
0.05 | 0.8 | 0.5 | 0.95 | 1 | 2 | 5 | 7 | 3.3 | 0.75 | 3 | 4 | 4 | 6 | 4.1 | 0.94 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.8 | 0.55 | 0.65 | 35 | 61 | 107 | 177 | 96.9 | 0.69 | 50 | 90 | 92 | 150 | 115 | 0.58 |
0.05 | 0.8 | 0.55 | 0.7 | 15 | 26 | 48 | 76 | 42 | 0.68 | 20 | 35 | 43 | 67 | 45.8 | 0.66 |
0.05 | 0.8 | 0.55 | 0.75 | 9 | 15 | 28 | 43 | 22.3 | 0.74 | 15 | 24 | 24 | 36 | 26.1 | 0.83 |
0.05 | 0.8 | 0.55 | 0.8 | 4 | 7 | 19 | 28 | 13.6 | 0.68 | 5 | 9 | 16 | 23 | 14.1 | 0.64 |
0.05 | 0.8 | 0.55 | 0.85 | 3 | 5 | 14 | 20 | 8.8 | 0.74 | 4 | 7 | 11 | 15 | 9.5 | 0.68 |
0.05 | 0.8 | 0.55 | 0.9 | 3 | 5 | 9 | 12 | 6.8 | 0.74 | 5 | 7 | 8 | 11 | 7.4 | 0.9 |
0.05 | 0.8 | 0.55 | 0.95 | 1 | 2 | 6 | 8 | 3.8 | 0.7 | 1 | 2 | 6 | 8 | 3.8 | 0.7 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.8 | 0.6 | 0.7 | 34 | 55 | 107 | 163 | 92 | 0.66 | 92 | 139 | 94 | 142 | 139.2 | 0.94 |
0.05 | 0.8 | 0.6 | 0.75 | 17 | 27 | 46 | 67 | 39.3 | 0.69 | 18 | 30 | 43 | 62 | 43.8 | 0.57 |
0.05 | 0.8 | 0.6 | 0.8 | 7 | 11 | 30 | 43 | 20.5 | 0.7 | 8 | 13 | 25 | 35 | 20.8 | 0.65 |
0.05 | 0.8 | 0.6 | 0.85 | 6 | 9 | 17 | 23 | 12.2 | 0.77 | 4 | 7 | 15 | 20 | 12.5 | 0.58 |
0.05 | 0.8 | 0.6 | 0.9 | 4 | 6 | 10 | 13 | 7.6 | 0.77 | 4 | 6 | 10 | 13 | 7.6 | 0.77 |
0.05 | 0.8 | 0.6 | 0.95 | 2 | 3 | 8 | 10 | 4.5 | 0.78 | 2 | 3 | 8 | 10 | 4.5 | 0.78 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.8 | 0.65 | 0.75 | 34 | 51 | 104 | 147 | 84.7 | 0.65 | 80 | 114 | 94 | 132 | 115.9 | 0.9 |
0.05 | 0.8 | 0.65 | 0.8 | 12 | 18 | 49 | 67 | 35.4 | 0.65 | 20 | 31 | 41 | 55 | 41.9 | 0.54 |
0.05 | 0.8 | 0.65 | 0.85 | 10 | 14 | 25 | 33 | 18.2 | 0.78 | 19 | 25 | 23 | 30 | 25.4 | 0.92 |
0.05 | 0.8 | 0.65 | 0.9 | 4 | 6 | 15 | 19 | 10.1 | 0.68 | 12 | 15 | 14 | 18 | 15.2 | 0.94 |
0.05 | 0.8 | 0.65 | 0.95 | 2 | 3 | 9 | 11 | 5.2 | 0.73 | 2 | 3 | 9 | 11 | 5.2 | 0.73 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.8 | 0.7 | 0.8 | 34 | 47 | 105 | 139 | 75.6 | 0.69 | 66 | 89 | 90 | 118 | 93.8 | 0.83 |
0.05 | 0.8 | 0.7 | 0.85 | 14 | 19 | 46 | 59 | 30.3 | 0.72 | 16 | 23 | 39 | 49 | 34.4 | 0.56 |
0.05 | 0.8 | 0.7 | 0.9 | 4 | 6 | 22 | 27 | 14.8 | 0.58 | 19 | 23 | 21 | 26 | 23.2 | 0.95 |
0.05 | 0.8 | 0.7 | 0.95 | 3 | 4 | 17 | 21 | 8.1 | 0.76 | 5 | 7 | 12 | 14 | 9.3 | 0.67 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.8 | 0.75 | 0.85 | 36 | 46 | 95 | 118 | 64.2 | 0.75 | 77 | 95 | 82 | 101 | 95.4 | 0.93 |
0.05 | 0.8 | 0.75 | 0.9 | 10 | 13 | 40 | 48 | 24.6 | 0.67 | 17 | 22 | 33 | 39 | 27.5 | 0.68 |
0.05 | 0.8 | 0.75 | 0.95 | 2 | 3 | 19 | 22 | 11 | 0.58 | 14 | 16 | 17 | 20 | 16.3 | 0.94 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.8 | 0.8 | 0.9 | 23 | 28 | 83 | 97 | 49.7 | 0.69 | 60 | 70 | 69 | 80 | 70.8 | 0.92 |
0.05 | 0.8 | 0.8 | 0.95 | 7 | 9 | 26 | 29 | 17.7 | 0.56 | 7 | 9 | 26 | 29 | 17.7 | 0.56 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.8 | 0.85 | 0.95 | 11 | 13 | 59 | 65 | 33.7 | 0.6 | 35 | 39 | 52 | 57 | 41.6 | 0.86 |
α=0.1, Power = 0.8 π0 = proportion of success at or below which treatment is abandoned π1 = proportion of success at or above which treatment will be accepted for further development and trials r1 = number of successes above which stage 2 can be entered, and at or below which the trial terminates after n1 cases, and the treatment rejected n1 = maximum sample size in stage 1 rTot = the total number of successes (stage 1 and 2 combined) above which the study can be terminated and the treatment accepted for further development and trials, and at or below which after nTot cases the treatment is rejected. nTot = the total maximum sample size (stage 1 and 2 combined) EN = expected sample size, an estimated average sample size that will be used before the trial terminates. This is a measure of efficiency in detecting PET = probability of early termination (when treatment is abandoned), a measure of efficiency in rejecting ineffective treatments.
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.8 | 0.05 | 0.15 | 2 | 30 | 10 | 102 | 43.5 | 0.81 | 2 | 45 | 9 | 82 | 59.5 | 0.61 |
0.01 | 0.8 | 0.05 | 0.2 | 1 | 16 | 6 | 50 | 22.4 | 0.81 | 1 | 25 | 6 | 44 | 31.8 | 0.64 |
0.01 | 0.8 | 0.05 | 0.25 | 1 | 12 | 5 | 36 | 14.8 | 0.88 | 0 | 11 | 4 | 26 | 17.5 | 0.57 |
0.01 | 0.8 | 0.05 | 0.3 | 0 | 5 | 4 | 27 | 10 | 0.77 | 0 | 7 | 3 | 18 | 10.3 | 0.7 |
0.01 | 0.8 | 0.05 | 0.35 | 0 | 4 | 4 | 24 | 7.7 | 0.81 | 0 | 7 | 3 | 15 | 9.4 | 0.7 |
0.01 | 0.8 | 0.05 | 0.4 | 0 | 4 | 3 | 15 | 6 | 0.81 | 0 | 6 | 3 | 13 | 7.9 | 0.74 |
0.01 | 0.8 | 0.05 | 0.45 | 0 | 3 | 3 | 14 | 4.6 | 0.86 | 0 | 4 | 2 | 9 | 4.9 | 0.81 |
0.01 | 0.8 | 0.05 | 0.5 | 0 | 3 | 2 | 9 | 3.9 | 0.86 | 0 | 4 | 2 | 8 | 4.7 | 0.81 |
0.01 | 0.8 | 0.05 | 0.55 | 0 | 3 | 2 | 7 | 3.6 | 0.86 | 0 | 3 | 2 | 7 | 3.6 | 0.86 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.8 | 0.1 | 0.2 | 5 | 41 | 23 | 149 | 65.1 | 0.78 | 6 | 58 | 20 | 122 | 81 | 0.64 |
0.01 | 0.8 | 0.1 | 0.25 | 3 | 22 | 14 | 80 | 32 | 0.83 | 3 | 30 | 12 | 62 | 41.3 | 0.65 |
0.01 | 0.8 | 0.1 | 0.3 | 2 | 14 | 9 | 46 | 19.1 | 0.84 | 2 | 18 | 8 | 37 | 23.1 | 0.73 |
0.01 | 0.8 | 0.1 | 0.35 | 1 | 8 | 8 | 37 | 13.4 | 0.81 | 1 | 11 | 6 | 25 | 15.2 | 0.7 |
0.01 | 0.8 | 0.1 | 0.4 | 1 | 7 | 6 | 25 | 9.7 | 0.85 | 1 | 9 | 5 | 19 | 11.3 | 0.77 |
0.01 | 0.8 | 0.1 | 0.45 | 1 | 6 | 5 | 19 | 7.5 | 0.89 | 0 | 5 | 4 | 14 | 8.7 | 0.59 |
0.01 | 0.8 | 0.1 | 0.5 | 1 | 5 | 4 | 16 | 5.9 | 0.92 | 1 | 8 | 4 | 12 | 8.7 | 0.81 |
0.01 | 0.8 | 0.1 | 0.55 | 1 | 5 | 3 | 10 | 5.4 | 0.92 | 0 | 4 | 3 | 9 | 5.7 | 0.66 |
0.01 | 0.8 | 0.1 | 0.6 | 0 | 2 | 3 | 10 | 3.5 | 0.81 | 0 | 3 | 3 | 8 | 4.4 | 0.73 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.8 | 0.15 | 0.25 | 10 | 56 | 39 | 188 | 83.8 | 0.79 | 12 | 76 | 34 | 157 | 104.3 | 0.65 |
0.01 | 0.8 | 0.15 | 0.3 | 5 | 26 | 23 | 101 | 39.9 | 0.82 | 7 | 42 | 18 | 73 | 51 | 0.71 |
0.01 | 0.8 | 0.15 | 0.35 | 3 | 15 | 16 | 65 | 23.9 | 0.82 | 3 | 19 | 12 | 44 | 26.9 | 0.68 |
0.01 | 0.8 | 0.15 | 0.4 | 2 | 10 | 11 | 41 | 15.6 | 0.82 | 2 | 13 | 9 | 30 | 18.2 | 0.69 |
0.01 | 0.8 | 0.15 | 0.45 | 2 | 9 | 8 | 27 | 11.5 | 0.86 | 2 | 13 | 7 | 21 | 15.5 | 0.69 |
0.01 | 0.8 | 0.15 | 0.5 | 1 | 5 | 8 | 27 | 8.6 | 0.84 | 1 | 7 | 6 | 17 | 9.8 | 0.72 |
0.01 | 0.8 | 0.15 | 0.55 | 1 | 5 | 5 | 14 | 6.5 | 0.84 | 1 | 6 | 5 | 13 | 7.6 | 0.78 |
0.01 | 0.8 | 0.15 | 0.6 | 1 | 4 | 5 | 15 | 5.2 | 0.89 | 0 | 3 | 4 | 10 | 5.7 | 0.61 |
0.01 | 0.8 | 0.15 | 0.65 | 0 | 2 | 4 | 10 | 4.2 | 0.72 | 0 | 3 | 4 | 9 | 5.3 | 0.61 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.8 | 0.2 | 0.3 | 14 | 62 | 56 | 215 | 99.8 | 0.75 | 45 | 173 | 49 | 183 | 173.2 | 0.98 |
0.01 | 0.8 | 0.2 | 0.35 | 7 | 29 | 31 | 109 | 45.8 | 0.79 | 9 | 42 | 26 | 87 | 56.6 | 0.68 |
0.01 | 0.8 | 0.2 | 0.4 | 4 | 16 | 21 | 69 | 26.7 | 0.8 | 6 | 25 | 17 | 52 | 30.9 | 0.78 |
0.01 | 0.8 | 0.2 | 0.45 | 2 | 9 | 14 | 42 | 17.6 | 0.74 | 4 | 16 | 12 | 34 | 19.6 | 0.8 |
0.01 | 0.8 | 0.2 | 0.5 | 2 | 8 | 11 | 31 | 12.7 | 0.8 | 3 | 12 | 10 | 26 | 14.9 | 0.79 |
0.01 | 0.8 | 0.2 | 0.55 | 2 | 7 | 9 | 24 | 9.5 | 0.85 | 2 | 9 | 8 | 19 | 11.6 | 0.74 |
0.01 | 0.8 | 0.2 | 0.6 | 1 | 4 | 8 | 21 | 7.1 | 0.82 | 5 | 12 | 6 | 14 | 12 | 0.98 |
0.01 | 0.8 | 0.2 | 0.65 | 1 | 4 | 6 | 14 | 5.8 | 0.82 | 2 | 6 | 5 | 11 | 6.5 | 0.9 |
0.01 | 0.8 | 0.2 | 0.7 | 0 | 2 | 5 | 10 | 4.9 | 0.64 | 0 | 2 | 5 | 10 | 4.9 | 0.64 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.8 | 0.25 | 0.4 | 11 | 36 | 41 | 123 | 50.5 | 0.83 | 11 | 42 | 34 | 97 | 61.3 | 0.65 |
0.01 | 0.8 | 0.25 | 0.45 | 5 | 17 | 25 | 69 | 29.2 | 0.77 | 6 | 24 | 21 | 55 | 36.2 | 0.61 |
0.01 | 0.8 | 0.25 | 0.5 | 4 | 13 | 17 | 43 | 19.2 | 0.79 | 5 | 17 | 16 | 39 | 22.2 | 0.77 |
0.01 | 0.8 | 0.25 | 0.55 | 2 | 7 | 14 | 34 | 13.6 | 0.76 | 2 | 9 | 12 | 27 | 16.2 | 0.6 |
