A new matching method is proposed for the estimation of the average treatment effect of social policy interventions (e.g., training programs or health care measures). Given an outcome variable, a treatment and a set of pre-treatment covariates, the method is based on the examination of random recursive partitions of the space of covariates using regression trees. A regression tree is grown either on the treated or on the untreated individuals {\it only} using as response variable a random permutation of the indexes 1...$n$ ($n$ being the number of units involved), while the indexes for the other group are predicted using this tree. The procedure is replicated in order to rule out the effect of specific permutations. The average treatment effect is estimated in each tree by matching treated and untreated in the same terminal nodes. The final estimator of the average treatment effect is obtained by averaging on all the trees grown. The method does not require any specific model assumption apart from the tree's complexity, which does not affect the estimator though. We show that this method is either an instrument to check whether two samples can be matched (by any method) and, when this is feasible, to obtain reliable estimates of the average treatment effect. We further propose a graphical tool to inspect the quality of the match. The method has been applied to the National Supported Work Demonstration data, previously analyzed by Lalonde (1986) and others.
An important task in early phase drug development is to identify patients, which respond better or worse to an experimental treatment. While a variety of different subgroup identification methods have been developed for the situation of trials that study an experimental treatment and control, much less work has been done in the situation when patients are randomized to different dose groups. In this article we propose new strategies to perform subgroup analyses in dose-finding trials and discuss the challenges, which arise in this new setting. We consider model-based recursive partitioning, wh…
We study the problem of learning to choose from m discrete treatment options (e.g., news item or medical drug) the one with best causal effect for a particular instance (e.g., user or patient) where the training data consists of passive observations of covariates, treatment, and the outcome of the treatment. The standard approach to this problem is regress and compare: split the training data by treatment, fit a regression model in each split, and, for a new instance, predict all m outcomes and pick the best. By reformulating the problem as a single learning task rather than m separate ones, w…
The identification of patient subgroups with differential treatment effects is the first step towards individualised treatments. A current draft guideline by the EMA discusses potentials and problems in subgroup analyses and formulated challenges to the development of appropriate statistical procedures for the data-driven identification of patient subgroups. We introduce model-based recursive partitioning as a procedure for the automated detection of patient subgroups that are identifiable by predictive factors. The method starts with a model for the overall treatment effect as defined for the…
Model-based recursive partitioning (MOB) can be used to identify subgroups with differing treatment effects. The detection rate of treatment-by-covariate interactions and the accuracy of identified subgroups using MOB depend strongly on the sample size. Using data from multiple randomized controlled clinical trials can overcome the problem of too small samples. However, naively pooling data from multiple trials may result in the identification of spurious subgroups as differences in study design, subject selection and other sources of between-trial heterogeneity are ignored. In order to accoun…
We consider the problem of identifying sub-groups of participants in a clinical trial that have enhanced treatment effect. Recursive partitioning methods that recursively partition the covariate space based on some measure of between groups treatment effect difference are popular for such sub-group identification. The most commonly used recursive partitioning method, the classification and regression tree algorithm, first creates a large tree by recursively partitioning the covariate space using some splitting criteria and then selects the final tree from all subtrees of the large tree. In the…
Sejong University（世宗大学）；University of Cambridge（剑桥大学）；UCLA（加州大学洛杉矶分校）；University of Virginia（弗吉尼亚大学）；Yonsei University（延世大学）；The Alan Turing Institute（艾伦·图灵研究所）
Subgroup analysis of treatment effects plays an important role in applications from medicine to public policy to recommender systems. It allows physicians (for example) to identify groups of patients for whom a given drug or treatment is likely to be effective and groups of patients for which it is not. Most of the current methods of subgroup analysis begin with a particular algorithm for estimating individualized treatment effects (ITE) and identify subgroups by maximizing the difference across subgroups of the average treatment effect in each subgroup. These approaches have several weaknesse…
Sorbonne Université（索邦大学）；Inserm（法国国家健康与医学研究院）；Sorbonne Public Health Institute（索邦公共卫生研究所）；Equipe PEPITES（PEPITES团队）；Assistance Publique - Hôpitaux de Paris（巴黎公立协助医院）；Hôpital Pitié Salpêtrière（皮蒂埃-萨尔佩特里耶尔医院）；Département de Santé Publique（公共卫生系）；Centre de Pharmacoépidémiologie (Cephepi)（药物流行病学中心）；APHP（巴黎公立协助医院）；Hôpital Saint-Antoine（圣安东医院）；Inria（法国国家计算机科学与控制研究院）；CNRS（法国国家科学研究中心）；Paris Brain Institute（巴黎脑研究所）
In this paper we study the problems of estimating heterogeneity in causal effects in experimental or observational studies and conducting inference about the magnitude of the differences in treatment effects across subsets of the population. In applications, our method provides a data-driven approach to determine which subpopulations have large or small treatment effects and to test hypotheses about the differences in these effects. For experiments, our method allows researchers to identify heterogeneity in treatment effects that was not specified in a pre-analysis plan, without concern about …
