Tests for paired lifetime data with frailty models

We consider the problem of hypothesis testing of the equality of marginal survival distributions observed from paired lifetime data. Usual procedures include the paired t-test, which may perform poor for certain types of data. We propose asymptotic tests based on gamma frailty models with Weibull conditional distributions, and investigate their theoretical properties using large sample theory. For finite samples, we conduct simulations to evaluate the powers of the associated tests. For moderate and less skewed data, the proposed tests are the most powerful among the commonly applied testing procedures. A data example is illustrated to demonstrate the methods.