0.01 | 0.8 | 0.25 | 0.6 | 2 | 6 | 12 | 29 | 9.9 | 0.83 | 2 | 8 | 9 | 19 | 11.5 | 0.68 |
0.01 | 0.8 | 0.25 | 0.65 | 1 | 4 | 8 | 17 | 7.4 | 0.74 | 2 | 7 | 7 | 14 | 8.7 | 0.76 |
0.01 | 0.8 | 0.25 | 0.7 | 2 | 5 | 8 | 16 | 6.1 | 0.9 | 2 | 6 | 7 | 13 | 7.2 | 0.83 |
0.01 | 0.8 | 0.25 | 0.75 | 1 | 3 | 6 | 12 | 4.4 | 0.84 | 0 | 2 | 5 | 9 | 5.1 | 0.56 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.8 | 0.3 | 0.45 | 13 | 37 | 50 | 129 | 54.7 | 0.81 | 18 | 59 | 42 | 104 | 77.1 | 0.6 |
0.01 | 0.8 | 0.3 | 0.5 | 7 | 20 | 29 | 69 | 31.2 | 0.77 | 8 | 25 | 26 | 60 | 36.3 | 0.68 |
0.01 | 0.8 | 0.3 | 0.55 | 5 | 13 | 24 | 56 | 20.1 | 0.83 | 3 | 11 | 18 | 39 | 23.1 | 0.57 |
0.01 | 0.8 | 0.3 | 0.6 | 4 | 10 | 17 | 37 | 14.1 | 0.85 | 6 | 18 | 13 | 26 | 20.2 | 0.72 |
0.01 | 0.8 | 0.3 | 0.65 | 2 | 6 | 12 | 24 | 10.6 | 0.74 | 7 | 15 | 10 | 19 | 15.2 | 0.95 |
0.01 | 0.8 | 0.3 | 0.7 | 2 | 5 | 11 | 21 | 7.6 | 0.84 | 2 | 6 | 9 | 16 | 8.6 | 0.74 |
0.01 | 0.8 | 0.3 | 0.75 | 1 | 3 | 9 | 17 | 6 | 0.78 | 2 | 5 | 7 | 12 | 6.1 | 0.84 |
0.01 | 0.8 | 0.3 | 0.8 | 1 | 3 | 6 | 10 | 4.5 | 0.78 | 1 | 3 | 6 | 10 | 4.5 | 0.78 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.8 | 0.35 | 0.5 | 13 | 33 | 60 | 137 | 57.5 | 0.76 | 19 | 52 | 49 | 108 | 71.5 | 0.65 |
0.01 | 0.8 | 0.35 | 0.55 | 8 | 20 | 34 | 72 | 32.4 | 0.76 | 12 | 30 | 30 | 62 | 37 | 0.78 |
0.01 | 0.8 | 0.35 | 0.6 | 5 | 12 | 25 | 51 | 20.3 | 0.79 | 7 | 17 | 21 | 41 | 22.1 | 0.79 |
0.01 | 0.8 | 0.35 | 0.65 | 4 | 9 | 20 | 39 | 14.2 | 0.83 | 3 | 9 | 16 | 29 | 16.8 | 0.61 |
0.01 | 0.8 | 0.35 | 0.7 | 3 | 7 | 13 | 23 | 10.2 | 0.8 | 4 | 9 | 12 | 21 | 11.1 | 0.83 |
0.01 | 0.8 | 0.35 | 0.75 | 3 | 6 | 12 | 21 | 7.8 | 0.88 | 7 | 12 | 9 | 15 | 12.1 | 0.97 |
0.01 | 0.8 | 0.35 | 0.8 | 2 | 4 | 10 | 17 | 5.6 | 0.87 | 4 | 7 | 8 | 13 | 7.3 | 0.94 |
0.01 | 0.8 | 0.35 | 0.85 | 0 | 1 | 7 | 11 | 4.5 | 0.65 | 2 | 4 | 6 | 9 | 4.6 | 0.87 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.8 | 0.4 | 0.55 | 15 | 34 | 65 | 132 | 58.6 | 0.75 | 20 | 49 | 56 | 111 | 73.4 | 0.61 |
0.01 | 0.8 | 0.4 | 0.6 | 11 | 23 | 43 | 84 | 33 | 0.84 | 13 | 32 | 34 | 63 | 44.3 | 0.6 |
0.01 | 0.8 | 0.4 | 0.65 | 6 | 13 | 26 | 47 | 20.8 | 0.77 | 8 | 18 | 24 | 42 | 24.3 | 0.74 |
0.01 | 0.8 | 0.4 | 0.7 | 5 | 10 | 19 | 33 | 13.8 | 0.83 | 5 | 12 | 17 | 28 | 17.4 | 0.67 |
0.01 | 0.8 | 0.4 | 0.75 | 3 | 6 | 16 | 27 | 9.8 | 0.82 | 9 | 15 | 13 | 21 | 15.2 | 0.97 |
0.01 | 0.8 | 0.4 | 0.8 | 2 | 4 | 14 | 23 | 7.4 | 0.82 | 2 | 5 | 10 | 15 | 8.2 | 0.68 |
0.01 | 0.8 | 0.4 | 0.85 | 2 | 4 | 9 | 13 | 5.6 | 0.82 | 7 | 10 | 8 | 12 | 10 | 0.99 |
0.01 | 0.8 | 0.4 | 0.9 | 1 | 2 | 9 | 14 | 3.9 | 0.84 | 2 | 4 | 6 | 8 | 4.7 | 0.82 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.8 | 0.45 | 0.6 | 22 | 43 | 74 | 137 | 58.7 | 0.83 | 48 | 90 | 62 | 112 | 91 | 0.95 |
0.01 | 0.8 | 0.45 | 0.65 | 11 | 21 | 47 | 83 | 32.4 | 0.82 | 16 | 34 | 36 | 61 | 43.1 | 0.66 |
0.01 | 0.8 | 0.45 | 0.7 | 7 | 13 | 32 | 54 | 20.3 | 0.82 | 9 | 19 | 25 | 40 | 25.9 | 0.67 |
0.01 | 0.8 | 0.45 | 0.75 | 5 | 9 | 23 | 37 | 13.6 | 0.83 | 11 | 18 | 18 | 28 | 18.5 | 0.95 |
0.01 | 0.8 | 0.45 | 0.8 | 4 | 7 | 16 | 24 | 9.6 | 0.85 | 5 | 9 | 13 | 19 | 10.7 | 0.83 |
0.01 | 0.8 | 0.45 | 0.85 | 3 | 5 | 13 | 19 | 6.8 | 0.87 | 6 | 9 | 10 | 14 | 9.2 | 0.95 |
0.01 | 0.8 | 0.45 | 0.9 | 1 | 2 | 11 | 16 | 4.8 | 0.8 | 5 | 7 | 8 | 11 | 7.1 | 0.96 |
0.01 | 0.8 | 0.45 | 0.95 | 1 | 2 | 7 | 9 | 3.4 | 0.8 | 3 | 4 | 6 | 8 | 4.2 | 0.96 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.8 | 0.5 | 0.65 | 23 | 41 | 81 | 137 | 57.7 | 0.83 | 60 | 101 | 66 | 109 | 101.2 | 0.98 |
0.01 | 0.8 | 0.5 | 0.7 | 12 | 21 | 46 | 74 | 31.2 | 0.81 | 13 | 25 | 39 | 61 | 37.4 | 0.65 |
0.01 | 0.8 | 0.5 | 0.75 | 7 | 12 | 33 | 51 | 19.6 | 0.81 | 11 | 20 | 25 | 37 | 24.3 | 0.75 |
0.01 | 0.8 | 0.5 | 0.8 | 4 | 7 | 22 | 32 | 12.7 | 0.77 | 17 | 24 | 18 | 26 | 24 | 0.99 |
0.01 | 0.8 | 0.5 | 0.85 | 3 | 5 | 17 | 24 | 8.6 | 0.81 | 5 | 8 | 14 | 19 | 9.6 | 0.86 |
0.01 | 0.8 | 0.5 | 0.9 | 3 | 5 | 11 | 14 | 6.7 | 0.81 | 4 | 6 | 10 | 13 | 6.8 | 0.89 |
0.01 | 0.8 | 0.5 | 0.95 | 2 | 3 | 8 | 10 | 3.9 | 0.88 | 2 | 3 | 8 | 10 | 3.9 | 0.88 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.8 | 0.55 | 0.7 | 21 | 35 | 80 | 124 | 54.9 | 0.78 | 28 | 50 | 69 | 105 | 71.4 | 0.61 |
0.01 | 0.8 | 0.55 | 0.75 | 12 | 19 | 53 | 80 | 29.5 | 0.83 | 12 | 21 | 40 | 58 | 33.6 | 0.66 |
0.01 | 0.8 | 0.55 | 0.8 | 7 | 11 | 33 | 47 | 17.9 | 0.81 | 7 | 12 | 26 | 36 | 19.3 | 0.7 |
0.01 | 0.8 | 0.55 | 0.85 | 6 | 9 | 20 | 27 | 11.7 | 0.85 | 15 | 20 | 18 | 24 | 20.1 | 0.98 |
0.01 | 0.8 | 0.55 | 0.9 | 4 | 6 | 14 | 18 | 8 | 0.84 | 12 | 15 | 13 | 17 | 15 | 0.99 |
0.01 | 0.8 | 0.55 | 0.95 | 3 | 4 | 11 | 14 | 4.9 | 0.91 | 1 | 2 | 10 | 12 | 5 | 0.7 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.8 | 0.6 | 0.75 | 23 | 35 | 82 | 118 | 51.2 | 0.8 | 31 | 49 | 70 | 99 | 62.6 | 0.73 |
0.01 | 0.8 | 0.6 | 0.8 | 13 | 19 | 49 | 68 | 27 | 0.84 | 15 | 23 | 40 | 54 | 30.4 | 0.76 |
0.01 | 0.8 | 0.6 | 0.85 | 7 | 10 | 35 | 47 | 16.2 | 0.83 | 7 | 12 | 25 | 32 | 20.8 | 0.56 |
0.01 | 0.8 | 0.6 | 0.9 | 5 | 7 | 19 | 24 | 9.7 | 0.84 | 3 | 5 | 17 | 21 | 10.4 | 0.66 |
0.01 | 0.8 | 0.6 | 0.95 | 2 | 3 | 14 | 17 | 6 | 0.78 | 4 | 6 | 12 | 14 | 7.9 | 0.77 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.8 | 0.65 | 0.8 | 19 | 27 | 86 | 116 | 46.4 | 0.78 | 30 | 44 | 69 | 91 | 57.1 | 0.72 |
0.01 | 0.8 | 0.65 | 0.85 | 10 | 14 | 45 | 58 | 23.7 | 0.78 | 25 | 33 | 38 | 48 | 34 | 0.93 |
0.01 | 0.8 | 0.65 | 0.9 | 5 | 7 | 29 | 36 | 13.8 | 0.77 | 8 | 11 | 24 | 29 | 14.6 | 0.8 |
0.01 | 0.8 | 0.65 | 0.95 | 3 | 4 | 20 | 24 | 7.6 | 0.82 | 5 | 7 | 14 | 16 | 9.1 | 0.77 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.8 | 0.7 | 0.8 | 47 | 64 | 167 | 218 | 99.9 | 0.77 | 62 | 86 | 149 | 193 | 117.9 | 0.7 |
0.01 | 0.8 | 0.7 | 0.85 | 19 | 25 | 80 | 101 | 39.7 | 0.81 | 31 | 43 | 64 | 79 | 54.8 | 0.67 |
0.01 | 0.8 | 0.7 | 0.9 | 10 | 13 | 40 | 48 | 20.1 | 0.8 | 33 | 39 | 35 | 42 | 39 | 0.99 |
0.01 | 0.8 | 0.7 | 0.95 | 3 | 4 | 28 | 33 | 11 | 0.76 | 9 | 11 | 21 | 24 | 12.5 | 0.89 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.8 | 0.75 | 0.85 | 35 | 45 | 155 | 190 | 85.6 | 0.72 | 58 | 76 | 135 | 164 | 107 | 0.65 |
0.01 | 0.8 | 0.75 | 0.9 | 18 | 22 | 74 | 88 | 32.7 | 0.84 | 30 | 38 | 56 | 65 | 44.2 | 0.77 |
0.01 | 0.8 | 0.75 | 0.95 | 10 | 12 | 32 | 36 | 15.8 | 0.84 | 27 | 30 | 29 | 33 | 30 | 0.99 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.8 | 0.8 | 0.9 | 37 | 44 | 135 | 156 | 65.9 | 0.8 | 109 | 125 | 115 | 132 | 125.1 | 0.99 |
0.01 | 0.8 | 0.8 | 0.95 | 12 | 14 | 53 | 59 | 22.9 | 0.8 | 42 | 46 | 45 | 50 | 46 | 0.99 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.8 | 0.85 | 0.95 | 24 | 27 | 99 | 108 | 43.8 | 0.79 | 27 | 31 | 85 | 92 | 49.1 | 0.7 |
α=0.1, Power = 0.8 π0 = proportion of success at or below which treatment is abandoned π1 = proportion of success at or above which treatment will be accepted for further development and trials r1 = number of successes above which stage 2 can be entered, and at or below which the trial terminates after n1 cases, and the treatment rejected n1 = maximum sample size in stage 1 rTot = the total number of successes (stage 1 and 2 combined) above which the study can be terminated and the treatment accepted for further development and trials, and at or below which after nTot cases the treatment is rejected. nTot = the total maximum sample size (stage 1 and 2 combined) EN = expected sample size, an estimated average sample size that will be used before the trial terminates. This is a measure of efficiency in detecting PET = probability of early termination (when treatment is abandoned), a measure of efficiency in rejecting ineffective treatments.
