There is an increasing interest in estimating heterogeneity in causal effects in randomized and observational studies. However, little research has been conducted to understand heterogeneity in an instrumental variables study. In this work, we present a method to estimate heterogeneous causal effects using an instrumental variable approach. The method has two parts. The first part uses subject-matter knowledge and interpretable machine learning techniques, such as classification and regression trees, to discover potential effect modifiers. The second part uses closed testing to test for the statistical significance of the effect modifiers while strongly controlling familywise error rate. We conducted this method on the Oregon Health Insurance Experiment, estimating the effect of Medicaid on the number of days an individual's health does not impede their usual activities, and found evidence of heterogeneity in older men who prefer English and don't self-identify as Asian and younger individuals who have at most a high school diploma or GED and prefer English.
We investigate the efficacy of surgical versus non-surgical management for two gastrointestinal conditions, colitis and diverticulitis, using observational data. We deploy an instrumental variable design with surgeons' tendencies to operate as an instrument. Assuming instrument validity, we find that non-surgical alternatives can reduce both hospital length of stay and the risk of complications, with estimated effects larger for septic patients than for non-septic patients. The validity of our instrument is plausible but not ironclad, necessitating a sensitivity analysis. Existing sensitivity …
Instrumental variable analysis is a widely used method to estimate causal effects in the presence of unmeasured confounding. When the instruments, exposure and outcome are not measured in the same sample, Angrist and Krueger (1992) suggested to use two-sample instrumental variable (TSIV) estimators that use sample moments from an instrument-exposure sample and an instrument-outcome sample. However, this method is biased if the two samples are from heterogeneous populations so that the distributions of the instruments are different. In linear structural equation models, we derive a new class of…
Harvard University（哈佛大学）；KU Leuven（鲁汶大学）；IMT School for Advanced Studies（IMT高等研究院）
This paper introduces an innovative Bayesian machine learning algorithm to draw interpretable inference on heterogeneous causal effects in the presence of imperfect compliance (e.g., under an irregular assignment mechanism). We show, through Monte Carlo simulations, that the proposed Bayesian Causal Forest with Instrumental Variable (BCF-IV) methodology outperforms other machine learning techniques tailored for causal inference in discovering and estimating the heterogeneous causal effects while controlling for the familywise error rate (or - less stringently - for the false discovery rate) at…
This paper studies the identifying power of an instrumental variable in the nonparametric heterogeneous treatment effect framework when a binary treatment is mismeasured and endogenous. Using a binary instrumental variable, I characterize the sharp identified set for the local average treatment effect under the exclusion restriction of an instrument and the deterministic monotonicity of the true treatment in the instrument. Even allowing for general measurement error (e.g., the measurement error is endogenous), it is still possible to obtain finite bounds on the local average treatment effect.…
Instrumental variable methods are widely used in medical and social science research to draw causal conclusions when the treatment and outcome are confounded by unmeasured confounding variables. One important feature of such studies is that the instrumental variable is often applied at the cluster level, e.g., hospitals' or physicians' preference for a certain treatment where each hospital or physician naturally defines a cluster. This paper proposes to embed such observational instrumental variable data into a cluster-randomized encouragement experiment using statistical matching. Potential o…
To effectively optimize and personalize treatments, it is necessary to investigate the heterogeneity of treatment effects. With the wide range of users being treated over many online controlled experiments, the typical approach of manually investigating each dimension of heterogeneity becomes overly cumbersome and prone to subjective human biases. We need an efficient way to search through thousands of experiments with hundreds of target covariates and hundreds of breakdown dimensions. In this paper, we propose a systematic paradigm for detecting, surfacing and characterizing heterogeneous tre…
This paper provides a link between causal inference and machine learning techniques - specifically, Classification and Regression Trees (CART) - in observational studies where the receipt of the treatment is not randomized, but the assignment to the treatment can be assumed to be randomized (irregular assignment mechanism). The paper contributes to the growing applied machine learning literature on causal inference, by proposing a modified version of the Causal Tree (CT) algorithm to draw causal inference from an irregular assignment mechanism. The proposed method is developed by merging the C…
What should researchers do when their baseline model is refuted? We provide four constructive answers. First, researchers can measure the extent of falsification. To do this, we consider continuous relaxations of the baseline assumptions of concern. We then define the falsification frontier: The smallest relaxations of the baseline model which are not refuted. This frontier provides a quantitative measure of the extent of falsification. Second, researchers can present the identified set for the parameter of interest under the assumption that the true model lies somewhere on this frontier. We c…
