Sample size calculations for failure time random variables in non-randomized studies

In non-randomized studies, sample size calculations for failure time random variables are often computed on the basis of the unadjusted log-rank test which assumes that the variable designating group membership is independent of other patient covariates. We show that by extending the methods proposed by Lipsitz and Parzen to time-to-event random variabes the power derived from the unadjusted log-rank test overestimates the true power of the comparison when the variable of interest is correlated with other covariates. We model the hazards by using exponential regression and derive the sample size formulae for both censored and uncensored data. We also present results of a simulation study to assess the validity of the derived formulae when the intended method of analysis is the proportional hazards regression model and the data continue to have an exponential distribution. We apply the methods proposed to the non-Hodgkin's lymphoma prognostic factors project data set.