Calculating the power or sample size for the logistic and proportional hazards models

An algorithm is presented for calculating the power for the logistic and proportional hazards models in which some of the covariates are discrete and the remainders are multivariate normal. The mean and covariance matrix of the multivariate normal covariates may depend on the discrete covariates. The algorithm, which finds the power of the Wald test, uses the result that the information matrix can be calculated using univariate numerical integration even when there are several continuous covariates. The algorithm is checked using simulation and in certain situations gives more accurate results than current methods which are based on simple formulae. The algorithm is used to explore properties of these models, in particular, the power gain from a prognostic covariate in the analysis of a clinical trial or observational study. The methods can be extended to determine power for other generalized linear models. Keywords: Sample sizePowerLogistic modelProportional hazards modelGeneralized linear modelsMultivariate normal integralsWald test Acknowledgements This work was funded by NIH under grants CA 74302, SBIR-MH 52969 and SBIR-MH 60033. The algorithm was developed for inclusion in the commercial software application 'Power and Precision' developed by Biostatistical Programming Associates Inc. David Schoenfeld is a paid consultant to Biostatistical Programming Associates Inc. and Michael Borenstein is the owner and president of the company.