A semiparametric estimator of survival for doubly truncated data

Abstract

Doubly truncated data are often encountered in the analysis of survival times, when the sample reduces to those individuals with terminating event falling on a given observational window. In this paper we assume that some information about the bivariate distribution function (df) of the truncation times is available. More specifically, we represent this information by means of a parametric model for the joint df of the truncation times. Under this assumption, a new semiparametric estimator of the lifetime df is derived. We obtain asymptotic results for the new estimator, and we show in simulations that it may be more efficient than the Efron-Petrosian nonparametric maximum likelihood estimator. Data on the age at diagnosis of childhood cancer in North Portugal are analyzed with the new method.

Computationally simple estimation and improved efficiency for special cases of double truncation

“…Weak convergence of the process n 1/2 { F̂ X (·; θ̂ c ) − F X (·)} was established by Moreira and Uña-Álvarez (2010b) and Shen (2010b) for finite dimensional parametric models, and is applicable to our estimator with finite K . These authors also derived an analytical variance estimator.…”

“…They also provided simulation results to suggest weak convergence. Moreira and Uña-Álvarez (2010b) and Shen (2010b) developed general asymptotic results for a semi-parametric estimator for the complete truncation dependence case (in addition to the more general case), including variance estimators.…”

“…Our estimator has increased flexibility and robustness over previously derived estimators, which were shown to be inconsistent if the parametric truncation distribution is misspecified. It benefits from the availability of convergence results and a variance estimator derived by Moreira and Uña-Álvarez (2010b) and Shen (2010b).…”

Median regression model with doubly truncated data

“…Furthermore, in the case of V = U + d 0 , one might parameterize the distribution function of U as G(x; θ) [28], where θ ∈ ⊂ R q and θ is a q-dimensional vector. Under this assumption, when Z is discrete, a more efficient estimator, sayŜ n (t |θ , z k ), can be obtained [14,21,22]. Thus, a more efficient estimator for β can be obtained by solving Equation (7) withŜ n (β z k | z k ) replaced byŜ n (β z k |θ , z k ).…”

Estimation of Kendall’s tau for bivariate doubly truncated data

“…In this situation, we can obtain an estimatorθ n by maximizing the conditional likelihood of (U * 1 , U * 2 )'s, given (T * 1 , T * 2 )'s (see Moreira & de Uña-Álvarez, 2010a, Qin & Wang, 2001, Shen, 2010b, Wang, 1989. The large-sample properties of the estimator Gθ n can be established using the arguments similar to those of Wang (1989).…”