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
Article first published online: 13 MAY 2013
Copyright © 2013 John Wiley & Sons, Ltd.
Statistics in Medicine
Volume 32, Issue 25, pages 4413–4425, 10 November 2013
How to Cite
Lachin, J. M. (2013), 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. Statist. Med., 32: 4413–4425. doi: 10.1002/sim.5839
- Issue published online: 7 OCT 2013
- Article first published online: 13 MAY 2013
- Manuscript Accepted: 2 APR 2013
- Manuscript Received: 9 DEC 2011
- sample size;
- logrank test;
- Cox proportional hazards model;
- multiple groups;
- exponential survival;
- stratified analysis;
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.