Methods for estimating heterogeneous treatment effect in observational data have largely focused on continuous or binary outcomes, and have been relatively less vetted with survival outcomes. Using flexible machine learning methods in the counterfactual framework is a promising approach to address challenges due to complex individual characteristics, to which treatments need to be tailored. To evaluate the operating characteristics of recent survival machine learning methods for the estimation of treatment effect heterogeneity and inform better practice, we carry out a comprehensive simulation study presenting a wide range of settings describing confounded heterogeneous survival treatment effects and varying degrees of covariate overlap. Our results suggest that the nonparametric Bayesian Additive Regression Trees within the framework of accelerated failure time model (AFT-BART-NP) consistently yields the best performance, in terms of bias, precision and expected regret. Moreover, the credible interval estimators from AFT-BART-NP provide close to nominal frequentist coverage for the individual survival treatment effect when the covariate overlap is at least moderate. Including a non-parametrically estimated propensity score as an additional fixed covariate in the AFT-BART-NP model formulation can further improve its efficiency and frequentist coverage. Finally, we demonstrate the application of flexible causal machine learning estimators through a comprehensive case study examining the heterogeneous survival effects of two radiotherapy approaches for localized high-risk prostate cancer.
The difference in restricted mean survival times between two groups is a clinically relevant summary measure. With observational data, there may be imbalances in confounding variables between the two groups. One approach to account for such imbalances is to estimate a covariate-adjusted restricted mean difference by modeling the covariate-adjusted survival distribution and then marginalizing over the covariate distribution. We demonstrate that the mean-squared error of the restricted mean difference is bounded by the mean-squared error of the covariate-adjusted survival distribution estimators…
Forest-based methods have recently gained in popularity for non-parametric treatment effect estimation. Building on this line of work, we introduce causal survival forests, which can be used to estimate heterogeneous treatment effects in a survival and observational setting where outcomes may be right-censored. Our approach relies on orthogonal estimating equations to robustly adjust for both censoring and selection effects under unconfoundedness. In our experiments, we find our approach to perform well relative to a number of baselines.
The purpose of this work is to improve the efficiency in estimating the average causal effect (ACE) on the survival scale where right-censoring exists and high-dimensional covariate information is available. We propose new estimators using regularized survival regression and survival random forests (SRF) to make the adjustment for the high dimensional covariates to improve efficiency. We study the behavior of the adjusted estimator under mild assumptions and show theoretical guarantees that the proposed estimators are more efficient than the unadjusted ones asymptotically when using SRF for ad…
No unmeasured confounding is often assumed in estimating treatment effects in observational data when using approaches such as propensity scores and inverse probability weighting. However, in many such studies due to the limitation of the databases, collected confounders are not exhaustive, and it is crucial to examine the extent to which the resulting estimate is sensitive to the unmeasured confounders. We consider this problem for survival and competing risks data. Due to the complexity of models for such data, we adapt the simulated potential confounders approach of Carnegie et al. (2016), …
The inverse probability weighting approach is popular for evaluating treatment effects in observational studies, but extreme propensity scores could bias the estimator and induce excessive variance. Recently, the overlap weighting approach has been proposed to alleviate this problem, which smoothly down-weighs the subjects with extreme propensity scores. Although advantages of overlap weighting have been extensively demonstrated in literature with continuous and binary outcomes, research on its performance with time-to-event or survival outcomes is limited. In this article, we propose two weig…
Centre for Big Data Research in Health (CBDRH)（健康大数据研究中心）
Causal inference for observational longitudinal studies often requires the accurate estimation of treatment effects on time-to-event outcomes in the presence of time-dependent patient history and time-dependent covariates. To tackle this longitudinal treatment effect estimation problem, we have developed a time-variant causal survival (TCS) model that uses the potential outcomes framework with an ensemble of recurrent subnetworks to estimate the difference in survival probabilities and its confidence interval over time as a function of time-dependent covariates and treatments. Using simulated …
