A Pairwise Likelihood Augmented Cox Estimator for Left-truncated Data

Abstract

Survival data collected from a prevalent cohort are subject to left truncation and the analysis is challenging. Conditional approaches for left-truncated data could be inefficient as they ignore the information in the marginal likelihood of the truncation times. Length-biased sampling methods may improve the estimation efficiency but only when the underlying truncation time is uniform; otherwise, they may generate biased estimates. We propose a semiparametric method for left-truncated data under the Cox model with no parametric distributional assumption about the truncation times. Our approach is to make inference based on the conditional likelihood augmented with a pairwise likelihood, which eliminates the truncation distribution, yet retains the information about the regression coefficients and the baseline hazard function in the marginal likelihood. An iterative algorithm is provided to solve for the regression coefficients and the baseline hazard function simultaneously. By empirical process and U-process theories, it has been shown that the proposed estimator is consistent and asymptotically normal with a closed-form consistent variance estimator. Simulation studies show substantial efficiency gain of our estimator in both the regression coefficients and the cumulative baseline hazard function over the conditional approach estimator. When the uniform truncation assumption holds, our estimator enjoys smaller biases and efficiency comparable to that of the full maximum likelihood estimator. An application to the analysis of a chronic kidney disease cohort study illustrates the utility of the method.

Amyotrophic Lateral Sclerosis Survival Associates With Neutrophils in a Sex-specific Manner

“…To account for this gap, a left-truncated survival analysis was performed. 12 To determine a functional form of continuous neutrophil counts, we first fit penalized spline regression models and found a nonlinear effect of neutrophils. Continuous neutrophil counts were categorized into 3 groups (neutrophil counts: <2, 2–4, and >4 × 10 6 neutrophils/mL of blood) based on the nonlinear effect of neutrophils identified by penalized spline regression ( figure 1 ).…”

Model selection and model averaging for analysis of truncated and censored data with measurement error

“…Condition (C1) is used to derive the maximizer from the target function. Condition (C4) is commonly assumed in the literature (e.g., [3,14,25]). Other conditions are standard in survival analysis which allow us to derive the asymptotic properties of the estimators.…”

“…Covariates X 1 , X 2 , X 3 and X 4 are error-prone due to the reasons including inaccurate measurement devices and/or procedures, the biological variability, and temporal variations. Similar to the settings in Section 6.1, we discuss three focus parameters: the hazard ratio (μ 1 ), the cumulative baseline hazard function (μ 2 ) at time t 0 , Λ 0 (t 0 ), and the survivor function (μ 3 ) at time t 0 , F(t 0 |v), with covariates taken as empirical means of variables, where for illustration, we take t 0 as the 50% percentiles of the observed survival times Y i (e.g., [25]), bearing in mind that other values of interest can also be specified as t 0 . Our goal is to select important variables from X 1 to X 4 for different focus parameters, with Z 1 and Z 2 always retained.…”

A pairwise pseudo‐likelihood approach for left‐truncated and interval‐censored data under the Cox model

“…Among others, for example, Huang and Qin (2012, 2013) and Wu et al. (2018) developed composite and pairwise likelihood‐based methods, respectively. To our best knowledge, there is no such work for general left truncated and interval censored data; this is the focus of this paper.…”