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.9 | 0.05 | 0.15 | 1 | 28 | 5 | 66 | 43.6 | 0.59 | 1 | 39 | 5 | 60 | 51.3 | 0.41 |
0.1 | 0.9 | 0.05 | 0.2 | 0 | 12 | 3 | 37 | 23.5 | 0.54 | 0 | 18 | 3 | 32 | 26.4 | 0.4 |
0.1 | 0.9 | 0.05 | 0.25 | 0 | 9 | 2 | 24 | 14.5 | 0.63 | 0 | 13 | 2 | 20 | 16.4 | 0.51 |
0.1 | 0.9 | 0.05 | 0.3 | 0 | 7 | 2 | 21 | 11.2 | 0.7 | 0 | 13 | 2 | 16 | 14.5 | 0.51 |
0.1 | 0.9 | 0.05 | 0.35 | 0 | 6 | 1 | 12 | 7.6 | 0.74 | 0 | 7 | 1 | 10 | 7.9 | 0.7 |
0.1 | 0.9 | 0.05 | 0.4 | 0 | 5 | 1 | 10 | 6.1 | 0.77 | 0 | 6 | 1 | 9 | 6.8 | 0.74 |
0.1 | 0.9 | 0.05 | 0.45 | 0 | 4 | 1 | 10 | 5.1 | 0.81 | 0 | 5 | 1 | 8 | 5.7 | 0.77 |
0.1 | 0.9 | 0.05 | 0.5 | 0 | 4 | 1 | 7 | 4.6 | 0.81 | 0 | 4 | 1 | 7 | 4.6 | 0.81 |
0.1 | 0.9 | 0.05 | 0.55 | 0 | 3 | 1 | 8 | 3.7 | 0.86 | 0 | 4 | 1 | 6 | 4.4 | 0.81 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.9 | 0.1 | 0.2 | 4 | 41 | 13 | 99 | 63.7 | 0.61 | 5 | 61 | 12 | 86 | 75.5 | 0.42 |
0.1 | 0.9 | 0.1 | 0.25 | 2 | 21 | 7 | 50 | 31.2 | 0.65 | 2 | 27 | 6 | 40 | 33.7 | 0.48 |
0.1 | 0.9 | 0.1 | 0.3 | 1 | 12 | 5 | 35 | 19.8 | 0.66 | 1 | 16 | 4 | 25 | 20.4 | 0.51 |
0.1 | 0.9 | 0.1 | 0.35 | 1 | 11 | 3 | 19 | 13.4 | 0.7 | 0 | 8 | 3 | 18 | 13.7 | 0.43 |
0.1 | 0.9 | 0.1 | 0.4 | 0 | 5 | 3 | 18 | 10.3 | 0.59 | 0 | 8 | 3 | 15 | 12 | 0.43 |
0.1 | 0.9 | 0.1 | 0.45 | 0 | 5 | 2 | 11 | 7.5 | 0.59 | 0 | 8 | 2 | 10 | 9.1 | 0.43 |
0.1 | 0.9 | 0.1 | 0.5 | 0 | 4 | 2 | 10 | 6.1 | 0.66 | 0 | 5 | 2 | 9 | 6.6 | 0.59 |
0.1 | 0.9 | 0.1 | 0.55 | 0 | 3 | 2 | 11 | 5.2 | 0.73 | 0 | 5 | 2 | 8 | 6.2 | 0.59 |
0.1 | 0.9 | 0.1 | 0.6 | 0 | 3 | 1 | 6 | 3.8 | 0.73 | 0 | 4 | 1 | 5 | 4.3 | 0.66 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.9 | 0.15 | 0.25 | 8 | 52 | 23 | 125 | 79.5 | 0.62 | 9 | 65 | 20 | 105 | 85.7 | 0.48 |
0.1 | 0.9 | 0.15 | 0.3 | 3 | 23 | 11 | 55 | 37.7 | 0.54 | 5 | 34 | 11 | 53 | 41.7 | 0.6 |
0.1 | 0.9 | 0.15 | 0.35 | 3 | 19 | 7 | 33 | 23.4 | 0.68 | 2 | 17 | 7 | 32 | 24.2 | 0.52 |
0.1 | 0.9 | 0.15 | 0.4 | 1 | 10 | 5 | 22 | 15.5 | 0.54 | 2 | 15 | 5 | 21 | 17.4 | 0.6 |
0.1 | 0.9 | 0.15 | 0.45 | 1 | 8 | 4 | 17 | 11.1 | 0.66 | 1 | 9 | 4 | 16 | 11.8 | 0.6 |
0.1 | 0.9 | 0.15 | 0.5 | 1 | 7 | 3 | 13 | 8.7 | 0.72 | 0 | 5 | 3 | 12 | 8.9 | 0.44 |
0.1 | 0.9 | 0.15 | 0.55 | 1 | 6 | 3 | 11 | 7.1 | 0.78 | 1 | 6 | 3 | 11 | 7.1 | 0.78 |
0.1 | 0.9 | 0.15 | 0.6 | 0 | 3 | 2 | 8 | 4.9 | 0.61 | 0 | 5 | 2 | 7 | 6.1 | 0.44 |
0.1 | 0.9 | 0.15 | 0.65 | 0 | 3 | 2 | 7 | 4.5 | 0.61 | 0 | 3 | 2 | 7 | 4.5 | 0.61 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.9 | 0.2 | 0.3 | 12 | 59 | 34 | 144 | 92.8 | 0.6 | 14 | 73 | 30 | 124 | 98.5 | 0.5 |
0.1 | 0.9 | 0.2 | 0.35 | 5 | 27 | 16 | 63 | 43.6 | 0.54 | 6 | 33 | 15 | 58 | 45.5 | 0.5 |
0.1 | 0.9 | 0.2 | 0.4 | 3 | 17 | 10 | 37 | 26 | 0.55 | 3 | 19 | 10 | 36 | 28.3 | 0.46 |
0.1 | 0.9 | 0.2 | 0.45 | 3 | 14 | 7 | 25 | 17.3 | 0.7 | 3 | 15 | 7 | 24 | 18.2 | 0.65 |
0.1 | 0.9 | 0.2 | 0.5 | 2 | 10 | 5 | 17 | 12.3 | 0.68 | 2 | 10 | 5 | 17 | 12.3 | 0.68 |
0.1 | 0.9 | 0.2 | 0.55 | 0 | 4 | 4 | 13 | 9.3 | 0.41 | 0 | 4 | 4 | 13 | 9.3 | 0.41 |
0.1 | 0.9 | 0.2 | 0.6 | 1 | 5 | 4 | 14 | 7.4 | 0.74 | 1 | 7 | 3 | 9 | 7.8 | 0.58 |
0.1 | 0.9 | 0.2 | 0.65 | 0 | 3 | 3 | 9 | 5.9 | 0.51 | 0 | 3 | 3 | 9 | 5.9 | 0.51 |
0.1 | 0.9 | 0.2 | 0.7 | 0 | 3 | 2 | 6 | 4.5 | 0.51 | 0 | 3 | 2 | 6 | 4.5 | 0.51 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.9 | 0.25 | 0.35 | 19 | 74 | 44 | 152 | 104.1 | 0.61 | 18 | 75 | 41 | 140 | 108.6 | 0.48 |
0.1 | 0.9 | 0.25 | 0.4 | 7 | 29 | 22 | 72 | 48.1 | 0.56 | 9 | 39 | 20 | 64 | 52.1 | 0.48 |
0.1 | 0.9 | 0.25 | 0.45 | 3 | 14 | 14 | 44 | 28.4 | 0.52 | 5 | 23 | 13 | 39 | 31.5 | 0.47 |
0.1 | 0.9 | 0.25 | 0.5 | 2 | 10 | 9 | 27 | 18.1 | 0.53 | 2 | 11 | 9 | 26 | 19.2 | 0.46 |
0.1 | 0.9 | 0.25 | 0.55 | 2 | 9 | 7 | 20 | 13.4 | 0.6 | 5 | 15 | 6 | 17 | 15.3 | 0.85 |
0.1 | 0.9 | 0.25 | 0.6 | 2 | 8 | 5 | 14 | 9.9 | 0.68 | 1 | 8 | 5 | 13 | 11.2 | 0.37 |
0.1 | 0.9 | 0.25 | 0.65 | 1 | 5 | 4 | 11 | 7.2 | 0.63 | 1 | 6 | 4 | 10 | 7.9 | 0.53 |
0.1 | 0.9 | 0.25 | 0.7 | 1 | 4 | 4 | 11 | 5.8 | 0.74 | 2 | 6 | 3 | 8 | 6.3 | 0.83 |
0.1 | 0.9 | 0.25 | 0.75 | 0 | 2 | 3 | 8 | 4.6 | 0.56 | 1 | 4 | 3 | 7 | 4.8 | 0.74 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.9 | 0.3 | 0.4 | 23 | 75 | 58 | 171 | 112.9 | 0.61 | 22 | 78 | 52 | 151 | 120.5 | 0.42 |
0.1 | 0.9 | 0.3 | 0.45 | 9 | 30 | 29 | 82 | 51.4 | 0.59 | 16 | 50 | 25 | 69 | 56 | 0.68 |
0.1 | 0.9 | 0.3 | 0.5 | 7 | 22 | 17 | 46 | 29.9 | 0.67 | 7 | 28 | 15 | 39 | 35 | 0.36 |
0.1 | 0.9 | 0.3 | 0.55 | 4 | 13 | 12 | 31 | 19.2 | 0.65 | 4 | 16 | 10 | 25 | 21 | 0.45 |
0.1 | 0.9 | 0.3 | 0.6 | 2 | 8 | 8 | 20 | 13.4 | 0.55 | 2 | 9 | 8 | 19 | 14.4 | 0.46 |
0.1 | 0.9 | 0.3 | 0.65 | 2 | 7 | 7 | 16 | 10.2 | 0.65 | 3 | 9 | 6 | 14 | 10.4 | 0.73 |
0.1 | 0.9 | 0.3 | 0.7 | 2 | 6 | 5 | 12 | 7.5 | 0.74 | 2 | 7 | 4 | 9 | 7.7 | 0.65 |
0.1 | 0.9 | 0.3 | 0.75 | 0 | 2 | 4 | 9 | 5.6 | 0.49 | 0 | 2 | 4 | 9 | 5.6 | 0.49 |
0.1 | 0.9 | 0.3 | 0.8 | 1 | 4 | 3 | 6 | 4.7 | 0.65 | 1 | 4 | 3 | 6 | 4.7 | 0.65 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.9 | 0.35 | 0.45 | 27 | 77 | 67 | 171 | 118.7 | 0.56 | 61 | 155 | 62 | 157 | 155.2 | 0.89 |
0.1 | 0.9 | 0.35 | 0.5 | 12 | 34 | 33 | 81 | 53.2 | 0.59 | 14 | 43 | 30 | 72 | 59.3 | 0.44 |
0.1 | 0.9 | 0.35 | 0.55 | 7 | 20 | 20 | 47 | 30.8 | 0.6 | 15 | 36 | 18 | 42 | 36.9 | 0.84 |
0.1 | 0.9 | 0.35 | 0.6 | 6 | 16 | 12 | 27 | 19.4 | 0.69 | 6 | 16 | 12 | 27 | 19.4 | 0.69 |
0.1 | 0.9 | 0.35 | 0.65 | 2 | 7 | 10 | 22 | 14 | 0.53 | 4 | 13 | 8 | 17 | 15 | 0.5 |
0.1 | 0.9 | 0.35 | 0.7 | 2 | 6 | 7 | 15 | 9.2 | 0.65 | 3 | 9 | 7 | 14 | 11 | 0.61 |
0.1 | 0.9 | 0.35 | 0.75 | 2 | 6 | 5 | 10 | 7.4 | 0.65 | 2 | 6 | 5 | 10 | 7.4 | 0.65 |
0.1 | 0.9 | 0.35 | 0.8 | 0 | 2 | 4 | 8 | 5.5 | 0.42 | 0 | 2 | 4 | 8 | 5.5 | 0.42 |
0.1 | 0.9 | 0.35 | 0.85 | 1 | 3 | 3 | 6 | 3.8 | 0.72 | 1 | 3 | 3 | 6 | 3.8 | 0.72 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.9 | 0.4 | 0.5 | 30 | 74 | 84 | 191 | 122.3 | 0.59 | 57 | 134 | 73 | 164 | 141.3 | 0.76 |
0.1 | 0.9 | 0.4 | 0.55 | 16 | 38 | 40 | 88 | 54.5 | 0.67 | 18 | 45 | 34 | 73 | 57.2 | 0.56 |
