Non- and semi-parametric survival analysis with left truncated and interval censored data

Left truncated and interval censored (LTIC) data arise naturally from many large-scale panel studies, such as the Massachusetts Health Care Panel Study (MHCPS). In these studies, the time of the event of interest, say survival time, is never observed exactly but only known to be in some time interval, which introduces the interval censoring. Left truncation occurs since the subjects are recruited after the natural time origin and only those subjects who have not experienced the event of interest are recruited into the study. This thesis is solely devoted to non- and semi-parametric analyses of this kind of lifetime data.;Chapter 1 discusses the estimation of the survival curve with LTIC data. The well-known nonparametric maximum likelihood estimator (NPMLE) is shown to be under-biased with LTIC data. Two alternatives are proposed. One is the monotone MLE, which is the nonparametric MLE under the monotone hazard assumption. Another is a smoothed nonparametric estimator computed via the EMS algorithm. By simulation both estimators are shown to overcome the under-estimation problem of the NPMLE. Furthermore, the consistency of the monotone MLE is also established.;Then in Chapter 2 I extend the monotone MLE to the Cox proportional hazards model. Though the (joint) NPMLE has been around for a while, to my knowledge there is no systematic study of its performance. It is found that the NPMLE estimates the regression coefficient well though it may under-estimate the baseline survival. In contrast, the monotone MLE works well in estimating both when a monotone hazard assumption is applicable. The partial likelihood approach is also explored by stochastic techniques.;At last, some rank invariant tests are considered to compare two survival curves. In particular, Peto and Peto's log-rank test and their generalized Wilcoxon test for right censored data are extended to LTIC data. When the truncation and censoring mechanisms are independent of the group membership, permutation tests are employed to compute the significance levels. Simulation studies are conducted to assess their performance under different distribution differences.;Throughout, MHCPS is taken as an illustrative example.