The effect of screening on some pretest-posttest test variances

The clinical trial design in which the endpoint is measured both at baseline and at the end of the study is used in a variety of situations. For two-group designs, test such as the t test or analysis of covariance are commonly used to evaluate treatment efficacy. Often such pretest-posttest trials restrict participation to subjects with a baseline measurement of the endpoint in a certain range. A range may define a disease, or it may be thought that subjects with extreme measurements are more responsive to treatment. This paper examines the effect of screening on the analysis of covariance and t-test variances relative to the population (i.e., unscreened) variances. Bivariate normal and bivariate gamma distributions are assumed for the (pretest, posttest) measurements. Because the sample size required to detect a specified difference between treatment and control is proportional to the variance, the results have direct application to setting sample size.