0.1 | 0.9 | 0.4 | 0.6 | 7 | 18 | 22 | 46 | 30.2 | 0.56 | 11 | 28 | 20 | 41 | 33.8 | 0.55 |
0.1 | 0.9 | 0.4 | 0.65 | 5 | 13 | 14 | 28 | 19.4 | 0.57 | 5 | 13 | 14 | 28 | 19.4 | 0.57 |
0.1 | 0.9 | 0.4 | 0.7 | 5 | 11 | 10 | 20 | 13.2 | 0.75 | 2 | 7 | 10 | 19 | 14 | 0.42 |
0.1 | 0.9 | 0.4 | 0.75 | 2 | 6 | 7 | 13 | 9.2 | 0.54 | 2 | 6 | 7 | 13 | 9.2 | 0.54 |
0.1 | 0.9 | 0.4 | 0.8 | 1 | 4 | 5 | 9 | 6.6 | 0.48 | 1 | 4 | 5 | 9 | 6.6 | 0.48 |
0.1 | 0.9 | 0.4 | 0.85 | 1 | 3 | 5 | 9 | 5.1 | 0.65 | 0 | 2 | 4 | 7 | 5.2 | 0.36 |
0.1 | 0.9 | 0.4 | 0.9 | 1 | 3 | 3 | 5 | 3.7 | 0.65 | 1 | 3 | 3 | 5 | 3.7 | 0.65 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.9 | 0.45 | 0.55 | 38 | 83 | 90 | 183 | 122.9 | 0.6 | 56 | 128 | 81 | 163 | 148.2 | 0.42 |
0.1 | 0.9 | 0.45 | 0.6 | 14 | 32 | 40 | 78 | 54.2 | 0.52 | 34 | 67 | 38 | 74 | 68 | 0.86 |
0.1 | 0.9 | 0.45 | 0.65 | 9 | 20 | 24 | 45 | 30.2 | 0.59 | 9 | 21 | 22 | 41 | 30.8 | 0.51 |
0.1 | 0.9 | 0.45 | 0.7 | 5 | 12 | 15 | 27 | 19.1 | 0.53 | 6 | 15 | 14 | 25 | 20.5 | 0.45 |
0.1 | 0.9 | 0.45 | 0.75 | 5 | 10 | 11 | 20 | 12.6 | 0.74 | 2 | 6 | 11 | 19 | 13.3 | 0.44 |
0.1 | 0.9 | 0.45 | 0.8 | 2 | 5 | 9 | 15 | 9.1 | 0.59 | 4 | 9 | 8 | 13 | 10.5 | 0.62 |
0.1 | 0.9 | 0.45 | 0.85 | 1 | 3 | 6 | 10 | 6 | 0.57 | 1 | 3 | 6 | 10 | 6 | 0.57 |
0.1 | 0.9 | 0.45 | 0.9 | 2 | 4 | 5 | 8 | 5 | 0.76 | 3 | 5 | 4 | 7 | 5.3 | 0.87 |
0.1 | 0.9 | 0.45 | 0.95 | 1 | 2 | 4 | 7 | 3 | 0.8 | 0 | 1 | 4 | 6 | 3.3 | 0.55 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.9 | 0.5 | 0.6 | 45 | 87 | 103 | 191 | 121.8 | 0.67 | 78 | 146 | 89 | 163 | 149.1 | 0.82 |
0.1 | 0.9 | 0.5 | 0.65 | 18 | 35 | 47 | 84 | 53 | 0.63 | 19 | 40 | 41 | 72 | 58 | 0.44 |
0.1 | 0.9 | 0.5 | 0.7 | 11 | 21 | 26 | 45 | 29 | 0.67 | 11 | 23 | 23 | 39 | 31 | 0.5 |
0.1 | 0.9 | 0.5 | 0.75 | 6 | 12 | 17 | 28 | 18.2 | 0.61 | 13 | 22 | 15 | 25 | 22.4 | 0.86 |
0.1 | 0.9 | 0.5 | 0.8 | 3 | 7 | 10 | 16 | 11.5 | 0.5 | 3 | 7 | 10 | 16 | 11.5 | 0.5 |
0.1 | 0.9 | 0.5 | 0.85 | 4 | 7 | 8 | 13 | 8.4 | 0.77 | 4 | 8 | 8 | 12 | 9.5 | 0.64 |
0.1 | 0.9 | 0.5 | 0.9 | 2 | 4 | 6 | 9 | 5.6 | 0.69 | 2 | 4 | 6 | 9 | 5.6 | 0.69 |
0.1 | 0.9 | 0.5 | 0.95 | 0 | 1 | 4 | 6 | 3.5 | 0.5 | 0 | 1 | 4 | 6 | 3.5 | 0.5 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.9 | 0.55 | 0.65 | 44 | 79 | 102 | 172 | 116.9 | 0.59 | 52 | 96 | 95 | 159 | 129.1 | 0.47 |
0.1 | 0.9 | 0.55 | 0.7 | 19 | 34 | 46 | 75 | 50.1 | 0.61 | 35 | 58 | 43 | 70 | 60.1 | 0.83 |
0.1 | 0.9 | 0.55 | 0.75 | 10 | 18 | 26 | 41 | 27 | 0.61 | 20 | 32 | 24 | 38 | 32.9 | 0.85 |
0.1 | 0.9 | 0.55 | 0.8 | 4 | 8 | 17 | 26 | 16.6 | 0.52 | 13 | 20 | 15 | 23 | 20.4 | 0.87 |
0.1 | 0.9 | 0.55 | 0.85 | 4 | 7 | 12 | 18 | 10.5 | 0.68 | 2 | 5 | 11 | 16 | 11.5 | 0.41 |
0.1 | 0.9 | 0.55 | 0.9 | 2 | 4 | 7 | 10 | 6.3 | 0.61 | 2 | 4 | 7 | 10 | 6.3 | 0.61 |
0.1 | 0.9 | 0.55 | 0.95 | 0 | 1 | 5 | 7 | 4.3 | 0.45 | 0 | 1 | 5 | 7 | 4.3 | 0.45 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.9 | 0.6 | 0.7 | 43 | 71 | 108 | 168 | 111.4 | 0.58 | 83 | 131 | 97 | 150 | 134.6 | 0.81 |
0.1 | 0.9 | 0.6 | 0.75 | 21 | 34 | 47 | 71 | 47.1 | 0.65 | 25 | 43 | 43 | 64 | 54.4 | 0.46 |
0.1 | 0.9 | 0.6 | 0.8 | 6 | 11 | 26 | 38 | 25.4 | 0.47 | 18 | 27 | 24 | 35 | 28.5 | 0.82 |
0.1 | 0.9 | 0.6 | 0.85 | 7 | 11 | 16 | 23 | 14.6 | 0.7 | 5 | 9 | 15 | 21 | 14.8 | 0.52 |
0.1 | 0.9 | 0.6 | 0.9 | 3 | 5 | 12 | 17 | 9 | 0.66 | 7 | 10 | 10 | 14 | 10.7 | 0.83 |
0.1 | 0.9 | 0.6 | 0.95 | 0 | 1 | 6 | 8 | 5.2 | 0.4 | 0 | 1 | 6 | 8 | 5.2 | 0.4 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.9 | 0.65 | 0.75 | 47 | 71 | 106 | 153 | 101.6 | 0.63 | 45 | 71 | 97 | 139 | 109.7 | 0.43 |
0.1 | 0.9 | 0.65 | 0.8 | 20 | 30 | 45 | 63 | 41.8 | 0.64 | 22 | 33 | 43 | 60 | 42.6 | 0.64 |
0.1 | 0.9 | 0.65 | 0.85 | 10 | 15 | 25 | 34 | 21.7 | 0.65 | 8 | 13 | 23 | 31 | 22 | 0.5 |
0.1 | 0.9 | 0.65 | 0.9 | 5 | 8 | 13 | 17 | 11.9 | 0.57 | 5 | 8 | 13 | 17 | 11.9 | 0.57 |
0.1 | 0.9 | 0.65 | 0.95 | 3 | 5 | 8 | 10 | 7.1 | 0.57 | 3 | 5 | 8 | 10 | 7.1 | 0.57 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.9 | 0.7 | 0.8 | 37 | 53 | 99 | 133 | 89.8 | 0.54 | 44 | 64 | 92 | 123 | 95.8 | 0.46 |
0.1 | 0.9 | 0.7 | 0.85 | 14 | 20 | 45 | 59 | 36.2 | 0.58 | 15 | 22 | 40 | 52 | 36.8 | 0.51 |
0.1 | 0.9 | 0.7 | 0.9 | 6 | 9 | 22 | 28 | 17.8 | 0.54 | 11 | 16 | 20 | 25 | 20 | 0.55 |
0.1 | 0.9 | 0.7 | 0.95 | 5 | 7 | 13 | 16 | 10 | 0.67 | 7 | 9 | 12 | 15 | 10.2 | 0.8 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.9 | 0.75 | 0.85 | 39 | 51 | 99 | 125 | 77 | 0.65 | 68 | 87 | 83 | 104 | 90.6 | 0.79 |
0.1 | 0.9 | 0.75 | 0.9 | 12 | 16 | 39 | 48 | 29 | 0.6 | 20 | 27 | 33 | 40 | 33.1 | 0.53 |
0.1 | 0.9 | 0.75 | 0.95 | 6 | 8 | 16 | 19 | 12 | 0.63 | 6 | 8 | 16 | 19 | 12 | 0.63 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.9 | 0.8 | 0.9 | 30 | 37 | 80 | 95 | 58.5 | 0.63 | 66 | 78 | 71 | 84 | 78.7 | 0.88 |
0.1 | 0.9 | 0.8 | 0.95 | 5 | 7 | 27 | 31 | 20.8 | 0.42 | 5 | 7 | 27 | 31 | 20.8 | 0.42 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.1 | 0.9 | 0.85 | 0.95 | 25 | 29 | 53 | 59 | 39.5 | 0.65 | 40 | 45 | 52 | 58 | 47.3 | 0.83 |
α=0.1, Power = 0.8 π0 = proportion of success at or below which treatment is abandoned π1 = proportion of success at or above which treatment will be accepted for further development and trials r1 = number of successes above which stage 2 can be entered, and at or below which the trial terminates after n1 cases, and the treatment rejected n1 = maximum sample size in stage 1 rTot = the total number of successes (stage 1 and 2 combined) above which the study can be terminated and the treatment accepted for further development and trials, and at or below which after nTot cases the treatment is rejected. nTot = the total maximum sample size (stage 1 and 2 combined) EN = expected sample size, an estimated average sample size that will be used before the trial terminates. This is a measure of efficiency in detecting PET = probability of early termination (when treatment is abandoned), a measure of efficiency in rejecting ineffective treatments.
