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 K 2 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.