Sample size and power for a logrank test and Cox proportional hazards model with multiple groups and strata,or a quantitative covariate with multiple strata

I describe general expressions for the evaluation of sample size and power for the K group Mantel‐logrank test or the Cox proportional hazards (PH) model score test. Under an exponential model, the method of Lachin and Foulkes for the 2 group case is extended to the group case using the non‐centrality parameter of the K ? 1 df chi‐square test. I also show similar results to apply to the K group score test in a Cox PH model. Lachin and Foulkes employed a truncated exponential distribution to provide for a non‐linear rate of enrollment. I present expressions for the mean time of enrollment and the expected follow‐up time in the presence of exponential losses to follow‐up. When used with the expression for the noncentrality parameter for the test, equations are derived for the evaluation of sample size and power under specific designs with r years of recruitment and T years total duration. I also describe sample size and power for a stratified‐adjusted K group test and for the assessment of a group by stratum interaction. Similarly, I describe computations for a stratified‐adjusted analysis of a quantitative covariate and a test of a stratum by covariate interaction in the Cox PH model. Copyright © 2013 John Wiley & Sons, Ltd.