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.9 | 0.05 | 0.15 | 2 | 37 | 7 | 84 | 50.2 | 0.72 | 2 | 46 | 7 | 77 | 58.6 | 0.59 |
0.05 | 0.9 | 0.05 | 0.2 | 1 | 21 | 4 | 41 | 26.7 | 0.72 | 1 | 29 | 4 | 38 | 32.9 | 0.57 |
0.05 | 0.9 | 0.05 | 0.25 | 0 | 9 | 3 | 30 | 16.8 | 0.63 | 0 | 15 | 3 | 25 | 20.4 | 0.46 |
0.05 | 0.9 | 0.05 | 0.3 | 0 | 9 | 2 | 17 | 12 | 0.63 | 0 | 13 | 2 | 16 | 14.5 | 0.51 |
0.05 | 0.9 | 0.05 | 0.35 | 0 | 6 | 2 | 17 | 8.9 | 0.74 | 0 | 8 | 2 | 14 | 10 | 0.66 |
0.05 | 0.9 | 0.05 | 0.4 | 0 | 5 | 2 | 14 | 7 | 0.77 | 0 | 7 | 2 | 12 | 8.5 | 0.7 |
0.05 | 0.9 | 0.05 | 0.45 | 0 | 4 | 2 | 14 | 5.9 | 0.81 | 0 | 8 | 2 | 10 | 8.7 | 0.66 |
0.05 | 0.9 | 0.05 | 0.5 | 0 | 4 | 1 | 7 | 4.6 | 0.81 | 0 | 4 | 1 | 7 | 4.6 | 0.81 |
0.05 | 0.9 | 0.05 | 0.55 | 0 | 3 | 1 | 8 | 3.7 | 0.86 | 0 | 4 | 1 | 6 | 4.4 | 0.81 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.9 | 0.1 | 0.2 | 5 | 47 | 18 | 130 | 74.3 | 0.67 | 6 | 70 | 16 | 109 | 91.8 | 0.44 |
0.05 | 0.9 | 0.1 | 0.25 | 2 | 21 | 10 | 66 | 36.8 | 0.65 | 3 | 31 | 9 | 55 | 40 | 0.62 |
0.05 | 0.9 | 0.1 | 0.3 | 2 | 18 | 6 | 35 | 22.5 | 0.73 | 2 | 22 | 6 | 33 | 26.2 | 0.62 |
0.05 | 0.9 | 0.1 | 0.35 | 1 | 11 | 5 | 27 | 15.8 | 0.7 | 1 | 13 | 5 | 25 | 17.5 | 0.62 |
0.05 | 0.9 | 0.1 | 0.4 | 1 | 9 | 4 | 20 | 11.5 | 0.77 | 1 | 12 | 4 | 18 | 14 | 0.66 |
0.05 | 0.9 | 0.1 | 0.45 | 0 | 5 | 3 | 14 | 8.7 | 0.59 | 0 | 7 | 3 | 13 | 10.1 | 0.48 |
0.05 | 0.9 | 0.1 | 0.5 | 0 | 4 | 3 | 13 | 7.1 | 0.66 | 0 | 5 | 3 | 12 | 7.9 | 0.59 |
0.05 | 0.9 | 0.1 | 0.55 | 0 | 4 | 2 | 9 | 5.7 | 0.66 | 0 | 5 | 2 | 8 | 6.2 | 0.59 |
0.05 | 0.9 | 0.1 | 0.6 | 0 | 3 | 2 | 8 | 4.4 | 0.73 | 0 | 5 | 2 | 7 | 5.8 | 0.59 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.9 | 0.15 | 0.25 | 9 | 57 | 31 | 162 | 93.6 | 0.65 | 11 | 78 | 27 | 136 | 107.6 | 0.49 |
0.05 | 0.9 | 0.15 | 0.3 | 5 | 30 | 17 | 82 | 45.1 | 0.71 | 6 | 42 | 14 | 64 | 51.8 | 0.55 |
0.05 | 0.9 | 0.15 | 0.35 | 3 | 19 | 10 | 44 | 26.9 | 0.68 | 3 | 23 | 9 | 38 | 29.9 | 0.54 |
0.05 | 0.9 | 0.15 | 0.4 | 2 | 13 | 7 | 29 | 17.9 | 0.69 | 2 | 16 | 7 | 27 | 20.8 | 0.56 |
0.05 | 0.9 | 0.15 | 0.45 | 1 | 9 | 5 | 19 | 13 | 0.6 | 1 | 9 | 5 | 19 | 13 | 0.6 |
0.05 | 0.9 | 0.15 | 0.5 | 1 | 7 | 5 | 18 | 10.1 | 0.72 | 0 | 6 | 4 | 14 | 11 | 0.38 |
0.05 | 0.9 | 0.15 | 0.55 | 1 | 6 | 4 | 14 | 7.8 | 0.78 | 0 | 4 | 4 | 13 | 8.3 | 0.52 |
0.05 | 0.9 | 0.15 | 0.6 | 1 | 5 | 3 | 11 | 6 | 0.84 | 1 | 7 | 3 | 9 | 7.6 | 0.72 |
0.05 | 0.9 | 0.15 | 0.65 | 0 | 3 | 3 | 9 | 5.3 | 0.61 | 0 | 3 | 3 | 9 | 5.3 | 0.61 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.9 | 0.2 | 0.3 | 15 | 71 | 45 | 184 | 109.5 | 0.66 | 18 | 92 | 40 | 160 | 124.6 | 0.52 |
0.05 | 0.9 | 0.2 | 0.35 | 8 | 37 | 22 | 83 | 51.4 | 0.69 | 8 | 42 | 21 | 77 | 58.4 | 0.53 |
0.05 | 0.9 | 0.2 | 0.4 | 4 | 19 | 15 | 54 | 30.4 | 0.67 | 5 | 24 | 13 | 45 | 31.2 | 0.66 |
0.05 | 0.9 | 0.2 | 0.45 | 4 | 16 | 11 | 38 | 20.4 | 0.8 | 4 | 19 | 9 | 29 | 22.3 | 0.67 |
0.05 | 0.9 | 0.2 | 0.5 | 2 | 10 | 7 | 22 | 13.9 | 0.68 | 2 | 12 | 7 | 21 | 16 | 0.56 |
0.05 | 0.9 | 0.2 | 0.55 | 2 | 8 | 7 | 22 | 10.8 | 0.8 | 1 | 7 | 6 | 17 | 11.2 | 0.58 |
0.05 | 0.9 | 0.2 | 0.6 | 1 | 5 | 6 | 18 | 8.4 | 0.74 | 1 | 8 | 5 | 13 | 10.5 | 0.5 |
0.05 | 0.9 | 0.2 | 0.65 | 1 | 5 | 4 | 11 | 6.6 | 0.74 | 1 | 6 | 4 | 10 | 7.4 | 0.66 |
0.05 | 0.9 | 0.2 | 0.7 | 1 | 4 | 4 | 11 | 5.3 | 0.82 | 2 | 6 | 3 | 8 | 6.2 | 0.9 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.9 | 0.25 | 0.35 | 24 | 89 | 61 | 207 | 122.8 | 0.71 | 30 | 125 | 54 | 179 | 155 | 0.45 |
0.05 | 0.9 | 0.25 | 0.4 | 10 | 37 | 31 | 99 | 56.2 | 0.69 | 13 | 57 | 27 | 83 | 72.1 | 0.42 |
0.05 | 0.9 | 0.25 | 0.45 | 6 | 22 | 19 | 57 | 32.5 | 0.7 | 6 | 26 | 17 | 49 | 37.1 | 0.52 |
0.05 | 0.9 | 0.25 | 0.5 | 5 | 17 | 13 | 37 | 21.7 | 0.77 | 4 | 16 | 12 | 33 | 22.3 | 0.63 |
0.05 | 0.9 | 0.25 | 0.55 | 2 | 9 | 9 | 24 | 15 | 0.6 | 3 | 13 | 9 | 23 | 17.2 | 0.58 |
0.05 | 0.9 | 0.25 | 0.6 | 2 | 8 | 7 | 18 | 11.2 | 0.68 | 2 | 9 | 7 | 17 | 12.2 | 0.6 |
0.05 | 0.9 | 0.25 | 0.65 | 1 | 5 | 6 | 15 | 8.7 | 0.63 | 1 | 6 | 6 | 14 | 9.7 | 0.53 |
0.05 | 0.9 | 0.25 | 0.7 | 1 | 4 | 6 | 15 | 6.9 | 0.74 | 1 | 6 | 4 | 9 | 7.4 | 0.53 |
0.05 | 0.9 | 0.25 | 0.75 | 0 | 2 | 4 | 9 | 5.1 | 0.56 | 0 | 2 | 4 | 9 | 5.1 | 0.56 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.9 | 0.3 | 0.4 | 28 | 89 | 77 | 222 | 133.4 | 0.67 | 41 | 142 | 68 | 193 | 171.3 | 0.42 |
0.05 | 0.9 | 0.3 | 0.45 | 13 | 40 | 40 | 110 | 60.8 | 0.7 | 27 | 77 | 33 | 88 | 78.5 | 0.86 |
0.05 | 0.9 | 0.3 | 0.5 | 8 | 24 | 24 | 63 | 34.7 | 0.73 | 7 | 24 | 21 | 53 | 36.6 | 0.56 |
0.05 | 0.9 | 0.3 | 0.55 | 5 | 15 | 16 | 40 | 22 | 0.72 | 8 | 22 | 14 | 34 | 24.2 | 0.81 |
0.05 | 0.9 | 0.3 | 0.6 | 3 | 10 | 12 | 28 | 16.3 | 0.65 | 7 | 18 | 10 | 23 | 18.7 | 0.86 |
0.05 | 0.9 | 0.3 | 0.65 | 2 | 7 | 9 | 20 | 11.6 | 0.65 | 2 | 10 | 8 | 17 | 14.3 | 0.38 |
0.05 | 0.9 | 0.3 | 0.7 | 2 | 6 | 7 | 15 | 8.3 | 0.74 | 3 | 9 | 7 | 14 | 10.4 | 0.73 |
0.05 | 0.9 | 0.3 | 0.75 | 1 | 4 | 6 | 12 | 6.8 | 0.65 | 2 | 6 | 5 | 10 | 7 | 0.74 |
0.05 | 0.9 | 0.3 | 0.8 | 2 | 5 | 4 | 8 | 5.5 | 0.84 | 2 | 5 | 4 | 8 | 5.5 | 0.84 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.9 | 0.35 | 0.5 | 16 | 43 | 44 | 105 | 62.7 | 0.68 | 16 | 46 | 40 | 94 | 67.4 | 0.56 |
0.05 | 0.9 | 0.35 | 0.55 | 7 | 20 | 26 | 59 | 35.6 | 0.6 | 12 | 37 | 24 | 53 | 45.9 | 0.45 |
0.05 | 0.9 | 0.35 | 0.6 | 5 | 14 | 18 | 39 | 23 | 0.64 | 7 | 19 | 16 | 34 | 24 | 0.67 |
0.05 | 0.9 | 0.35 | 0.65 | 5 | 12 | 14 | 30 | 15.8 | 0.79 | 5 | 14 | 12 | 24 | 17.6 | 0.64 |
0.05 | 0.9 | 0.35 | 0.7 | 3 | 8 | 10 | 20 | 11.5 | 0.71 | 8 | 16 | 9 | 18 | 16.1 | 0.93 |
0.05 | 0.9 | 0.35 | 0.75 | 2 | 6 | 7 | 13 | 8.5 | 0.65 | 2 | 6 | 7 | 13 | 8.5 | 0.65 |
0.05 | 0.9 | 0.35 | 0.8 | 2 | 5 | 6 | 11 | 6.4 | 0.76 | 2 | 5 | 6 | 11 | 6.4 | 0.76 |
0.05 | 0.9 | 0.35 | 0.85 | 1 | 3 | 5 | 9 | 4.7 | 0.72 | 1 | 3 | 5 | 9 | 4.7 | 0.72 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.9 | 0.4 | 0.55 | 19 | 45 | 49 | 104 | 64 | 0.68 | 24 | 62 | 45 | 94 | 78.9 | 0.47 |
