On accelerated failure time models for forward and backward recurrence times

In prevalent cohort studies where subjects are recruited via cross-sectional sampling, the observed event times T are length biased and follow a multiplicative censoring scheme. For such studies there is an associated initiation time (T = 0). In many prevalent cohort studies the initiating time may be unobservable. In this case we only observe the time from sampling to the event of interest. This is referred to as the Forward Recurrence Time (FRT). We denote FRT by Tf. Since the onset time is unknown, standard left-trucation survival analysis methods are not applicable.; In other scenarios like the current duration sampling scheme, the time of the initiating event may be known but there is no subsequent follow-up after sampling. Here we observe the Backward Recurrence Times (BRT) denoted by Tb.; It is well known that AFT models are invariant under length-biased and cross-sectional sampling and a certain stationarity condition. In the usual AFT model, we assume that the covariate distribution carries no information for the regression parameter (theta) which allows for inference conditional on the covariates with out loss of efficiency. However, in the case of FRT or BRT the length-biased covariate distribution is functionally dependent on theta. Thus for the FRT and the BRT cases it is not clear if an unconditional analysis may result in gain in information for estimating theta.; In this dissertation we study semiparametric efficient estimation of theta for AFT models fitted to forward and backward recurrence times. We show that if the covariate distribution is completely unspecified then there is no loss of information under a "naive" conditional on the covariates analysis. We also derive a semi-parametric asymptotically efficient estimator for theta in an AFT model based on a smoothed self-consistent estimator for the error density which is applicable to AFT models for T as well as Tf and Tb. We analyze the French Observatory of Fecundity data of consisting BRT versions of time to pregnancy. Simulation studies are also included to study the performance of our estimator with realistic sample sizes and for comparing the latter to the popular linear-rank test based estimators.