| In many biomedical follow-up studies, a subject may experience multiple events, times of which are typically of prime interest. To analyze such multiple event-time data, Wei, Lin and Weissfeld (1989) proposed a so-called marginal proportional hazards model, which is an extension of the well-known Cox proportional hazards model to accommodate multivariate event times. Their approach has a major advantage in that there is no need to specify the joint distribution among the subject-specific failure times. However, the (marginal) proportional hazards assumption may not be suitable in some cases and alternative regression models, such as that of the accelerated failure times, may sometimes be more desirable. In this thesis, we propose inference procedures for semi-parametric regression analysis of the marginal accelerated failure times. The approach is motivated by and makes use of the least absolute deviation (LAD) method for censored data (Powell, 1984). Powell's estimate is based on minimization of a simple objection function that is a modification to the L 1 loss function used for the usual least absolute deviation estimation for uncensored data. It has been well investigated in the econometrics literature. Because of a similar structure between multiple/recurrent event-time data and the censored regression data in the econometrics data dealt with by Powell's method, we are able to extend the objection function in censored LAD to handle multiple event-time data. We show that the resulting estimate is numerically well defined, consistent and asymptotically normal, whose variance-covariance matrix, however, involves the densities and joint densities of error terms. Because of the involvement of the multivariate densities, the variance-covariance matrix is especially difficult to estimate well. To avoid estimation of the densities, we propose a resampling method, which is an extension of Bilias, Chen and Ying (2000) for Powell's estimate. We justify the approach by proving that the conditional distribution of the resampling estimate is approximately the same as the unconditional distribution of the original estimate. The methods are illustrated with two examples. Simulation results are also reported. Extensions and other related issues are discussed. |