0.05 | 0.9 | 0.4 | 0.6 | 11 | 25 | 32 | 66 | 36 | 0.73 | 12 | 29 | 27 | 54 | 38.1 | 0.64 |
0.05 | 0.9 | 0.4 | 0.65 | 7 | 16 | 20 | 39 | 22.5 | 0.72 | 9 | 23 | 18 | 34 | 27.9 | 0.56 |
0.05 | 0.9 | 0.4 | 0.7 | 4 | 10 | 13 | 24 | 15.1 | 0.63 | 4 | 10 | 13 | 24 | 15.1 | 0.63 |
0.05 | 0.9 | 0.4 | 0.75 | 3 | 7 | 11 | 20 | 10.8 | 0.71 | 6 | 12 | 10 | 18 | 12.9 | 0.84 |
0.05 | 0.9 | 0.4 | 0.8 | 2 | 5 | 8 | 14 | 7.9 | 0.68 | 3 | 8 | 8 | 13 | 10 | 0.59 |
0.05 | 0.9 | 0.4 | 0.85 | 1 | 3 | 6 | 10 | 5.5 | 0.65 | 1 | 3 | 6 | 10 | 5.5 | 0.65 |
0.05 | 0.9 | 0.4 | 0.9 | 2 | 4 | 5 | 8 | 4.7 | 0.82 | 2 | 4 | 5 | 8 | 4.7 | 0.82 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.9 | 0.45 | 0.6 | 19 | 40 | 60 | 116 | 64 | 0.68 | 49 | 93 | 50 | 95 | 93.1 | 0.94 |
0.05 | 0.9 | 0.45 | 0.65 | 11 | 23 | 33 | 61 | 34.9 | 0.69 | 14 | 31 | 30 | 54 | 40.6 | 0.58 |
0.05 | 0.9 | 0.45 | 0.7 | 7 | 15 | 20 | 35 | 21.9 | 0.65 | 9 | 19 | 19 | 33 | 23.6 | 0.67 |
0.05 | 0.9 | 0.45 | 0.75 | 5 | 10 | 17 | 29 | 15 | 0.74 | 5 | 12 | 14 | 23 | 17.2 | 0.53 |
0.05 | 0.9 | 0.45 | 0.8 | 2 | 5 | 11 | 18 | 10.3 | 0.59 | 3 | 7 | 10 | 16 | 10.5 | 0.61 |
0.05 | 0.9 | 0.45 | 0.85 | 1 | 3 | 9 | 14 | 7.7 | 0.57 | 1 | 4 | 8 | 12 | 8.9 | 0.39 |
0.05 | 0.9 | 0.45 | 0.9 | 2 | 4 | 6 | 9 | 5.2 | 0.76 | 2 | 4 | 6 | 9 | 5.2 | 0.76 |
0.05 | 0.9 | 0.45 | 0.95 | 0 | 1 | 5 | 7 | 3.7 | 0.55 | 0 | 1 | 5 | 7 | 3.7 | 0.55 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.9 | 0.5 | 0.65 | 22 | 42 | 60 | 105 | 62.3 | 0.68 | 28 | 57 | 54 | 93 | 75 | 0.5 |
0.05 | 0.9 | 0.5 | 0.7 | 13 | 24 | 36 | 61 | 34 | 0.73 | 14 | 27 | 32 | 53 | 36.1 | 0.65 |
0.05 | 0.9 | 0.5 | 0.75 | 7 | 13 | 25 | 41 | 21.1 | 0.71 | 12 | 21 | 20 | 32 | 23.1 | 0.81 |
0.05 | 0.9 | 0.5 | 0.8 | 5 | 9 | 18 | 29 | 14.1 | 0.75 | 13 | 20 | 14 | 22 | 20.1 | 0.94 |
0.05 | 0.9 | 0.5 | 0.85 | 4 | 7 | 12 | 18 | 9.5 | 0.77 | 7 | 11 | 10 | 15 | 11.5 | 0.89 |
0.05 | 0.9 | 0.5 | 0.9 | 2 | 4 | 7 | 10 | 5.9 | 0.69 | 2 | 4 | 7 | 10 | 5.9 | 0.69 |
0.05 | 0.9 | 0.5 | 0.95 | 0 | 1 | 6 | 8 | 4.5 | 0.5 | 0 | 1 | 6 | 8 | 4.5 | 0.5 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.9 | 0.55 | 0.7 | 22 | 38 | 68 | 110 | 59.8 | 0.7 | 50 | 81 | 56 | 89 | 81.7 | 0.91 |
0.05 | 0.9 | 0.55 | 0.75 | 10 | 18 | 35 | 54 | 32.1 | 0.61 | 20 | 33 | 32 | 49 | 36.3 | 0.79 |
0.05 | 0.9 | 0.55 | 0.8 | 7 | 12 | 24 | 36 | 19.3 | 0.7 | 8 | 14 | 21 | 31 | 19.7 | 0.66 |
0.05 | 0.9 | 0.55 | 0.85 | 3 | 6 | 14 | 20 | 12.2 | 0.56 | 3 | 6 | 14 | 20 | 12.2 | 0.56 |
0.05 | 0.9 | 0.55 | 0.9 | 3 | 5 | 12 | 17 | 8.1 | 0.74 | 7 | 10 | 10 | 14 | 10.4 | 0.9 |
0.05 | 0.9 | 0.55 | 0.95 | 1 | 2 | 10 | 14 | 5.6 | 0.7 | 2 | 4 | 7 | 9 | 6 | 0.61 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.9 | 0.6 | 0.7 | 54 | 88 | 138 | 212 | 132.4 | 0.64 | 121 | 186 | 128 | 196 | 186.7 | 0.93 |
0.05 | 0.9 | 0.6 | 0.75 | 21 | 34 | 64 | 95 | 55.6 | 0.65 | 48 | 72 | 57 | 84 | 73.2 | 0.9 |
0.05 | 0.9 | 0.6 | 0.8 | 12 | 19 | 37 | 53 | 29.5 | 0.69 | 15 | 26 | 32 | 45 | 35.9 | 0.48 |
0.05 | 0.9 | 0.6 | 0.85 | 7 | 11 | 23 | 32 | 17.2 | 0.7 | 8 | 14 | 20 | 27 | 20.3 | 0.51 |
0.05 | 0.9 | 0.6 | 0.9 | 5 | 8 | 13 | 17 | 10.8 | 0.68 | 5 | 8 | 13 | 17 | 10.8 | 0.68 |
0.05 | 0.9 | 0.6 | 0.95 | 3 | 5 | 8 | 10 | 6.7 | 0.66 | 3 | 5 | 8 | 10 | 6.7 | 0.66 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.9 | 0.65 | 0.75 | 52 | 78 | 142 | 203 | 120.3 | 0.66 | 84 | 129 | 127 | 180 | 152.3 | 0.54 |
0.05 | 0.9 | 0.65 | 0.8 | 21 | 31 | 67 | 93 | 50.3 | 0.69 | 34 | 52 | 55 | 75 | 61.8 | 0.57 |
0.05 | 0.9 | 0.65 | 0.85 | 10 | 15 | 33 | 44 | 25.2 | 0.65 | 28 | 37 | 30 | 40 | 37.2 | 0.94 |
0.05 | 0.9 | 0.65 | 0.9 | 7 | 10 | 21 | 27 | 14.4 | 0.74 | 11 | 15 | 18 | 23 | 16.4 | 0.83 |
0.05 | 0.9 | 0.65 | 0.95 | 5 | 7 | 13 | 16 | 9.1 | 0.77 | 6 | 8 | 12 | 15 | 9.2 | 0.83 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.9 | 0.7 | 0.8 | 51 | 71 | 135 | 180 | 106.5 | 0.67 | 120 | 159 | 122 | 162 | 159.2 | 0.95 |
0.05 | 0.9 | 0.7 | 0.85 | 18 | 25 | 61 | 79 | 43.4 | 0.66 | 33 | 44 | 53 | 68 | 48.5 | 0.81 |
0.05 | 0.9 | 0.7 | 0.9 | 11 | 15 | 29 | 36 | 21.2 | 0.7 | 13 | 18 | 26 | 32 | 22.7 | 0.67 |
0.05 | 0.9 | 0.7 | 0.95 | 7 | 9 | 15 | 18 | 10.8 | 0.8 | 7 | 9 | 15 | 18 | 10.8 | 0.8 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.9 | 0.75 | 0.85 | 47 | 61 | 124 | 155 | 90.1 | 0.69 | 93 | 117 | 111 | 138 | 119.3 | 0.89 |
0.05 | 0.9 | 0.75 | 0.9 | 18 | 23 | 52 | 63 | 34.3 | 0.72 | 19 | 25 | 45 | 54 | 36 | 0.62 |
0.05 | 0.9 | 0.75 | 0.95 | 7 | 9 | 24 | 28 | 14.7 | 0.7 | 19 | 22 | 22 | 26 | 22.2 | 0.94 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.9 | 0.8 | 0.9 | 36 | 44 | 108 | 127 | 70.8 | 0.68 | 69 | 82 | 94 | 110 | 85.9 | 0.86 |
0.05 | 0.9 | 0.8 | 0.95 | 16 | 19 | 37 | 42 | 24.4 | 0.76 | 31 | 35 | 35 | 40 | 35.3 | 0.94 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.05 | 0.9 | 0.85 | 0.95 | 26 | 30 | 75 | 83 | 47 | 0.68 | 35 | 40 | 68 | 75 | 49.2 | 0.74 |
α=0.1, Power = 0.8 π0 = proportion of success at or below which treatment is abandoned π1 = proportion of success at or above which treatment will be accepted for further development and trials r1 = number of successes above which stage 2 can be entered, and at or below which the trial terminates after n1 cases, and the treatment rejected n1 = maximum sample size in stage 1 rTot = the total number of successes (stage 1 and 2 combined) above which the study can be terminated and the treatment accepted for further development and trials, and at or below which after nTot cases the treatment is rejected. nTot = the total maximum sample size (stage 1 and 2 combined) EN = expected sample size, an estimated average sample size that will be used before the trial terminates. This is a measure of efficiency in detecting PET = probability of early termination (when treatment is abandoned), a measure of efficiency in rejecting ineffective treatments.
