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) based on the test statistic proposed by Gart (1985) is a special case of the sample size formula derived in this note.