Case-Control Studies with a Dichotomous Exposure Outcome : Unmatched Study with an Unequal Number of Cases and Controls


  1. Schlesselman, J.J.; "Case-Control Studies: Design Conduct, Analysis." Oxford University Press, New York, 1982 (Chapter 6)
  2. Schlesselman, J.J.: "Sample size requirements in cohort and case-control studies of disease", Am J. Epid 99: 381-384, 1974

The terms "case-control" and "cohort" studies are sometimes used interchangeably to describe studies which are designed to identify the relationship between the exposure to a risk factor and the subsequent development of a particular disease. However, there is an important distinction between the two studies and the sample size requirements for these studies are different.

The matched case-control study can generally be thought of as a retrospective or historical study. This study uses two groups of individuals. The cases comprise that group which has some disease and we wish to determine the prevalence of exposure to some risk factor, the exposure usually having occurred many years ago. The control individuals do not have the disease of interest. Controls and cases are usually "paired up" according to some matching criteria, perhaps race, sex or age, but the matching may employ more than one control for each case or vice-versa. Sample size calculations depend on the number of exposure-discordant case-control combinations. Discordant means the case is not exposed but the control is or the case is exposed but the control is not. The estimated proportion of exposed controls, p0, and the estimated proportion of exposed cases, p1, determines the expected number of discordant pairs. Apart from the specification of the Type I (alpha) and Type II (beta) errors, the sample size requirements depend on the prevalence of the exposure, p0, in the controls and the relative odds (odds ratio), R, of exposure in the cases which one regards as important to detect.

The program follows the development of calculations in Sections 6.2 & 6.3 in Schlesselman's book for the unmatched situation. In particular, equations 6.6, 6.7, 6.9 and 6.11 are used. For the matched case-control study, Section 6.6 is followed using equations 6.20, 6.22, 6.23 and 6.24.

The user must specify the prevalence of exposure to the risk factor(s) in the disease-free controls for the matched situation. The program can compute any one of the following:

  1. One-sided significance level.
  2. Power of the experiment.
  3. Detectable relative odds (odds ratio) or
  4. Required sample size,

when the user supplies values for the other three.


The development by Schlesselman for the matched case-control study bases the sample size calculation on the expected number of discordant pairs of cases and controls. These calculations assume that each case has the same probability of exposure, p1, and each control has probability, p0. However, the matching covariate, e.g. age, usually affects the probability of exposure, hence the reason for matching.

This system has two other options which the user may consider more appropriate in those situations where the probabilities vary across the matching covariate:

  1. Trials with several independent 2 x 2 tables (Ref : Gail)
    OPTION 6.2
  2. Case-control studies with multiple controls per case and variability of exposure (Ref : Slud)
    OPTION 6.3