A comparison of two simple hazard ratio estimators based on the logrank test

Two hazard ratio estimators based on the logrank test are investigated using a simulation study. The Pike estimator (ratio of relative death rates) was shown to be consistently less biased than the Peto (1-step) estimator. The latter has recently been advocated as the method of choice for point and interval estimation. Both estimators exhibited bias with increasing hazard ratios, although the bias was minimal for effects less than 3. The confidence intervals also did not achieve the nominal coverage with increasing hazard ratios, but again the Pike estimator was superior. The coverage could be improved by recalculation of the variance incorporating the point estimate. For a hazard ratio of less than 3 we recommend the use of the Pike estimator, otherwise it is necessary to use a more complex method of estimation.