Jianwen Cai

We consider nonparametrically estimating the joint distribution of a survival time and mark variable, where the survival time is subject to right censoring and the mark variable is only observed when the survival time is not censored. The possibility of dependent censoring is allowed for using inverse probability of censoring weights. The proposed estimator is shown to be consistent and asymptotically normal. Finite sample behavior of the proposed methods are investigated via simulation study. Finally, we illustrate the nonparametric estimator from a recent HIV vaccine efficacy trial.

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.

An estimated quadratic inference function method is proposed for correlated failure time data with auxiliary covariates. The proposed method makes efficient use of the auxiliary information for the incomplete exposure covariates and preserves the property of the quadratic inference function method that requires the covariates to be completely observed. It can improve the estimation efficiency and easily deal with the situation when the cluster size is large. The proposed estimator which minimizes the estimated quadratic inference function is shown to be consistent and asymptotically normal. A chi-squared test based on the estimated quadratic inference function is proposed to test hypotheses about the regression parameters. The small-sample performance of the proposed method is investigated through extensive simulation studies. The proposed method is then applied to analyze the Study of Left Ventricular Dysfunction (SOLVD) data as an illustration.