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）
Popular guidance on observational data analysis states that outcomes should be blinded when determining matching criteria or propensity scores. Such a blinding is informally said to maintain the "objectivity" of the analysis, and to prevent analysts from fishing for positive results by exploiting chance imbalances. Contrary to this notion, we show that outcome blinding is not a sufficient safeguard against fishing. Blinded and unblinded analysts can produce bias of the same order of magnitude in cases where the outcomes can be approximately predicted from baseline covariates. We illustrate thi…
Statistical-Computational Trade-offs for Recursive Adaptive Partitioning Estimators
Department of Statistics and Data Science, National University of Singapore（统计与数据科学系，新加坡国立大学）；Department of Operations Research and Financial Engineering, Princeton University（运筹学与金融工程系，普林斯顿大学）；Department of Statistics, University of California, Davis（统计系，加州大学戴维斯分校）
The problem of community detection in networks is usually formulated as finding a single partition of the network into some "correct" number of communities. We argue that it is more interpretable and in some regimes more accurate to construct a hierarchical tree of communities instead. This can be done with a simple top-down recursive partitioning algorithm, starting with a single community and separating the nodes into two communities by spectral clustering repeatedly, until a stopping rule suggests there are no further communities. This class of algorithms is model-free, computationally effi…
We introduce a nonparametric prior on the conditional distribution of a (univariate or multivariate) response given a set of predictors. The prior is constructed in the form of a two-stage generative procedure, which in the first stage recursively partitions the predictor space, and then in the second stage generates the conditional distribution by a multi-scale nonparametric density model on each predictor partition block generated in the first stage. This design allows adaptive smoothing on both the predictor space and the response space, and it results in the full posterior conjugacy of the…
We consider the estimation of treatment effects in settings when multiple treatments are assigned over time and treatments can have a causal effect on future outcomes or the state of the treated unit. We propose an extension of the double/debiased machine learning framework to estimate the dynamic effects of treatments, which can be viewed as a Neyman orthogonal (locally robust) cross-fitted version of $g$-estimation in the dynamic treatment regime. Our method applies to a general class of non-linear dynamic treatment models known as Structural Nested Mean Models and allows the use of machine …
The University of Chicago（芝加哥大学）；University of Texas at Austin（德克萨斯大学奥斯汀分校）
Motivated by the rising abundance of observational data with continuous treatments, we investigate the problem of estimating the average dose-response curve (ADRF). Available parametric methods are limited in their model space, and previous attempts in leveraging neural network to enhance model expressiveness relied on partitioning continuous treatment into blocks and using separate heads for each block; this however produces in practice discontinuous ADRFs. Therefore, the question of how to adapt the structure and training of neural network to estimate ADRFs remains open. This paper makes two…
Adobe Research（Adobe研究院）；University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）
Treatment effect estimation is a fundamental problem in causal inference. We focus on designing efficient randomized controlled trials, to accurately estimate the effect of some treatment on a population of $n$ individuals. In particular, we study sample-constrained treatment effect estimation, where we must select a subset of $s \ll n$ individuals from the population to experiment on. This subset must be further partitioned into treatment and control groups. Algorithms for partitioning the entire population into treatment and control groups, or for choosing a single representative subset, hav…
University of Pittsburgh（匹兹堡大学）；Southwestern University of Finance and Economics（西南财经大学）
Accurately estimating personalized treatment effects within a study site (e.g., a hospital) has been challenging due to limited sample size. Furthermore, privacy considerations and lack of resources prevent a site from leveraging subject-level data from other sites. We propose a tree-based model averaging approach to improve the estimation accuracy of conditional average treatment effects (CATE) at a target site by leveraging models derived from other potentially heterogeneous sites, without them sharing subject-level data. To our best knowledge, there is no established model averaging approac…
There is strong interest in estimating how the magnitude of treatment effects of an intervention vary across sub-groups of the population of interest. In our paper, we propose a two-study approach to first propose and then test heterogeneous treatment effects. In Study 1, we use a large observational dataset to learn sub-groups with the most distinctive treatment-outcome relationships ('high/low-impact sub-groups'). We adopt a model-based recursive partitioning approach to propose the high/low impact sub-groups, and validate them by using sample-splitting. While the first study rules out noise…
We propose a simple recursive data-based partitioning scheme which produces piecewise-constant or piecewise-linear density estimates on intervals, and show how this scheme can determine the optimal $L_1$ minimax rate for some discrete nonparametric classes.