A Guide to Estimating Conditional Average Treatment Effects in Competing Risks Settings
Department of Statistics, TU Dortmund University（图恩-多特蒙德大学统计学系）；Research Center Trustworthy Data Science and Security, University Alliance Ruhr (UA Ruhr)（鲁尔大学联盟可信数据科学与安全研究中心）；Institute for Mathematics, University of Augsburg（艾希施泰特大学数学研究所）
Peter the Great St.Petersburg Polytechnic University（彼得大帝圣彼得堡理工大学）
A method for estimating the conditional average treatment effect under condition of censored time-to-event data called BENK (the Beran Estimator with Neural Kernels) is proposed. The main idea behind the method is to apply the Beran estimator for estimating the survival functions of controls and treatments. Instead of typical kernel functions in the Beran estimator, it is proposed to implement kernels in the form of neural networks of a specific form called the neural kernels. The conditional average treatment effect is estimated by using the survival functions as outcomes of the control and t…
Investigating the causal relationship between exposure and the time-to-event outcome is an important topic in biomedical research. Previous literature has discussed the potential issues of using the hazard ratio as a marginal causal effect measure due to its noncollapsibility property. In this paper, we advocate using the restricted mean survival time (RMST) difference as the marginal causal effect measure, which is collapsible and has a simple interpretation as the difference of area under survival curves over a certain time horizon. To address both measured and unmeasured confounding, a matc…
Observing the unobserved confounding through its effects: toward randomized trial-like estimates from real-world survival data
Operations Research Center, Massachusetts Institute of Technology（麻省理工学院运营研究中心）；Sloan School of Management, Massachusetts Institute of Technology（麻省理工学院斯隆管理学院）；Department of Surgery, Memorial Sloan Kettering Cancer Center（纪念斯隆凯特琳癌症中心外科部）；Charité-Universitätsmedizin Berlin, Corporate Member of Freie Universität Berlin and Humboldt-Universität zu Berlin（柏林夏里特医学院，柏林自由大学和洪堡大学联合成员）
A new method for clustered survival data]{A new method for clustered survival data: Estimation of treatment effect heterogeneity and variable selection
The aim of clinical effectiveness research using repositories of electronic health records is to identify what health interventions 'work best' in real-world settings. Since there are several reasons why the net benefit of intervention may differ across patients, current comparative effectiveness literature focuses on investigating heterogeneous treatment effect and predicting whether an individual might benefit from an intervention. The majority of this literature has concentrated on the estimation of the effect of treatment on binary outcomes. However, many medical interventions are evaluate…
Guiding Treatment Strategies: The Role of Adjuvant Anti-Her2 Neu Therapy and Skin/Nipple Involvement in Local Recurrence-Free Survival in Breast Cancer Patients
Longitudinal observational patient data can be used to investigate the causal effects of time-varying treatments on time-to-event outcomes. Several methods have been developed for controlling for the time-dependent confounding that typically occurs. The most commonly used is inverse probability weighted estimation of marginal structural models (MSM-IPTW). An alternative, the sequential trials approach, is increasingly popular, in particular in combination with the target trial emulation framework. This approach involves creating a sequence of `trials' from new time origins, restricting to indi…
ETH Zurich（苏黎世联邦理工学院）；University of Cambridge（剑桥大学）；LMU Munich（慕尼黑大学）；The Alan Turing Institute（阿兰·图灵研究所）；UCLA（加州大学洛杉矶分校）
Estimating heterogeneous treatment effects is an important problem across many domains. In order to accurately estimate such treatment effects, one typically relies on data from observational studies or randomized experiments. Currently, most existing works rely exclusively on observational data, which is often confounded and, hence, yields biased estimates. While observational data is confounded, randomized data is unconfounded, but its sample size is usually too small to learn heterogeneous treatment effects. In this paper, we propose to estimate heterogeneous treatment effects by combining …
From Observational Data to Clinical Recommendations: A Causal Framework for Estimating Patient-level Treatment Effects and Learning Policies
Faculty of Data and Decision Sciences, Technion（数据与决策科学学院，技术ion）；Blavatnik School of Computer Science, Tel-Aviv University（Blavatnik计算机科学学院，特拉维夫大学）；Department of Cardiology, Rambam Health Care Campus（心内科部，拉马姆医疗中心）；The Bruce Rappaport Faculty of Medicine, Technion（布鲁斯·拉帕波特医学院，技术ion）；Department of Statistics and Operations Research, School of Mathematical Sciences, Tel Aviv University（统计与运筹学部，数学科学学院，特拉维夫大学）
