Sample size and duration for cohort studies of survival time with covariables

The determination of sample size and duration for cohort studies with covariables is considered. An exponential model, using the form due to Feigl and Zelen (1965, Biometrics 21, 826-838) for the hazard with covariates and asymptotic normality of the maximum likelihood estimators of the parameters, is assumed. Emphasis is on applications involving two parameters, namely an underlying hazard and the coefficient of a single concomitant variable. The results of George and Desu (1974, Journal of Chronic Diseases 27, 15-24) are reproduced and extended to take account of censoring. An example with more than two dose groups is presented. For situations where the sample size is fixed and Type I error is specified, extension of the follow-up time is considered for the purpose of achieving the desired Type II error, given a null hypothesis and specific alternative hypothesis. Generalizations to situations with other forms for the hazard rate and multiple covariables are indicated.