Semiparametric analysis of survival data with left truncation and right censoring

Let T, C and V denote the lifetime, censoring and truncation variables, respectively. Assume that (C, V) is independent of T and P(C >= V) = 1. Let F, Q and G denote the common distribution functions of T, C and V, respectively. For left-truncated and right-censored (LTRC) data, one can observe nothing if T < V and observe (X, delta, V), with X = min(T, C) and delta = I([T <= C]), if T >= V. For LTRC data, the truncation product-limit estimate <(F)over cap>(n) is the maximum likelihood estimate (MLE) for nonparametric models. If the distribution of V is parameterized as G(x; theta) and the distributions of T and C are left unspecified, the product-limit estimate (F) over cap (n) is not the MLE for this semiparametric model. In this article, for LTRC data, two semiparametric estimates are proposed for the semiparametric model. A simulation study is conducted to compare the performances of the two semiparametric estimators against that of (F) over cap (n). The proposed semiparametric method is applied to a Charming House data. (C) 2009 Elsevier B.V. All rights reserved.