One of the most common ways researchers compare survival outcomes across treatments when confounding is present is using Cox regression. This model is limited by its underlying assumption of proportional hazards; in some cases, substantial violations may occur. Here we present and compare approaches which attempt to address this issue, including Cox models with time-varying hazard ratios; parametric accelerated failure time models; Kaplan-Meier curves; and pseudo-observations. To adjust for differences between treatment groups, we use Inverse Probability of Treatment Weighting based on the pro…
Despite the major advances taken in causal modeling, causality is still an unfamiliar topic for many statisticians. In this paper, it is demonstrated from the beginning to the end how causal effects can be estimated from observational data assuming that the causal structure is known. To make the problem more challenging, the causal effects are highly nonlinear and the data are missing at random. The tools used in the estimation include causal models with design, causal calculus, multiple imputation and generalized additive models. The main message is that a trained statistician can estimate ca…
Observational health data can be leveraged to measure the real-world use and potential benefits or risks of existing medical interventions. However, lack of programming proficiency and advanced knowledge of causal inference methods excludes some clinicians and non-computational researchers from performing such analyses. Code-free dashboard tools provide accessible means to estimate and visualize treatment effects from observational health data. We present TreatmentEstimatoR, an R Shiny dashboard that facilitates the estimation of treatment effects from observational data without any programmin…
We propose a new approach to estimate the causal effects of maritime traffic when natural or policy experiments are not available. We apply this method to the case of Marseille, a large Mediterranean port city, where air pollution emitted by cruise vessels is a growing concern. Using a recent matching algorithm designed for time series data, we create hypothetical randomized experiments to estimate the change in local air pollution caused by a short-term increase in cruise traffic. We then rely on randomization inference to compute nonparametric 95\% uncertainty intervals. We find that cruise …
Quantum Neural Networks for Propensity Score Estimation and Survival Analysis in Observational Biomedical Studies
Department of Computer Science, Faculty of Electrical Engineering and Computer science, VSB-Technical University of Ostrava（计算机科学系，电气工程与计算机科学学院，VSB技术大学奥斯特拉瓦）；VSB-Technical University of Ostrava（VSB技术大学奥斯特拉瓦）；IT4Innovations National Supercomputing Center, VSB - Technical University of Ostrava（IT4Innovations国家超级计算中心，VSB技术大学奥斯特拉瓦）；Department of Applied Mathematics, Faculty of Electrical Engineering and Computer science, VSB-Technical University of Ostrava（应用数学系，电气工程与计算机科学学院，VSB技术大学奥斯特拉瓦）；Department of Surgical Studies, Faculty of Medicine, University of Ostrava（外科研究系，医学院，奥斯特拉瓦大学）；Department of Surgery, University Hospital Ostrava（外科系，奥斯特拉瓦大学医院）
LaMME（拉梅实验室）；Paris Saclay University / UEVE（巴黎萨克雷大学/埃夫里大学）；LaMME - CNRS（拉梅实验室-法国国家科学研究中心）；IBISC（IBISC实验室）
Individual Treatment Effects (ITE) estimation methods have risen in popularity in the last years. Most of the time, individual effects are better presented as Conditional Average Treatment Effects (CATE). Recently, representation balancing techniques have gained considerable momentum in causal inference from observational data, still limited to continuous (and binary) outcomes. However, in numerous pathologies, the outcome of interest is a (possibly censored) survival time. Our paper proposes theoretical guarantees for a representation balancing framework applied to counterfactual inference in…
Though they may offer valuable patient and disease information that is impossible to study in a randomized trial, clinical disease registries also require special care and attention in causal inference. Registry data may be incomplete, inconsistent, and subject to confounding. In this paper we aim to address several analytical issues in estimating treatment effects that plague clinical registries such as the Emory amyotrophic lateral sclerosis (ALS) Clinic Registry. When attempting to assess the effect of a surgical insertion of a percutaneous endoscopic gastrostomy (PEG) tube on body mass ind…
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）
The estimation of heterogeneous treatment effects (HTEs) has attracted considerable interest in many disciplines, most prominently in medicine and economics. Contemporary research has so far primarily focused on continuous and binary responses where HTEs are traditionally estimated by a linear model, which allows the estimation of constant or heterogeneous effects even under certain model misspecifications. More complex models for survival, count, or ordinal outcomes require stricter assumptions to reliably estimate the treatment effect. Most importantly, the noncollapsibility issue necessitat…
