In the presence of heterogeneity between the randomized controlled trial (RCT) participants and the target population, evaluating the treatment effect solely based on the RCT often leads to biased quantification of the real-world treatment effect. To address the problem of lack of generalizability for the treatment effect estimated by the RCT sample, we leverage observational studies with large samples that are representative of the target population. This paper concerns evaluating treatment effects on survival outcomes for a target population and considers a broad class of estimands that are functionals of treatment-specific survival functions, including differences in survival probability and restricted mean survival times. Motivated by two intuitive but distinct approaches, i.e., imputation based on survival outcome regression and weighting based on inverse probability of sampling, censoring, and treatment assignment, we propose a semiparametric estimator through the guidance of the efficient influence function. The proposed estimator is doubly robust in the sense that it is consistent for the target population estimands if either the survival model or the weighting model is correctly specified, and is locally efficient when both are correct. In addition, as an alternative to parametric estimation, we employ the nonparametric method of sieves for flexible and robust estimation of the nuisance functions and show that the resulting estimator retains the root-n consistency and efficiency, the so-called it rate-double robustness. Simulation studies confirm the theoretical properties of the proposed estimator and show it outperforms competitors. We apply the proposed method to estimate the effect of adjuvant chemotherapy on survival in patients with early-stage resected non-small lung cancer.
Instrumental variable (IV) methods allow us the opportunity to address unmeasured confounding in causal inference. However, most IV methods are only applicable to discrete or continuous outcomes with very few IV methods for censored survival outcomes. In this work we propose nonparametric estimators for the local average treatment effect on survival probabilities under both nonignorable and ignorable censoring. We provide an efficient influence function-based estimator and a simple estimation procedure when the IV is either binary or continuous. The proposed estimators possess double-robustnes…
Contrasting marginal counterfactual survival curves across treatment arms is an effective and popular approach for inferring the causal effect of an intervention on a right-censored time-to-event outcome. A key challenge to drawing such inferences in observational settings is the possible existence of unmeasured confounding, which may invalidate most commonly used methods that assume no hidden confounding bias. In this paper, rather than making the standard no unmeasured confounding assumption, we extend the recently proposed proximal causal inference framework of Miao et al. (2018), Tchetgen …
Doubly Robust Conformalized Survival Analysis with Right-Censored Data
Department of Data Sciences and Operations（数据科学与运营系）；Department of Computer Science, University of Southern California（计算机科学系，南加州大学）；Merck & Co., Inc.（默克公司）
In the absence of data from a randomized trial, researchers often aim to use observational data to draw causal inference about the effect of a treatment on a time-to-event outcome. In this context, interest often focuses on the treatment-specific survival curves; that is, the survival curves were the entire population under study to be assigned to receive the treatment or not. Under certain causal conditions, including that all confounders of the treatment-outcome relationship are observed, the treatment-specific survival can be identified with a covariate-adjusted survival function. Several e…
The generalized g-formula can be used to estimate the probability of survival under a sustained treatment strategy. When treatment strategies are deterministic, estimators derived from the so-called efficient influence function (EIF) for the g-formula will be doubly robust to model misspecification. In recent years, several practical applications have motivated estimation of the g-formula under non-deterministic treatment strategies where treatment assignment at each time point depends on the observed treatment process. In this case, EIF-based estimators may or may not be doubly robust. In thi…
This paper studies Cox's regression hazard model with an unobservable random frailty where no specific distribution is postulated for the frailty variable, and the marginal lifetime distribution allows both parametric and non-parametric models. Laplace's approximation method and gradient search on smooth manifolds embedded in Euclidean space are applied, and a non-iterative profile likelihood optimization method is proposed for estimating the regression coefficients. The proposed method is compared with the Expected-Maximization method developed based on a gamma frailty assumption, and also in…
Heterogeneous Treatment Effect in Time-to-Event Outcomes: Harnessing Censored Data with Recursively Imputed Trees
