Abstract: Testing for lifetime utility or cost is complicated with incomplete follow-up data. First, the marginal distribution in each sample is potentially nowhere identifiable. Second, the associated survival time may distribute differently across samples, whereas the difference is a nuisance. To overcome these difficulties, we propose to test the equivalence of the joint distributions of the variable of interest and survival time after calibrating the latter under the accelerated failure time model. Formulating the problem in the marked point process framework, we build upon and extend the well-known weighted log-rank statistics. Asymptotic theory has been developed and optimal weight functions derived. These tests are applied to a randomized clinical trial. Simulations show that they perform well with practical sample sizes.
Key words and phrases: Accelerated failure time model, dependent censoring, estimating equation, identifiability, lifetime medical cost, log-rank statistic, marked point process, minimum dispersion statistic, optimization, Pitman efficiency, quality adjusted survival time, semiparametric inference.