Estimation of the proportional hazard in two-treatment-group clinical trials

Two easily-computed approximate methods of obtaining an estimate of the ratio of the hazard rates for two treatments in survival analysis are compared, by simulation, with the partial maximum likelihood (CML) estimator which assumes the Cox model with no covariates. The two methods studied are the Mantel-Haenszel estimator, and the O/E method which employs the ratio of the 'relative death rates' for the two treatments. Uncensored and censored cases are examined for both continuous and tied data with the assumption of either an underlying exponential distribution or a Weibull distribution with shape parameter 2. The O/E method is biased but, within the range of values of the ratio of the hazard rates of interest in clinical trials, it is more efficient in terms of mean square error than either CML or the Mantel-Haenszel method for all but the largest trials. The Mantel-Haenszel method is minimally biased, gives answers very close to those obtained using CML, and may be used to provide satisfactory approximate confidence intervals.