Faculty of Data and Decisions Sciences, Technion - Israel Institute of Technology（数据与决策科学学院，技术ion-以色列理工学院）；Department of Statistics and Operations Research, Tel Aviv University（统计与运筹学系，特拉维夫大学）
Imputing missing potential outcomes using an estimated regression function is a natural idea for estimating causal effects. In the literature, estimators that combine imputation and regression adjustments are believed to be comparable to augmented inverse probability weighting. Accordingly, people for a long time conjectured that such estimators, while avoiding directly constructing the weights, are also doubly robust (Imbens, 2004; Stuart, 2010). Generalizing an earlier result of the authors (Lin et al., 2021), this paper formalizes this conjecture, showing that a large class of regression-ad…
Randomized controlled trials (RCT's) allow researchers to estimate causal effects in an experimental sample with minimal identifying assumptions. However, to generalize or transport a causal effect from an RCT to a target population, researchers must adjust for a set of treatment effect moderators. In practice, it is impossible to know whether the set of moderators has been properly accounted for. In the following paper, I propose a three parameter sensitivity analysis for generalizing or transporting experimental results using weighted estimators, with several advantages over existing methods…
We develop an encompassing framework for matching, covariate balancing, and doubly-robust methods for causal inference from observational data called generalized optimal matching (GOM). The framework is given by generalizing a new functional-analytical formulation of optimal matching, giving rise to the class of GOM methods, for which we provide a single unified theory to analyze tractability, consistency, and efficiency. Many commonly used existing methods are included in GOM and, using their GOM interpretation, can be extended to optimally and automatically trade off balance for variance and…
Recently, many researchers have advanced data-driven methods for modeling heterogeneous treatment effects (HTEs). Even still, estimation of HTEs is a difficult task -- these methods frequently over- or under-estimate the treatment effects, leading to poor calibration of the resulting models. However, while many methods exist for evaluating the calibration of prediction and classification models, formal approaches to assess the calibration of HTE models are limited to the calibration slope. In this paper, we define an analogue of the \smash{($\ell_2$)} expected calibration error for HTEs, and p…
Comparative effectiveness evidence from randomized trials may not be directly generalizable to a target population of substantive interest when, as in most cases, trial participants are not randomly sampled from the target population. Motivated by the need to generalize evidence from two trials conducted in the AIDS Clinical Trials Group (ACTG), we consider weighting, regression and doubly robust estimators to estimate the causal effects of HIV interventions in a specified population of people living with HIV in the USA. We focus on a non-nested trial design and discuss strategies for both poi…
An individualized treatment regime (ITR) is a decision rule that assigns treatments based on patients' characteristics. The value function of an ITR is the expected outcome in a counterfactual world had this ITR been implemented. Recently, there has been increasing interest in combining heterogeneous data sources, such as leveraging the complementary features of randomized controlled trial (RCT) data and a large observational study (OS). Usually, a covariate shift exists between the source and target population, rendering the source-optimal ITR unnecessarily optimal for the target population. …
To generalize inferences from a randomized trial to the target population of all trial-eligible individuals, investigators can use nested trial designs, where the randomized individuals are nested within a cohort of trial-eligible individuals, including those who are not offered or refuse randomization. In these designs, data on baseline covariates are collected from the entire cohort, and treatment and outcome data need only be collected from randomized individuals. In this paper, we describe nested trial designs that improve research economy by collecting additional baseline covariate data a…
Harvard University（哈佛大学）；Massachusetts General Hospital（麻省总医院）
Reinforcement learning (RL) has shown great success in estimating sequential treatment strategies which take into account patient heterogeneity. However, health-outcome information, which is used as the reward for reinforcement learning methods, is often not well coded but rather embedded in clinical notes. Extracting precise outcome information is a resource intensive task, so most of the available well-annotated cohorts are small. To address this issue, we propose a semi-supervised learning (SSL) approach that efficiently leverages a small sized labeled data with true outcome observed, and a…
