Likelihood approach for marginal proportional hazards regression in the presence of dependent censoring

In many public health problems, an important goal is to identify the effect of some treatment/intervention on the risk of failure for the whole population. A marginal proportional hazards regression model is often used to analyze such an effect. When dependent censoring is explained by many auxiliary covariates, we utilize two working models to condense high-dimensional covariates to achieve dimension reduction. Then the estimator of the treatment effect is obtained by maximizing a pseudo-likelihood function over a sieve space. Such an estimator is shown to be consistent and asymptotically normal when either of the two working models is correct; additionally, when both working models are correct, its asymptotic variance is the same as the semiparametric efficiency bound.Comment: Published at http://dx.doi.org/10.1214/009053604000001291 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Estimating marginal survival function by adjusting for dependent censoring using many covariates

One goal in survival analysis of right-censored data is to estimate the marginal survival function in the presence of dependent censoring. When many auxiliary covariates are sufficient to explain the dependent censoring, estimation based on either a semiparametric model or a nonparametric model of the conditional survival function can be problematic due to the high dimensionality of the auxiliary information. In this paper, we use two working models to condense these high-dimensional covariates in dimension reduction; then an estimate of the marginal survival function can be derived nonparametrically in a low-dimensional space. We show that such an estimator has the following double robust property: when either working model is correct, the estimator is consistent and asymptotically Gaussian; when both working models are correct, the asymptotic variance attains the efficiency bound.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Statistics (http://www.imstat.org/aos/) at http://dx.doi.org/10.1214/00905360400000050

Asymptotic results for maximum likelihood estimators in joint analysis of repeated measurements and survival time

Maximum likelihood estimation has been extensively used in the joint analysis of repeated measurements and survival time. However, there is a lack of theoretical justification of the asymptotic properties for the maximum likelihood estimators. This paper intends to fill this gap. Specifically, we prove the consistency of the maximum likelihood estimators and derive their asymptotic distributions. The maximum likelihood estimators are shown to be semiparametrically efficient.Comment: Published at http://dx.doi.org/10.1214/009053605000000480 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Counting Process Based Dimension Reduction Methods for Censored Outcomes

We propose a class of dimension reduction methods for right censored survival data using a counting process representation of the failure process. Semiparametric estimating equations are constructed to estimate the dimension reduction subspace for the failure time model. The proposed method addresses two fundamental limitations of existing approaches. First, using the counting process formulation, it does not require any estimation of the censoring distribution to compensate the bias in estimating the dimension reduction subspace. Second, the nonparametric part in the estimating equations is adaptive to the structural dimension, hence the approach circumvents the curse of dimensionality. Asymptotic normality is established for the obtained estimators. We further propose a computationally efficient approach that simplifies the estimation equation formulations and requires only a singular value decomposition to estimate the dimension reduction subspace. Numerical studies suggest that our new approaches exhibit significantly improved performance for estimating the true dimension reduction subspace. We further conduct a real data analysis on a skin cutaneous melanoma dataset from The Cancer Genome Atlas. The proposed method is implemented in the R package "orthoDr".Comment: First versio

Maximum likelihood estimation for semiparametric transformation models with interval-censored data

Interval censoring arises frequently in clinical, epidemiological, financial and sociological studies, where the event or failure of interest is known only to occur within an interval induced by periodic monitoring. We formulate the effects of potentially time-dependent covariates on the interval-censored failure time through a broad class of semiparametric transformation models that encompasses proportional hazards and proportional odds models. We consider nonparametric maximum likelihood estimation for this class of models with an arbitrary number of monitoring times for each subject. We devise an EM-type algorithm that converges stably, even in the presence of time-dependent covariates, and show that the estimators for the regression parameters are consistent, asymptotically normal, and asymptotically efficient with an easily estimated covariance matrix. Finally, we demonstrate the performance of our procedures through simulation studies and application to an HIV/AIDS study conducted in Thailand

Variable Selection for Case-Cohort Studies with Failure Time Outcome

Case-cohort designs are widely used in large cohort studies to reduce the cost associated with covariate measurement. In many such studies the number of covariates is very large, so an efficient variable selection method is necessary. In this paper, we study the properties of variable selection using the smoothly clipped absolute deviation penalty in a case-cohort design with a diverging number of parameters. We establish the consistency and asymptotic normality of the maximum penalized pseudo-partial likelihood estimator, and show that the proposed variable selection procedure is consistent and has an asymptotic oracle property. Simulation studies compare the finite sample performance of the procedure with Akaike information criterion- and Bayesian information criterion-based tuning parameter selection methods. We make recommendations for use of the procedures in case-cohort studies, and apply them to the Busselton Health Study

Elastic Integrative Analysis of Randomized Trial and Real-World Data for Treatment Heterogeneity Estimation

Parallel randomized trial (RT) and real-world (RW) data are becoming increasingly available for treatment evaluation. Given the complementary features of the RT and RW data, we propose a test-based elastic integrative analysis of the RT and RW data for accurate and robust estimation of the heterogeneity of treatment effect (HTE), which lies at the heart of precision medicine. When the RW data are not subject to bias, e.g., due to unmeasured confounding, our approach combines the RT and RW data for optimal estimation by exploiting semiparametric efficiency theory. Utilizing the design advantage of RTs, we construct a built-in test procedure to gauge the reliability of the RW data and decide whether or not to use RW data in an integrative analysis. We characterize the asymptotic distribution of the test-based elastic integrative estimator under local alternatives, which provides a better approximation of the finite-sample behaviors of the test and estimator when the idealistic assumption required for the RW data is weakly violated. We provide a data-adaptive procedure to select the threshold of the test statistic that promises the smallest mean square error of the proposed estimator of the HTE. Lastly, we construct an elastic confidence interval that has a good finite-sample coverage property. We apply the proposed method to characterize who can benefit from adjuvant chemotherapy in patients with stage IB non-small cell lung cancer