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.9 | 0.05 | 0.15 | 3 | 44 | 13 | 144 | 61.7 | 0.82 | 3 | 65 | 11 | 108 | 82.6 | 0.59 |
0.01 | 0.9 | 0.05 | 0.2 | 1 | 21 | 7 | 61 | 32.3 | 0.72 | 2 | 34 | 7 | 57 | 39.5 | 0.76 |
0.01 | 0.9 | 0.05 | 0.25 | 1 | 15 | 6 | 47 | 20.5 | 0.83 | 1 | 23 | 5 | 35 | 26.8 | 0.68 |
0.01 | 0.9 | 0.05 | 0.3 | 1 | 12 | 5 | 35 | 14.7 | 0.88 | 0 | 11 | 4 | 25 | 17 | 0.57 |
0.01 | 0.9 | 0.05 | 0.35 | 0 | 6 | 4 | 25 | 11 | 0.74 | 2 | 15 | 3 | 18 | 15.1 | 0.96 |
0.01 | 0.9 | 0.05 | 0.4 | 0 | 5 | 3 | 18 | 7.9 | 0.77 | 0 | 8 | 3 | 15 | 10.4 | 0.66 |
0.01 | 0.9 | 0.05 | 0.45 | 0 | 4 | 3 | 18 | 6.6 | 0.81 | 0 | 7 | 3 | 13 | 8.8 | 0.7 |
0.01 | 0.9 | 0.05 | 0.5 | 0 | 4 | 2 | 10 | 5.1 | 0.81 | 0 | 5 | 2 | 9 | 5.9 | 0.77 |
0.01 | 0.9 | 0.05 | 0.55 | 0 | 3 | 3 | 14 | 4.6 | 0.86 | 0 | 5 | 2 | 8 | 5.7 | 0.77 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.9 | 0.1 | 0.2 | 8 | 66 | 28 | 187 | 91.6 | 0.79 | 9 | 87 | 25 | 160 | 114.1 | 0.63 |
0.01 | 0.9 | 0.1 | 0.25 | 4 | 31 | 17 | 102 | 44.7 | 0.81 | 4 | 39 | 14 | 78 | 52.7 | 0.65 |
0.01 | 0.9 | 0.1 | 0.3 | 2 | 17 | 11 | 59 | 27 | 0.76 | 3 | 27 | 10 | 49 | 33.2 | 0.72 |
0.01 | 0.9 | 0.1 | 0.35 | 2 | 14 | 9 | 44 | 18.8 | 0.84 | 2 | 18 | 8 | 35 | 22.5 | 0.73 |
0.01 | 0.9 | 0.1 | 0.4 | 1 | 9 | 7 | 30 | 13.7 | 0.77 | 1 | 13 | 6 | 24 | 17.2 | 0.62 |
0.01 | 0.9 | 0.1 | 0.45 | 1 | 8 | 5 | 20 | 10.2 | 0.81 | 1 | 9 | 5 | 19 | 11.3 | 0.77 |
0.01 | 0.9 | 0.1 | 0.5 | 1 | 7 | 5 | 18 | 8.6 | 0.85 | 0 | 6 | 4 | 14 | 9.7 | 0.53 |
0.01 | 0.9 | 0.1 | 0.55 | 1 | 6 | 4 | 14 | 6.9 | 0.89 | 0 | 4 | 4 | 13 | 7.1 | 0.66 |
0.01 | 0.9 | 0.1 | 0.6 | 0 | 3 | 4 | 13 | 5.7 | 0.73 | 1 | 7 | 3 | 9 | 7.3 | 0.85 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.9 | 0.15 | 0.3 | 7 | 38 | 27 | 122 | 54.9 | 0.8 | 9 | 54 | 23 | 98 | 66.6 | 0.71 |
0.01 | 0.9 | 0.15 | 0.35 | 4 | 22 | 17 | 69 | 32.6 | 0.77 | 5 | 30 | 15 | 58 | 38.1 | 0.71 |
0.01 | 0.9 | 0.15 | 0.4 | 3 | 15 | 14 | 55 | 22.1 | 0.82 | 3 | 19 | 11 | 39 | 25.3 | 0.68 |
0.01 | 0.9 | 0.15 | 0.45 | 2 | 11 | 10 | 34 | 16.1 | 0.78 | 2 | 14 | 9 | 29 | 19.3 | 0.65 |
0.01 | 0.9 | 0.15 | 0.5 | 2 | 9 | 9 | 31 | 12.1 | 0.86 | 2 | 12 | 7 | 21 | 14.4 | 0.74 |
0.01 | 0.9 | 0.15 | 0.55 | 1 | 6 | 7 | 21 | 9.4 | 0.78 | 1 | 7 | 6 | 17 | 9.8 | 0.72 |
0.01 | 0.9 | 0.15 | 0.6 | 1 | 5 | 6 | 18 | 7.1 | 0.84 | 1 | 8 | 5 | 13 | 9.7 | 0.66 |
0.01 | 0.9 | 0.15 | 0.65 | 1 | 5 | 5 | 13 | 6.3 | 0.84 | 0 | 4 | 4 | 10 | 6.9 | 0.52 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.9 | 0.2 | 0.35 | 11 | 46 | 37 | 134 | 63.2 | 0.8 | 27 | 99 | 32 | 112 | 99.4 | 0.97 |
0.01 | 0.9 | 0.2 | 0.4 | 6 | 25 | 24 | 80 | 37.1 | 0.78 | 9 | 38 | 21 | 67 | 44.3 | 0.78 |
0.01 | 0.9 | 0.2 | 0.45 | 5 | 19 | 17 | 53 | 24.5 | 0.84 | 4 | 21 | 15 | 44 | 30.5 | 0.59 |
0.01 | 0.9 | 0.2 | 0.5 | 3 | 12 | 13 | 38 | 17.3 | 0.79 | 2 | 11 | 12 | 33 | 19.4 | 0.62 |
0.01 | 0.9 | 0.2 | 0.55 | 2 | 8 | 12 | 34 | 13.3 | 0.8 | 3 | 13 | 9 | 23 | 15.5 | 0.75 |
0.01 | 0.9 | 0.2 | 0.6 | 1 | 5 | 9 | 24 | 10 | 0.74 | 2 | 9 | 8 | 19 | 11.6 | 0.74 |
0.01 | 0.9 | 0.2 | 0.65 | 1 | 5 | 7 | 17 | 8.2 | 0.74 | 2 | 7 | 7 | 16 | 8.3 | 0.85 |
0.01 | 0.9 | 0.2 | 0.7 | 1 | 4 | 7 | 16 | 6.2 | 0.82 | 1 | 5 | 6 | 13 | 7.1 | 0.74 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.9 | 0.25 | 0.4 | 15 | 51 | 51 | 156 | 70.5 | 0.81 | 19 | 70 | 42 | 124 | 85.4 | 0.71 |
0.01 | 0.9 | 0.25 | 0.45 | 8 | 27 | 32 | 91 | 40.7 | 0.79 | 23 | 66 | 26 | 71 | 66.1 | 0.97 |
0.01 | 0.9 | 0.25 | 0.5 | 6 | 19 | 23 | 62 | 26.5 | 0.83 | 7 | 26 | 19 | 48 | 32.9 | 0.69 |
0.01 | 0.9 | 0.25 | 0.55 | 3 | 11 | 15 | 37 | 18.5 | 0.71 | 8 | 22 | 14 | 34 | 22.9 | 0.93 |
0.01 | 0.9 | 0.25 | 0.6 | 3 | 10 | 12 | 28 | 14 | 0.78 | 7 | 18 | 11 | 25 | 18.4 | 0.94 |
0.01 | 0.9 | 0.25 | 0.65 | 2 | 7 | 10 | 22 | 10.7 | 0.76 | 2 | 8 | 9 | 19 | 11.5 | 0.68 |
0.01 | 0.9 | 0.25 | 0.7 | 2 | 6 | 8 | 17 | 7.9 | 0.83 | 1 | 5 | 8 | 16 | 9 | 0.63 |
0.01 | 0.9 | 0.25 | 0.75 | 1 | 4 | 7 | 14 | 6.6 | 0.74 | 2 | 6 | 7 | 13 | 7.2 | 0.83 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.9 | 0.3 | 0.45 | 19 | 55 | 62 | 164 | 75.4 | 0.81 | 24 | 80 | 52 | 133 | 103.6 | 0.55 |
0.01 | 0.9 | 0.3 | 0.5 | 11 | 31 | 38 | 94 | 43.1 | 0.81 | 27 | 67 | 32 | 77 | 67.3 | 0.97 |
0.01 | 0.9 | 0.3 | 0.55 | 7 | 20 | 24 | 55 | 28 | 0.77 | 7 | 21 | 23 | 52 | 29.6 | 0.72 |
0.01 | 0.9 | 0.3 | 0.6 | 4 | 12 | 18 | 39 | 19.5 | 0.72 | 5 | 15 | 17 | 36 | 20.8 | 0.72 |
0.01 | 0.9 | 0.3 | 0.65 | 5 | 12 | 15 | 32 | 14.4 | 0.88 | 3 | 10 | 13 | 26 | 15.6 | 0.65 |
0.01 | 0.9 | 0.3 | 0.7 | 2 | 6 | 12 | 24 | 10.6 | 0.74 | 2 | 7 | 10 | 19 | 11.2 | 0.65 |
0.01 | 0.9 | 0.3 | 0.75 | 3 | 7 | 9 | 17 | 8.3 | 0.87 | 2 | 6 | 9 | 16 | 8.6 | 0.74 |
0.01 | 0.9 | 0.3 | 0.8 | 2 | 5 | 8 | 14 | 6.5 | 0.84 | 1 | 4 | 7 | 12 | 6.8 | 0.65 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.9 | 0.35 | 0.5 | 24 | 60 | 73 | 170 | 78.8 | 0.83 | 59 | 135 | 62 | 141 | 135.1 | 0.99 |
0.01 | 0.9 | 0.35 | 0.55 | 12 | 30 | 43 | 94 | 44.1 | 0.78 | 36 | 77 | 37 | 79 | 77 | 0.99 |
0.01 | 0.9 | 0.35 | 0.6 | 8 | 19 | 33 | 70 | 28.5 | 0.81 | 11 | 29 | 25 | 50 | 35.2 | 0.7 |
0.01 | 0.9 | 0.35 | 0.65 | 5 | 12 | 23 | 46 | 19.2 | 0.79 | 5 | 14 | 19 | 36 | 21.9 | 0.64 |
0.01 | 0.9 | 0.35 | 0.7 | 5 | 11 | 16 | 30 | 13.8 | 0.85 | 4 | 12 | 14 | 25 | 17.4 | 0.58 |
0.01 | 0.9 | 0.35 | 0.75 | 3 | 7 | 13 | 23 | 10.2 | 0.8 | 9 | 16 | 11 | 19 | 16.1 | 0.98 |
0.01 | 0.9 | 0.35 | 0.8 | 2 | 5 | 10 | 17 | 7.8 | 0.76 | 7 | 12 | 9 | 15 | 12.1 | 0.97 |
0.01 | 0.9 | 0.35 | 0.85 | 1 | 3 | 9 | 14 | 6.1 | 0.72 | 1 | 4 | 8 | 12 | 7.5 | 0.56 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.9 | 0.4 | 0.55 | 23 | 53 | 79 | 163 | 81.4 | 0.74 | 36 | 86 | 71 | 144 | 104.6 | 0.68 |
0.01 | 0.9 | 0.4 | 0.6 | 14 | 31 | 48 | 94 | 44.8 | 0.78 | 26 | 54 | 43 | 83 | 56.5 | 0.91 |
0.01 | 0.9 | 0.4 | 0.65 | 10 | 21 | 33 | 62 | 28.1 | 0.83 | 24 | 45 | 28 | 51 | 45.2 | 0.97 |
0.01 | 0.9 | 0.4 | 0.7 | 5 | 11 | 24 | 43 | 18.9 | 0.75 | 8 | 18 | 21 | 36 | 22.7 | 0.74 |
0.01 | 0.9 | 0.4 | 0.75 | 5 | 10 | 18 | 31 | 13.5 | 0.83 | 4 | 10 | 16 | 26 | 15.9 | 0.63 |
0.01 | 0.9 | 0.4 | 0.8 | 4 | 8 | 12 | 19 | 9.9 | 0.83 | 4 | 8 | 12 | 19 | 9.9 | 0.83 |
0.01 | 0.9 | 0.4 | 0.85 | 3 | 6 | 10 | 15 | 7.6 | 0.82 | 3 | 6 | 10 | 15 | 7.6 | 0.82 |
0.01 | 0.9 | 0.4 | 0.9 | 2 | 4 | 9 | 13 | 5.6 | 0.82 | 3 | 6 | 8 | 11 | 6.9 | 0.82 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.9 | 0.45 | 0.6 | 30 | 60 | 91 | 171 | 80.2 | 0.82 | 75 | 139 | 78 | 144 | 139.1 | 0.99 |
0.01 | 0.9 | 0.45 | 0.65 | 16 | 31 | 58 | 105 | 44.2 | 0.82 | 23 | 50 | 46 | 80 | 61.6 | 0.61 |
0.01 | 0.9 | 0.45 | 0.7 | 10 | 19 | 39 | 67 | 27.8 | 0.82 | 26 | 44 | 31 | 52 | 44.2 | 0.98 |
0.01 | 0.9 | 0.45 | 0.75 | 7 | 13 | 27 | 44 | 18.5 | 0.82 | 7 | 16 | 21 | 33 | 23.4 | 0.56 |
0.01 | 0.9 | 0.45 | 0.8 | 5 | 9 | 19 | 30 | 12.5 | 0.83 | 4 | 9 | 16 | 24 | 14.7 | 0.62 |
0.01 | 0.9 | 0.45 | 0.85 | 4 | 7 | 14 | 21 | 9.1 | 0.85 | 5 | 10 | 12 | 17 | 11.8 | 0.74 |
0.01 | 0.9 | 0.45 | 0.9 | 2 | 4 | 10 | 14 | 6.4 | 0.76 | 2 | 4 | 10 | 14 | 6.4 | 0.76 |
0.01 | 0.9 | 0.45 | 0.95 | 1 | 2 | 10 | 14 | 4.4 | 0.8 | 2 | 4 | 7 | 9 | 5.2 | 0.76 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.9 | 0.5 | 0.65 | 30 | 55 | 97 | 166 | 78.2 | 0.79 | 81 | 137 | 84 | 142 | 137.1 | 0.99 |
0.01 | 0.9 | 0.5 | 0.7 | 15 | 27 | 59 | 97 | 42.5 | 0.78 | 43 | 70 | 49 | 79 | 70.2 | 0.98 |
0.01 | 0.9 | 0.5 | 0.75 | 11 | 19 | 37 | 58 | 26 | 0.82 | 15 | 26 | 32 | 49 | 29.8 | 0.84 |
0.01 | 0.9 | 0.5 | 0.8 | 7 | 12 | 26 | 39 | 17.2 | 0.81 | 9 | 16 | 22 | 32 | 19.6 | 0.77 |
0.01 | 0.9 | 0.5 | 0.85 | 4 | 7 | 19 | 27 | 11.5 | 0.77 | 7 | 13 | 16 | 22 | 15.6 | 0.71 |
