Calibration regression of censored lifetime medical cost

Analysis of lifetime medical cost is challenged by its irregular distribution and by incomplete follow-up, particularly the latter with limited study duration as is typical in medical research. This article proposes the so-called calibration regression to address these issues by modeling not only lifetime medical cost but also survival time, in a semiparametric fashion. It is postulated that both outcomes, on possibly transformed scales, linearly relate to the covariates however, the bivariate model error distribution is completely unspecified. Whereas this conceptually simple model is a natural multivariate generalization of the accelerated failure time model, this article propose's an inference procedure by extending the weighted log-rank estimating function to the marked point process framework, The resulting estimators are consistent and asymptotically normal. In addition, robustness and efficiency issues are discussed. Furthermore, a novel sample-based variance estimation procedure is proposed for estimators based on nonsmooth estimating functions in general. Finally, simulation studies show that this proposal is reliable for practical use. An illustration with application to a lung cancer clinical trial is provided.