Significance Tests in Cox Proportional Hazard Model for Survival Times of Complex Survey Data

We consider the Cox PH (proportional hazard) model applied to survival times under complex survey sampling such as cluster sampling. Observations in the same cluster are correlated each other and furthermore they have unequal selection probabilities between clusters. These are the main properties of complex survey data in contrast to the data of simple random sampling. Significance tests for regression coefficients in Cox PH model are based on pseudo partial-likelihood function that incorporates weights of observations. The weight is usually given as the inverse of selection probability of individual unit. The asymptotic distribution of LRT (likelihood ratio test) is not the usual chi-squared distribution but it is given as a linear combination of independent chi-squared random variables. There have been several approaches to approximate the percentage points of asymptotic distribution. We compare the performance of tests and their approximation through a Monte Carlo study.