title: 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.
abstract: 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.
authors.affiliation: The Biostatistics Center, Departments of Epidemiology and Biostatistics, and Statistics, The George Washington University, 6110 Executive Boulevard, Suite 750, Rockville, Maryland, USA. 20852. jml@biostat.bsc.gwu.edu
authors.forename: John M
authors.initials: JM
authors.lastname: Lachin
mesh_terms: D000704:Analysis of Variance; D001786:Blood Glucose / Q000187:drug effects*; D016009:Chi-Square Distribution; D002986:Clinical Trials as Topic / Q000379:methods / Q000592:standards; D003924:Diabetes Mellitus, Type 2 / Q000188:drug therapy*; D006801:Humans; D007004:Hypoglycemic Agents / Q000627:therapeutic use*; D016013:Likelihood Functions; D016016:Proportional Hazards Models; D018401:Sample Size; D016896:Treatment Outcome
chemical_list: D001786:Blood Glucose; D007004:Hypoglycemic Agents
keywords: Cox proportional hazards model; exponential survival; interactions; logrank test; multiple groups; power; sample size; stratified analysis