Power of the Mantel–Haenszel and other tests for discrete or grouped time-to-event data under a chained binomial model
Article first published online: 16 JUL 2012
Copyright © 2012 John Wiley & Sons, Ltd.
Statistics in Medicine
Volume 32, Issue 2, pages 220–229, 30 January 2013
How to Cite
Lachin, J. M. (2013), Power of the Mantel–Haenszel and other tests for discrete or grouped time-to-event data under a chained binomial model. Statist. Med., 32: 220–229. doi: 10.1002/sim.5480
- Issue published online: 17 DEC 2012
- Article first published online: 16 JUL 2012
- Manuscript Accepted: 26 MAR 2012
- Manuscript Revised: 19 MAR 2012
- Manuscript Received: 5 JAN 2012
- sample size;
- Mantel–Haenszel test;
- chained binomial model;
- Cox proportional hazards model;
- Prentice–Gloeckler discrete proportional hazards model
Power for time-to-event analyses is usually assessed under continuous-time models. Often, however, times are discrete or grouped, as when the event is only observed when a procedure is performed. Wallenstein and Wittes (Biometrics, 1993) describe the power of the Mantel–Haenszel test for discrete lifetables under their chained binomial model for specified vectors of event probabilities over intervals of time. Herein, the expressions for these probabilities are derived under a piecewise exponential model allowing for staggered entry and losses to follow-up.
Radhakrishna (Biometrics, 1965) showed that the Mantel–Haenszel test is maximally efficient under the alternative of a constant odds ratio and derived the optimal weighted test under other alternatives. Lachin (Biostatistical Methods: The Assessment of Relative Risks, 2011) described the power function of this family of weighted Mantel–Haenszel tests. Prentice and Gloeckler (Biometrics, 1978) described a generalization of the proportional hazards model for grouped time data and the corresponding maximally efficient score test. Their test is also shown to be a weighted Mantel–Haenszel test, and its power function is likewise obtained.
There is trivial loss in power under the discrete chained binomial model relative to the continuous-time case provided that there is a modest number of periodic evaluations. Relative to the case of homogeneity of odds ratios, there can be substantial loss in power when there is substantial heterogeneity of odds ratios, especially when heterogeneity occurs early in a study when most subjects are at risk, but little loss in power when there is heterogeneity late in a study. Copyright © 2012 John Wiley & Sons, Ltd.