New method for estimating survival curves based upon subpopulations

摘要

The overall Kaplan-Meier estimate of the survival curve underlying a study population does not individually account for the ages at which patients were first seen and thence followed up in the study. Since the number of patients in these age-specific subgroups varies quite arbitrarily for a given study, the overall Kaplan-Meier curve which assumes that all patients were seen from the beginning of the study usually either overestimates or underestimates the survival probability, depending on the varying sample sizes. In this paper, we therefore propose an estimate of the overall survival curve underlying a study population based on the individual age-specific Kaplan-Meier estimates and the probability distribution of the age at which patients were first seen in the study. In the particular case when there is no censoring, it is shown that the usual overall Kaplan-Meier survival curve which assumes that all patients irrespective of their age at entry into the study were followed from the beginning of the study is identical with the proposed estimate. This result does not seem to necessarily hold good in the presence of arbitrary censoring. Further, the estimate is unbiased and consistent, a property which the Kaplan-Meier estimate also enjoys. The efficiency of the proposed estimate relative to the Kaplan-Meier estimate is being investigated and will be reported along with results of its application in a separate communication.