0.01 | 0.9 | 0.5 | 0.9 | 3 | 5 | 15 | 21 | 8 | 0.81 | 5 | 8 | 12 | 16 | 9.2 | 0.86 |
0.01 | 0.9 | 0.5 | 0.95 | 1 | 2 | 13 | 18 | 6 | 0.75 | 8 | 10 | 9 | 12 | 10 | 0.99 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.9 | 0.55 | 0.7 | 29 | 49 | 101 | 159 | 74.6 | 0.77 | 83 | 130 | 87 | 135 | 130.1 | 0.98 |
0.01 | 0.9 | 0.55 | 0.75 | 18 | 29 | 63 | 96 | 40.4 | 0.83 | 19 | 33 | 50 | 74 | 46.1 | 0.68 |
0.01 | 0.9 | 0.55 | 0.8 | 10 | 16 | 40 | 58 | 24.3 | 0.8 | 15 | 26 | 32 | 45 | 32.1 | 0.68 |
0.01 | 0.9 | 0.55 | 0.85 | 7 | 11 | 24 | 33 | 15.2 | 0.81 | 19 | 26 | 22 | 30 | 26.1 | 0.98 |
0.01 | 0.9 | 0.55 | 0.9 | 3 | 5 | 18 | 24 | 9.9 | 0.74 | 7 | 10 | 16 | 21 | 11.1 | 0.9 |
0.01 | 0.9 | 0.55 | 0.95 | 4 | 6 | 12 | 15 | 7.5 | 0.84 | 4 | 6 | 12 | 15 | 7.5 | 0.84 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.9 | 0.6 | 0.75 | 29 | 45 | 106 | 155 | 69.7 | 0.78 | 38 | 61 | 89 | 128 | 81.9 | 0.69 |
0.01 | 0.9 | 0.6 | 0.8 | 15 | 23 | 58 | 81 | 36.8 | 0.76 | 38 | 54 | 50 | 69 | 54.6 | 0.96 |
0.01 | 0.9 | 0.6 | 0.85 | 11 | 16 | 37 | 50 | 21.7 | 0.83 | 27 | 36 | 31 | 41 | 36.1 | 0.98 |
0.01 | 0.9 | 0.6 | 0.9 | 6 | 9 | 22 | 28 | 13.4 | 0.77 | 5 | 9 | 20 | 25 | 16.7 | 0.52 |
0.01 | 0.9 | 0.6 | 0.95 | 5 | 7 | 15 | 18 | 8.7 | 0.84 | 7 | 9 | 14 | 17 | 9.6 | 0.93 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.9 | 0.65 | 0.8 | 27 | 39 | 103 | 140 | 63 | 0.76 | 76 | 103 | 87 | 117 | 103.3 | 0.98 |
0.01 | 0.9 | 0.65 | 0.85 | 18 | 25 | 53 | 69 | 32.6 | 0.83 | 46 | 59 | 47 | 61 | 59 | 0.99 |
0.01 | 0.9 | 0.65 | 0.9 | 7 | 10 | 32 | 40 | 17.8 | 0.74 | 25 | 31 | 29 | 36 | 31.1 | 0.98 |
0.01 | 0.9 | 0.65 | 0.95 | 4 | 6 | 18 | 21 | 10.8 | 0.68 | 4 | 6 | 18 | 21 | 10.8 | 0.68 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.9 | 0.7 | 0.85 | 27 | 36 | 99 | 126 | 54.3 | 0.8 | 79 | 99 | 80 | 101 | 99 | 0.99 |
0.01 | 0.9 | 0.7 | 0.9 | 13 | 17 | 53 | 65 | 26.7 | 0.8 | 38 | 46 | 43 | 52 | 46.1 | 0.98 |
0.01 | 0.9 | 0.7 | 0.95 | 8 | 10 | 29 | 34 | 13.6 | 0.85 | 16 | 19 | 25 | 29 | 19.5 | 0.95 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.9 | 0.75 | 0.9 | 25 | 31 | 87 | 104 | 43.9 | 0.82 | 66 | 78 | 71 | 84 | 78.1 | 0.99 |
0.01 | 0.9 | 0.75 | 0.95 | 8 | 10 | 45 | 52 | 20.2 | 0.76 | 31 | 35 | 35 | 40 | 35.1 | 0.99 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.9 | 0.8 | 0.9 | 49 | 59 | 166 | 193 | 90 | 0.77 | 142 | 164 | 145 | 168 | 164 | 0.99 |
0.01 | 0.9 | 0.8 | 0.95 | 16 | 19 | 60 | 67 | 30.4 | 0.76 | 22 | 26 | 55 | 61 | 33.2 | 0.79 |
| Optimal Model | Minimax Model |
α | Pw | π0 | π1 | r1 | n1 | rTot | nTot | EN | PET | r1 | n1 | rTot | nTot | EN | PET |
0.01 | 0.9 | 0.85 | 0.95 | 41 | 46 | 123 | 135 | 60.3 | 0.84 | 99 | 108 | 107 | 117 | 108.1 | 0.99 |
α=0.1, Power = 0.8 π0 = proportion of success at or below which treatment is abandoned π1 = proportion of success at or above which treatment will be accepted for further development and trials r1 = number of successes above which stage 2 can be entered, and at or below which the trial terminates after n1 cases, and the treatment rejected n1 = maximum sample size in stage 1 rTot = the total number of successes (stage 1 and 2 combined) above which the study can be terminated and the treatment accepted for further development and trials, and at or below which after nTot cases the treatment is rejected. nTot = the total maximum sample size (stage 1 and 2 combined) EN = expected sample size, an estimated average sample size that will be used before the trial terminates. This is a measure of efficiency in detecting PET = probability of early termination (when treatment is abandoned), a measure of efficiency in rejecting ineffective treatments.
Javascript Program
R Code
See Technical considerations section for commentary
" Simon's Procedure for Phase II
Simon R (1989) Optimal two-stage designs for phase II clinical trials. Control Clin Trials 10:1-10
Machin D, Campbell M, Fayers, P, Pinol A (1997) Sample Size Tables for Clinical Studies. Second Ed.
Blackwell Science IBSN 0-86542-870-0 p. 256-257
Algorithm adapted from text book by Machin et.al.
"
# Data
# a = alpha, probability to Type I Error
# pw = power 1 - beta where beta is probability of Type II Error
#p0 = success rate below which treatment being trialed is rejected as inadequate
#p1 = success rate above which treatment being trialed is accepted as worthy of further evaluation
a = 0.05
pw = 0.8
p0 = 0.1
p1 = 0.3
# Program Starts
#calculate start and finish equation 10.12 p.257
za = qnorm(a)
b = 1 - pw # beta Type II error
zb = qnorm(b)
cp = (p0 + p1) / 2
cx = (za + zb) / (p1 - p0)
start = floor(cp * (1.0 - cp) * cx^2)
finish = start + 30
# Reference matrices
# precalculated values for formulae 10.10 and 10.11, p. 256
mxbP0 <- matrix(1,finish+1,finish+1)
mxbP1 <- matrix(1,finish+1,finish+1)
for(i in 0 : finish)
{
for(j in 0 : finish)
{
bincoef = choose(i,j)
mxbP0[i+1,j+1] = bincoef * p0^j * (1.0-p0)^(i-j)
mxbP1[i+1,j+1] = bincoef * p1^j * (1.0-p1)^(i-j)
}
}
mxBP0 <- matrix(0,finish+1,finish+1)
mxBP1 <- matrix(0,finish+1,finish+1)
for(i in 0 : finish)
{
for(j in 0 : finish)
{
for(x in 0 : j)
{
mxBP0[i+1, j+1] = mxBP0[i+1 , j+1] + mxbP0[i+1 , x+1]
mxBP1[i+1, j+1] = mxBP1[i+1 , j+1] + mxbP1[i+1 , x+1]
}
}
}
# Optimal and Minimax are vectors for results in each loop
#OptimalFinal and MinimaxFinal are the best results when the calculations are
# repeated from start-10 to start. Best is having the lowest total sample size nTot
#initialize the 4 vectors and set the minimum nTot to impossibly high value
Minimax <-c(0,0,0,0,0,0)
Optimal <- Minimax
OptimalFinal <- Optimal
MinimaxFinal <- Minimax
minNTot = 1e10
startF = start # startF is start value inotially calculated
start = startF - 10 # start is set back by 10 for iteration
if(start<2) # making sure is is not zero
{
start = 2
}
while(start<=startF) #loop begins from startF-10 to startF
{
start = start + 1
Minimax <-c(0,0,0,0,0,0) # clear working vectors for each loop
Optimal <- Minimax
MinEN = start # calculation begins
Pr = 1
rs = 0
for(ntot in start : finish)
{
for(n1 in 1 : ntot-1)
{
n2 = ntot - n1
rr = ceiling(Pr * ntot)
rx = rs
for(rtot in rx : rr)
{
minv = n1
if(rtot<minv)
{
minv = rtot
}
for(r1 in 0 : minv)
{
if((r1<rtot) & (r1>=(n1 + rtot - ntot)))
{
PET = mxBP1[n1+1,r1+1]
testbeta = 0; # test beta begins
for(x in (r1+1) : minv)
{
if(rtot-x>=0)
{
lb = mxbP1[n1+1,x+1]
bb = mxBP1[n2+1,rtot-x+1]
testbeta = testbeta + lb*bb
}
}
testbeta = testbeta + PET
y = b - testbeta
if(y>0)
{
PET = mxBP0[n1+1,r1+1]
testalpha = 0;
for(x in r1+1 : minv)
{
if(rtot-x>0)
{
lb = mxbP0[n1+1,x+1]
bb = mxBP0[n2+1,rtot-x+1]
testalpha = testalpha + lb*bb
}
}
testalpha = testalpha + PET
EN = n1 + (1 - PET) * n2
z = testalpha - (1 - a)
if((z>0) & (EN<MinEN))
{
rs = rtot;
Pr = 1 * rtot / ntot
Optimal <- c(r1,n1,rtot,ntot,round(EN,1),round(PET,1))
if((Minimax[4]<1) | (Minimax[4]==ntot))
{
Minimax <- Optimal
}
MinEN = EN
}
}
}
}
}
}
}
# ckeck whether current Minimax nTot is less than the minimum
# if so then replace the result vectors with the current and reset the minimum value
if(Minimax[4]>0 & Minimax[4]<minNTot)
{
OptimalFinal <- Optimal
MinimaxFinal <- Minimax
minNTot = (Minimax[4])
}
} # end of loop
Results <- c("r1","n1","rTotal","nTotal","EN","PET")
Optimal <- OptimalFinal
Minimax <- MinimaxFinal
data.frame(Results,Optimal,Minimax)
Simon R (1989) Optimal two-stage designs for phase II clinical trials.
Control Clin Trials 10:1-10
Machin D, Campbell M, Fayers, P, Pinol A (1997) Sample Size Tables for
Clinical Studies. Second Ed. Blackwell Science IBSN 0-86542-870-0 p. 256-257
|