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

				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.