Regression Analysis of Left-truncated and Case I Interval-censored Data with the Additive Hazards Model

Combined estimating equation approaches for the additive hazards model with left-truncated and interval-censored data

Interval-censored failure time data arise commonly in various scientific studies where the failure time of interest is only known to lie in a certain time interval rather than observed exactly. In addition, left truncation on the failure event may occur and can greatly complicate the statistical analysis. In this paper, we investigate regression analysis of left-truncated and interval-censored data with the commonly used additive hazards model. Specifically, we propose a conditional estimating equation approach for the estimation, and further improve its estimation efficiency by combining the conditional estimating equation and the pairwise pseudo-score-based estimating equation that can eliminate the nuisance functions from the marginal likelihood of the truncation times. Asymptotic properties of the proposed estimators are discussed including the consistency and asymptotic normality. Extensive simulation studies are conducted to evaluate the empirical performance of the proposed methods, and suggest that the combined estimating equation approach is obviously more efficient than the conditional estimating equation approach. We then apply the proposed methods to a set of real data for illustration.

A flexible parametric approach for analyzing arbitrarily censored data that are potentially subject to left truncation under the proportional hazards model

The proportional hazards (PH) model is, arguably, the most popular model for the analysis of lifetime data arising from epidemiological studies, among many others. In such applications, analysts may be faced with censored outcomes and/or studies which institute enrollment criterion leading to left truncation. Censored outcomes arise when the event of interest is not observed but rather is known relevant to an observation time(s). Left truncated data occur in studies that exclude participants who have experienced the event prior to being enrolled in the study. If not accounted for, both of these features can lead to inaccurate inferences about the population under study. Thus, to overcome this challenge, herein we propose a novel unified PH model that can be used to accommodate both of these features. In particular, our approach can seamlessly analyze exactly observed failure times along with interval-censored observations, while aptly accounting for left truncation. To facilitate model fitting, an expectation-maximization algorithm is developed through the introduction of carefully structured latent random variables. To provide modeling flexibility, a monotone spline representation is used to approximate the cumulative baseline hazard function. The performance of our methodology is evaluated through a simulation study and is further illustrated through the analysis of two motivating data sets; one that involves child mortality in Nigeria and the other prostate cancer.

Estimation of partly linear additive hazards model with left-truncated and right-censored data

In this article, we consider an additive hazards semiparametric model for left-truncated and right-censored data where the risk function has a partly linear structure, we call it the partly linear additive hazards model. The nonlinear components are assumed to be B-splines functions, so the model can be viewed as a semiparametric model with an unknown baseline hazard function and a partly linear parametric risk function, which can model both linear and nonlinear covariate effects, hence is more flexible than a purely linear or nonlinear model. We construct a pseudo-score function to estimate the coefficients of the linear covariates and the B-spline basis functions. The proposed estimators are asymptotically normal under the assumption that the true nonlinear functions are B-spline functions whose knot locations and number of knots are held fixed. On the other hand, when the risk functions are unknown non-parametric functions, the proposed method provides a practical solution to the underlying inference problems. We conduct simulation studies to empirically examine the finite-sample performance of the proposed method and analyze a real dataset for illustration.