Suppose one is interested in estimating causal effects in the presence of potentially unmeasured confounding with the aid of a valid instrumental variable. This paper investigates the problem of making inferences about the average treatment effect when data are fused from two separate sources, one of which contains information on the treatment and the other contains information on the outcome, while values for the instrument and a vector of baseline covariates are recorded in both. We provide a general set of sufficient conditions under which the average treatment effect is nonparametrically i…
Unobserved heterogeneous treatment effects have been emphasized in recent policy evaluation literature. In this paper, we extend Lu and White (2014)'s testing method for unobserved heterogeneous treatment effects by developing nonparametric tests under the standard exogenous instrumental variable assumption and allowing for endogenous treatment. Specifically, we propose Kolmogorov--Smirnov--type statistics that are consistent and simple to implement. To illustrate, we apply the proposed test method with two empirical applications: treatment effects of job training program on earnings as well a…
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）
Mendelian randomization is the use of genetic variants to make causal inferences from observational data. The field is currently undergoing a revolution fuelled by increasing numbers of genetic variants demonstrated to be associated with exposures in genome-wide association studies, and the public availability of summarized data on genetic associations with exposures and outcomes from large consortia. A Mendelian randomization analysis with many genetic variants can be performed relatively simply using summarized data. However, a causal interpretation is only assured if each genetic variant sa…
This paper studies treatment effect models in which individuals are classified into unobserved groups based on heterogeneous treatment rules. Using a finite mixture approach, we propose a marginal treatment effect (MTE) framework in which the treatment choice and outcome equations can be heterogeneous across groups. Under the availability of instrumental variables specific to each group, we show that the MTE for each group can be separately identified. Based on our identification result, we propose a two-step semiparametric procedure for estimating the group-wise MTE. We illustrate the usefuln…
This paper proposes computationally efficient methods that can be used for instrumental variable quantile regressions (IVQR) and related methods with statistical guarantees. This is much needed when we investigate heterogenous treatment effects since interactions between the endogenous treatment and control variables lead to an increased number of endogenous covariates. We prove that the GMM formulation of IVQR is NP-hard and finding an approximate solution is also NP-hard. Hence, solving the problem from a purely computational perspective seems unlikely. Instead, we aim to obtain an estimate …
We consider the problem of predicting a response variable from a set of covariates on a data set that differs in distribution from the training data. Causal parameters are optimal in terms of predictive accuracy if in the new distribution either many variables are affected by interventions or only some variables are affected, but the perturbations are strong. If the training and test distributions differ by a shift, causal parameters might be too conservative to perform well on the above task. This motivates anchor regression, a method that makes use of exogeneous variables to solve a relaxati…
Mendelian Randomization (MR) is a popular method in epidemiology and genetics that uses genetic variation as instrumental variables for causal inference. Existing MR methods usually assume most genetic variants are valid instrumental variables that identify a common causal effect. There is a general lack of awareness that this effect homogeneity assumption can be violated when there are multiple causal pathways involved, even if all the instrumental variables are valid. In this article, we introduce a latent mixture model MR-PATH that groups instruments that yield similar causal effect estimat…
From personalised medicine to targeted advertising, it is an inherent task to provide a sequence of decisions with historical covariates and outcome data. This requires understanding of both the dynamics and heterogeneity of treatment effects. In this paper, we are concerned with detecting abrupt changes in the treatment effects in terms of the conditional average treatment effect (CATE) in a sequential fashion. To be more specific, at each time point, we consider a nonparametric model to allow for maximal flexibility and robustness. Along the time, we allow for temporal dependence on historic…
We propose a kernel-based partial permutation test for checking the equality of functional relationship between response and covariates among different groups. The main idea, which is intuitive and easy to implement, is to keep the projections of the response vector $\boldsymbol{Y}$ on leading principle components of a kernel matrix fixed and permute $\boldsymbol{Y}$'s projections on the remaining principle components. The proposed test allows for different choices of kernels, corresponding to different classes of functions under the null hypothesis. First, using linear or polynomial kernels, …
One of the fundamental task in graph data mining is to find a planted community(dense subgraph), which has wide application in biology, finance, spam detection and so on. For a real network data, the existence of a dense subgraph is generally unknown. Statistical tests have been devised to testing the existence of dense subgraph in a homogeneous random graph. However, many networks present extreme heterogeneity, that is, the degrees of nodes or vertexes don't concentrate on a typical value. The existing tests designed for homogeneous random graph are not straightforwardly applicable to the het…
