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Register a new userEstimating Treatment Effect under Additive Hazards Models with High-dimensional Covariates
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Estimating causal effects for survival outcomes in the high-dimensional setting is an extremely important topic for many biomedical applications as well as areas of social sciences. We propose a new orthogonal score method for treatment effect estimation and inference that results in asymptotically valid confidence intervals assuming only good estimation properties of the hazard outcome model and the conditional probability of treatment. This guarantee allows us to provide valid inference for the conditional treatment effect under the high-dimensional additive hazards model under considerably more generality than existing approaches. In addition, we develop a new Hazards Difference (HDi), estimator. We showcase that our approach has double-robustness properties in high dimensions: with cross-fitting, the HDi estimate is consistent under a wide variety of treatment assignment models; the HDi estimate is also consistent when the hazards model is misspecified and instead the true data generating mechanism follows a partially linear additive hazards model. We further develop a novel sparsity doubly robust result, where either the outcome or the treatment model can be a fully dense high-dimensional model. We apply our methods to study the treatment effect of radical prostatectomy versus conservative management for prostate cancer patients using the SEER-Medicare Linked Data.
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With a large number of baseline covariates, we propose a new semi-parametric modeling strategy for heterogeneous treatment effect estimation and individualized treatment selection, which are two major goals in personalized medicine. We achieve the first goal through estimating a covariate-specific treatment effect (CSTE) curve modeled as an unknown function of a weighted linear combination of all baseline covariates. The weight or the coefficient for each covariate is estimated by fitting a sparse semi-parametric logistic single-index coefficient model. The CSTE curve is estimated by a spline-backfitted kernel procedure, which enables us to further construct a simultaneous confidence band (SCB) for the CSTE curve under a desired confidence level. Based on the SCB, we find the subgroups of patients that benefit from each treatment, so that we can make individualized treatment selection. The innovations of the proposed method are three-fold. First, the proposed method can quantify variability associated with the estimated optimal individualized treatment rule with high-dimensional covariates. Second, the proposed method is very flexible to depict both local and global associations between the treatment and baseline covariates in the presence of high-dimensional covariates, and thus it enjoys flexibility while achieving dimensionality reduction. Third, the SCB achieves the nominal confidence level asymptotically, and it provides a uniform inferential tool in making individualized treatment decisions.
The purpose of this paper is to construct confidence intervals for the regression coefficients in the Fine-Gray model for competing risks data with random censoring, where the number of covariates can be larger than the sample size. Despite strong motivation from biomedical applications, a high-dimensional Fine-Gray model has attracted relatively little attention among the methodological or theoretical literature. We fill in this gap by developing confidence intervals based on a one-step bias-correction for a regularized estimation. We develop a theoretical framework for the partial likelihood, which does not have independent and identically distributed entries and therefore presents many technical challenges. We also study the approximation error from the weighting scheme under random censoring for competing risks and establish new concentration results for time-dependent processes. In addition to the theoretical results and algorithms, we present extensive numerical experiments and an application to a study of non-cancer mortality among prostate cancer patients using the linked Medicare-SEER data.
Though Gaussian graphical models have been widely used in many scientific fields, limited progress has been made to link graph structures to external covariates because of substantial challenges in theory and computation. We propose a Gaussian graphical regression model, which regresses both the mean and the precision matrix of a Gaussian graphical model on covariates. In the context of co-expression quantitative trait locus (QTL) studies, our framework facilitates estimation of both population- and subject-level gene regulatory networks, and detection of how subject-level networks vary with genetic variants and clinical conditions. Our framework accommodates high dimensional responses and covariates, and encourages covariate effects on both the mean and the precision matrix to be sparse. In particular for the precision matrix, we stipulate simultaneous sparsity, i.e., group sparsity and element-wise sparsity, on effective covariates and their effects on network edges, respectively. We establish variable selection consistency first under the case with known mean parameters and then a more challenging case with unknown means depending on external covariates, and show in both cases that the convergence rate of the estimated precision parameters is faster than that obtained by lasso or group lasso, a desirable property for the sparse group lasso estimation. The utility and efficacy of our proposed method is demonstrated through simulation studies and an application to a co-expression QTL study with brain cancer patients.
A new class of survival frailty models based on the Generalized Inverse-Gaussian (GIG) distributions is proposed. We show that the GIG frailty models are flexible and mathematically convenient like the popular gamma frailty model. Furthermore, our proposed class is robust and does not present some computational issues experienced by the gamma model. By assuming a piecewise-exponential baseline hazard function, which gives a semiparametric flavour for our frailty class, we propose an EM-algorithm for estimating the model parameters and provide an explicit expression for the information matrix. Simulated results are addressed to check the finite sample behavior of the EM-estimators and also to study the performance of the GIG models under misspecification. We apply our methodology to a TARGET (Therapeutically Applicable Research to Generate Effective Treatments) data about survival time of patients with neuroblastoma cancer and show some advantages of the GIG frailties over existing models in the literature.
We focus on the problem of generalizing a causal effect estimated on a randomized controlled trial (RCT) to a target population described by a set of covariates from observational data. Available methods such as inverse propensity weighting are not designed to handle missing values, which are however common in both data sources. In addition to coupling the assumptions for causal effect identifiability and for the missing values mechanism and to defining appropriate estimation strategies, one difficulty is to consider the specific structure of the data with two sources and treatment and outcome only available in the RCT. We propose and compare three multiple imputation strategies (separate imputation, joint imputation with fixed effect, joint imputation without source information), as well as a technique that uses estimators that can handle missing values directly without imputing them. These methods are assessed in an extensive simulation study, showing the empirical superiority of fixed effect multiple imputation followed with any complete data generalizing estimators. This work is motivated by the analysis of a large registry of over 20,000 major trauma patients and a RCT studying the effect of tranexamic acid administration on mortality. The analysis illustrates how the missing values handling can impact the conclusion about the effect generalized from the RCT to the target population.
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