A Note on the Log‐Rank Test in Life Table Analysis with Correlated Observations

Survival data consisting of independent sets of correlated failure times may arise in many situations. For example, we may take repeated observations of the failure time of interest from each patient or observations of the failure time on siblings, or consider the failure times on littermates in toxicological experiments. Because the failure times taken on the same patient or related family members or from the same litter are likely correlated, use of the classical log‐rank test in these situations can be quite misleading with respect to type I error. To avoid this concern, this paper develops two closed‐form asymptotic summary tests, that account for the intraclass correlation between the failure times within patients or units. In fact, one of these two test includes the classical log‐rank test as a special case when the intraclass correlation equals 0. Furthermore, to evaluate the finite‐sample performance of the two tests developed here, this paper applies Monte Carlo simulation and notes that they can actually perform quite well in a variety of situations considered here.