Exact Waiting Time Survival Function

Abstract

Although Kaplan-Meier survival function is the most commonly used statistical technique of survival analysis, it possesses a disadvantage. It may occur that Kaplan-Meier gives same survival probabilities for two groups having the same number of events and censored observations, although time spans between consecutive events (i.e. waiting times) may considerable vary. Therefore, severity of a disease, in terms of survival times, has no role in the conventional concept of Kaplan-Meier. To overcome this problem, in this paper we propose an exact waiting time survival function by explicitly considering waiting times between events. A new variance estimator, reducing to binomial variance in case of data free from censoring and time differences between two consecutive events equalling to 1, is presented. In order to compare the performance of the new estimator with conventional Kaplan-Meier estimator for small to large sample sizes, as well as for small to heavy censoring, we conducted a simulation study. The outcome shows that on average Pitman Closeness Criteria gives results in favour of our new estimator and confidence intervals have higher coverage rates, as compared to that obtained by Kaplan-Meier estimator, especially for lower confidence limits. Furthermore widths of confidence intervals are smaller than those based on Kaplan-Meier and Greenwood standard error. The proposed procedures are applied to a lung cancer data set.