Extensive instructions and literature exists for Matched Paired Controlled studies, and the subject will not be covered in detail or with authority on this page. Discussions are primarily to orientate the user on the resources available here. It is assumed that users will already understand how the model is used or having access to expert help on the subject.

This page presents calculations for sample size determination during the planning stage, and estimation of power once data collection is completed.

Matched pair studies consists of selecting an Index case, and match this case with 1 or more Control cases which have similar characteristics.

Matched pair studies can be either prospective or retrospective. Although method of data analysis differs accordingly, the sample size and power estimation for the two models, as presented on this page, are similar

• An example of prospective study is to match a smoker with 1 or more non-smokers, and follow them to see if the rates of developing lung cancer differ.
• An example of retrospective study is to match a lung cancer case with 1 or more cases with no cancer, and compare them retrospectively whether the rates of prior smoking differs.

Terms used on this page

An Index case is a case with characteristics being investigated. In the prospective smoking study, an index case is one who smoked, In the retrospective cancer study, an index case is the one with cancer

A Control case is one without the characteristic in question, but is similar to the Index case as much as possible under the research condition.

a cluster is 1 Index case, plus 1 or more matched Control cases

The ratio of the cluster Ra is the ratio of Control to Index cases, Ra = N_C / N_I. As each Index case is matched with 1 or more Control cases, Ra is always >= 1

lambda (λ) is the proportion of positives, either expected at the planning stage, or observed once the data is collected

• lambdaC (λ_C) is the proportion of positives in the Control group
• lambdaI (λ_I) is the proportion of positives in the Index group

Sample Size (SSiz) in this model represents the number of clusters, each cluster containing 1 Index case plus 1 or more Control case

Alpha (α, p) is the probability of Type I Error, to be used to determine statistical significance

Beta (β) is the probability of Type II Error. Power = 1 - β

Examples

Please note the following examples used artificially generated numbers to demonstrate the statistical procedures, and are not reflective of reality.

Sample size

We think taking a particular drug during pregnancy may cause the baby to develop an unusual malformation, and wish to test this. As both malformation and exposure to the drug are uncommon, and ethical consideration precluded a prospective trial, we used the Retrospective Matched Pair Control Model.

We think that 1% (λ_I=0.01) of mothers who have malformed babies might have taken this drug, and 0.1% (λ_C=0.001) of mothers with normal babies might have taken this drug.

For every mother with a malformed baby, we will pick 10 mothers (Ra = N_C/N_I = 10) who are demographically similar but have normal babies, and we want to know how many clusters, each with 1 Index and 10 Control cases, we will need.

Using α = 0.05, power = 0.8, λ_C=0.001, λ_I=0.01, Ra = 10, the sample size required is 311 clusters, each with 1 mother with malformed babies plus 10 similar mothers with no malformed babies.

Power calculation

In the study of taking a drug during pregnancy and malformed babies, we managed to collect data from 311 clusters, each has 1 mother with malformed baby, and 10 similar mothers with non-malformed babies (311 indexed and 3110 control).

We found 5 of the 311 mothers of the malformed babies group had taken the drug being investigated (&lambada;_I = 5 / 311 = 0.16 or 16%), and 4 of the 3110 mothers from the normal babies group took the drug (λ_C = 4 / 3110 = 0.001 or 0.1%). The power of the data is 0.87, suggesting that it has sufficient power (at the p<0.05 and power >0.8)level to allow confidence interpretation of the results.

We then used the odds Ratio program in the comparison between 2 proportions page to evaluate the data obtained. The Index group (with malformation) had 5 mothers exposed to the drug (Pos=5) and 306 mothers not so exposed (Neg=306), an odd of 5 / 306 = 0.0163. Control group (without malformation) had 4 mothers exposed to the drug (Pos=4) and 3106 mothers not exposed (Neg=3106), an odd of 4 / 3106 = 0.0013. The odds ratio is 0.0163 / 0.0013 = 12.69, with the 1 tail 95% confidence interval >4.2. In other words, the odd of exposure to the drug in mothers with malformed babies was more than 4.2 times greater than that in mothers with non-malformed babies. We can therefore conclude that delivering a baby with malformation is related to prior exposure to the drug during pregnancy

References

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. 145-146

Power = 1 - β, where β = Probability of Type II Error
α = Probability of Type I Error
Ra = Number of Control cases to 1 Index case in a cluster
λ_C = Expected proportion of positives in Control Group
λ_I = Expected proportion of positives in Index Group
Sample Size in number of clusters