In observational studies of survival time featuring a binary time-dependent treatment, the hazard ratio (an instantaneous measure) is often used to represent the treatment effect. However, investigators are often more interested in the difference in survival functions. We propose semiparametric methods to estimate the causal effect of treatment among the treated with respect to survival probability. The objective is to compare post-treatment survival with the survival function that would have been observed in the absence of treatment. For each patient, we compute a prognostic score (based on t…
We consider the estimation of joint causal effects from observational data. In particular, we propose new methods to estimate the effect of multiple simultaneous interventions (e.g., multiple gene knockouts), under the assumption that the observational data come from an unknown linear structural equation model with independent errors. We derive asymptotic variances of our estimators when the underlying causal structure is partly known, as well as high-dimensional consistency when the causal structure is fully unknown and the joint distribution is multivariate Gaussian. We also propose a genera…
The Hazard Ratio (HR) is often reported as the main causal effect when studying survival data. Despite its popularity, the HR suffers from an unclear causal interpretation. As already pointed out in the literature, there is a built-in selection bias in the HR, because similarly to the truncation by death problem, the HR conditions on post-treatment survival. A recently proposed alternative, inspired by the Survivor Average Causal Effect (SACE), is the causal HR, defined as the ratio between hazards across treatment groups among the study participants that would have survived regardless of thei…
Recommendation systems are an increasingly prominent part of the web, accounting for up to a third of all traffic on several of the world's most popular sites. Nevertheless, little is known about how much activity such systems actually cause over and above activity that would have occurred via other means (e.g., search) if recommendations were absent. Although the ideal way to estimate the causal impact of recommendations is via randomized experiments, such experiments are costly and may inconvenience users. In this paper, therefore, we present a method for estimating causal effects from purel…
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…
Understanding and quantifying cause and effect is an important problem in many domains. The generally-agreed solution to this problem is to perform a randomised controlled trial. However, even when randomised controlled trials can be performed, they usually have relatively short duration's due to cost considerations. This makes learning long-term causal effects a very challenging task in practice, since the long-term outcome is only observed after a long delay. In this paper, we study the identification and estimation of long-term treatment effects when both experimental and observational data…
Patients with end-stage kidney disease can expect to wait for several years before they receive a transplant, all the while their health deteriorates. How would the survival change if we managed to reduce these waiting times? To provide an answer, we present a continuous-time marginal structural model (MSM) of hypothetical scenarios in which the time until treatment is changed. In these scenarios, the treatment process is defined on a hypothetical time scale where time passes at a different rate compared to the time actually observed. Changing the time of the treatment process corresponds to c…
Estimating treatment effects, especially individualized treatment effects (ITE), using observational data is challenging due to the complex situations of confounding bias. Existing approaches for estimating treatment effects from longitudinal observational data are usually built upon a strong assumption of "unconfoundedness", which is hard to fulfill in real-world practice. In this paper, we propose the Variational Temporal Deconfounder (VTD), an approach that leverages deep variational embeddings in the longitudinal setting using proxies (i.e., surrogate variables that serve for unobservable …
Clinical trials involving novel immuno-oncology (IO) therapies frequently exhibit survival profiles which violate the proportional hazards assumption due to a delay in treatment effect, and in such settings, the survival curves in the two treatment arms may have a crossing before the two curves eventually separate. To flexibly model such scenarios, we describe a nonparametric approach for estimating the treatment arm-specific survival functions which constrains these two survival functions to cross at most once without making any additional assumptions about how the survival curves are related…
Estimating marginal treatment effects from observational studies and indirect treatment comparisons: When are standardization-based methods preferable to those based on propensity score weighting?
