Analysis of Generalized Semiparametric Regression Models for Cumulative Incidence Functions with Missing Covariates

Additive subdistribution hazards regression for competing risks data in case-cohort studies

In survival data analysis, a competing risk is an event whose occurrence precludes or alters the chance of the occurrence of the primary event of interest. In large cohort studies with long-term follow-up, there are often competing risks. Further, if the event of interest is rare in such large studies, the case-cohort study design is widely used to reduce the cost and achieve the same efficiency as a cohort study. The conventional additive hazards modeling for competing risks data in case-cohort studies involves the cause-specific hazard function, under which direct assessment of covariate effects on the cumulative incidence function, or the subdistribution, is not possible. In this paper, we consider an additive hazard model for the subdistribution of a competing risk in case-cohort studies. We propose estimating equations based on inverse probability weighting methods for the estimation of the model parameters. Consistency and asymptotic normality of the proposed estimators are established. The performance of the proposed methods in finite samples is examined through simulation studies and the proposed approach is applied to a case-cohort dataset from the Sister Study.

Estimation of conditional cumulative incidence functions under generalized semiparametric regression models with missing covariates, with application to analysis of biomarker correlates in vaccine trials

This article studies generalized semiparametric regression models for conditional cumulative incidence functions with competing risks data when covariates are missing by sampling design or happenstance. A doubly-robust augmented inverse probability weighted complete-case (AIPW) approach to estimation and inference is investigated. This approach modifies IPW complete-case estimating equations by exploiting the key features in the relationship between the missing covariates and the phase-one data to improve efficiency. An iterative numerical procedure is derived to solve the nonlinear estimating equations. The asymptotic properties of the proposed estimators are established. A simulation study examining the finite-sample performances of the proposed estimators shows that the AIPW estimators are more efficient than the IPW estimators. The developed method is applied to the RV144 HIV-1 vaccine efficacy trial to investigate vaccine-induced IgG binding antibodies to HIV-1 as correlates of acquisition of HIV-1 infection while taking account of whether the HIV-1 sequences are near or far from the HIV-1 sequences represented in the vaccine construct.

Competing risks regression models with covariates-adjusted censoring weight under the generalized case-cohort design

A generalized case-cohort design has been used when measuring exposures is expensive and events are not rare in the full cohort. This design collects expensive exposure information from a (stratified) randomly selected subset from the full cohort, called the subcohort, and a fraction of cases outside the subcohort. For the full cohort study with competing risks, He et al. (Scand J Stat 43:103-122, 2016) studied the non-stratified proportional subdistribution hazards model with covariate-dependent censoring to directly evaluate covariate effects on the cumulative incidence function. In this paper, we propose a stratified proportional subdistribution hazards model with covariate-adjusted censoring weights for competing risks data under the generalized case-cohort design. We consider a general class of weight functions to account for the generalized case-cohort design. Then, we derive the optimal weight function which minimizes the asymptotic variance of parameter estimates within the general class of weight functions. The proposed estimator is shown to be consistent and asymptotically normally distributed. The simulation studies show (i) the proposed estimator with covariate-adjusted weight is unbiased when the censoring distribution depends on covariates; and (ii) the proposed estimator with the optimal weight function gains parameter estimation efficiency. We apply the proposed method to stem cell transplantation and diabetes data sets.