Semiparametric analysis of survival data with left truncation and right censoring

Abstract

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 , δ , V ) , with X = min ( T , C ) and δ = I [ T ≤ C ] , if T ≥ V . For LTRC data, the truncation product-limit estimate F ˆ n is the maximum likelihood estimate (MLE) for nonparametric models. If the distribution of V is parameterized as G ( x ; θ ) and the distributions of T and C are left unspecified, the product-limit estimate F ˆ 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 ˆ n . The proposed semiparametric method is applied to a Channing House data.