A Note on Sample Size Calculation Based on Propensity Analysis in Nonrandomized Trials

In nonrandomized trials, patients are not randomly assigned to treatment groups with equal probability. Instead, the probability of assignment varies from patient to patient depending on patients baseline covariates. This often results in a non-comparable treatment groups due to treatment imbalance. As a result, the United States Food and Drug Administration (FDA) recommended that the method of propensity score analysis be employed to overcome this problem. In this note, a formula for sample size calculation is developed based on a proposed weighted Mantel–Haenszel test on the strata defined by the propensity score analysis. It was shown that the sample size formula derived by Nam (1998 Nam , J. M. ( 1998 ). Power and sample size for stratified prospective studies using the score method for testing relative risk . Biometrics 54 : 331 – 336 . [INFOTRIEVE] [CSA] [CROSSREF] [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) based on the test statistic proposed by Gart (1985 Gart , J. J. ( 1985 ). Approximate tests and interval estimation of the common relative risk in the combination of 2 × 2 tables . Biometrika 72 : 673 – 677 . [CSA] [Web of Science ®] , [Google Scholar]) is a special case of the sample size formula derived in this note.