Propensity score methods were proposed by Rosenbaum and Rubin [Biometrika 70 (1983) 41--55] as central tools to help assess the causal effects of interventions. Since their introduction more than two decades ago, they have found wide application in a variety of areas, including medical research, economics, epidemiology and education, especially in those situations where randomized experiments are either difficult to perform, or raise ethical questions, or would require extensive delays before answers could be obtained. In the past few years, the number of published applications using propensity score methods to evaluate medical and epidemiological interventions has increased dramatically. Nevertheless, thus far, we believe that there have been few applications of propensity score methods to evaluate marketing interventions (e.g., advertising, promotions), where the tradition is to use generally inappropriate techniques, which focus on the prediction of an outcome from background characteristics and an indicator for the intervention using statistical tools such as least-squares regression, data mining, and so on. With these techniques, an estimated parameter in the model is used to estimate some global ``causal'' effect. This practice can generate grossly incorrect answers that can be self-perpetuating: polishing the Ferraris rather than the Jeeps ``causes'' them to continue to win more races than the Jeeps $\Leftrightarrow$ visiting the high-prescribing doctors rather than the low-prescribing doctors ``causes'' them to continue to write more prescriptions. This presentation will take ``causality'' seriously, not just as a casual concept implying some predictive association in a data set, and will illustrate why propensity score methods are generally superior in practice to the standard predictive approaches for estimating causal effects.
This article provides an assessment of the causal effect of customer relationship management (CRM) applications on one-to-one marketing effectiveness. We use a potential outcomes based propensity score approach to assess this causal effect. We find that firms using CRM systems have greater levels of one-to-one marketing effectiveness. We discuss the strengths and challenges of using the propensity score approach to design and execute CRM related observational studies. We also discuss the applicability of the framework in this paper to study typical causal questions in business and electronic c…
Most work in causal inference considers deterministic interventions that set each unit's treatment to some fixed value. However, under positivity violations these interventions can lead to non-identification, inefficiency, and effects with little practical relevance. Further, corresponding effects in longitudinal studies are highly sensitive to the curse of dimensionality, resulting in widespread use of unrealistic parametric models. We propose a novel solution to these problems: incremental interventions that shift propensity score values rather than set treatments to fixed values. Incrementa…
In observational clinic registries, time to treatment is often of interest, but treatment can be given at any time during follow-up and there is no structure or intervention to ensure regular clinic visits for data collection. To address these challenges, we introduce the time-dependent propensity process as a generalization of the propensity score. We show that the propensity process balances the entire time-varying covariate history which cannot be achieved by existing propensity score methods and that treatment assignment is strongly ignorable conditional on the propensity process. We devel…
We apply causal machine learning algorithms to assess the causal effect of a marketing intervention, namely a coupon campaign, on the sales of a retailer. Besides assessing the average impacts of different types of coupons, we also investigate the heterogeneity of causal effects across different subgroups of customers, e.g., between clients with relatively high vs. low prior purchases. Finally, we use optimal policy learning to determine (in a data-driven way) which customer groups should be targeted by the coupon campaign in order to maximize the marketing intervention's effectiveness in term…
Incremental Propensity Score Effects for Criminology: An Application Assessing the Relationship Between Homelessness, Behavioral Health Problems, and Recidivism
Observational cohort studies with oversampled exposed subjects are typically implemented to understand the causal effect of a rare exposure. Because the distribution of exposed subjects in the sample differs from the source population, estimation of a propensity score function (i.e., probability of exposure given baseline covariates) targets a nonparametrically nonidentifiable parameter. Consistent estimation of propensity score functions is an important component of various causal inference estimators, including double robust machine learning and inverse probability weighted estimators. This …
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；University of Oxford（牛津大学）；Alan Turing Institute（艾伦·图灵研究所）
We propose a novel approach for inferring the individualized causal effects of a treatment (intervention) from observational data. Our approach conceptualizes causal inference as a multitask learning problem; we model a subject's potential outcomes using a deep multitask network with a set of shared layers among the factual and counterfactual outcomes, and a set of outcome-specific layers. The impact of selection bias in the observational data is alleviated via a propensity-dropout regularization scheme, in which the network is thinned for every training example via a dropout probability that …
The generalized propensity score (GPS) is an extension of the propensity score for use with quantitative or continuous exposures (e.g., dose of medication or years of education). Current GPS methods allow estimation of the dose-response relationship between a single continuous exposure and an outcome. However, in many real-world settings, there are multiple exposures occurring simultaneously that could be causally related to the outcome. We propose a multivariate GPS method (mvGPS) that allows estimation of a dose-response surface that relates the joint distribution of multiple continuous expo…
Chance imbalance in baseline characteristics is common in randomized clinical trials. Regression adjustment such as the analysis of covariance (ANCOVA) is often used to account for imbalance and increase precision of the treatment effect estimate. An objective alternative is through inverse probability weighting (IPW) of the propensity scores. Although IPW and ANCOVA are asymptotically equivalent, the former may demonstrate inferior performance in finite samples. In this article, we point out that IPW is a special case of the general class of balancing weights, and advocate to use overlap weig…
Causal inference methods are widely applied in various decision-making domains such as precision medicine, optimal policy and economics. Central to these applications is the treatment effect estimation of intervention strategies. Current estimation methods are mostly restricted to the deterministic treatment, which however, is unable to address the stochastic space treatment policies. Moreover, previous methods can only make binary yes-or-no decisions based on the treatment effect, lacking the capability of providing fine-grained effect estimation degree to explain the process of decision maki…
Randomized clinical trials are considered the gold standard for estimating causal effects. Nevertheless, in studies that are aimed at examining adverse effects of interventions, such trials are often impractical because of ethical and financial considerations. In observational studies, matching on the generalized propensity scores was proposed as a possible solution to estimate the treatment effects of multiple interventions. However, the derivation of point and interval estimates for these matching procedures can become complex with non-continuous or censored outcomes. We propose a novel Appr…
Coronavirus disease 2019 (COVID-19) pandemic is an unprecedented global public health challenge. In the United States (US), state governments have implemented various non-pharmaceutical interventions (NPIs), such as physical distance closure (lockdown), stay-at-home order, mandatory facial mask in public in response to the rapid spread of COVID-19. To evaluate the effectiveness of these NPIs, we propose a nested case-control design with propensity score weighting under the quasi-experiment framework to estimate the average intervention effect on disease transmission across states. We further d…
Modern longitudinal studies collect feature data at many timepoints, often of the same order of sample size. Such studies are typically affected by {dropout} and positivity violations. We tackle these problems by generalizing effects of recent incremental interventions (which shift propensity scores rather than set treatment values deterministically) to accommodate multiple outcomes and subject dropout. We give an identifying expression for incremental intervention effects when dropout is conditionally ignorable (without requiring treatment positivity), and derive the nonparametric efficiency …
Georgia Institute of Technology（佐治亚理工学院）；Microsoft Research India（微软印度研究院）；Microsoft（微软）；Microsoft Research AI（微软人工智能研究院）
For many kinds of interventions, such as a new advertisement, marketing intervention, or feature recommendation, it is important to target a specific subset of people for maximizing its benefits at minimum cost or potential harm. However, a key challenge is that no data is available about the effect of such a prospective intervention since it has not been deployed yet. In this work, we propose a split-treatment analysis that ranks the individuals most likely to be positively affected by a prospective intervention using past observational data. Unlike standard causal inference methods, the spli…
Transport operators have a range of intervention options available to improve or enhance their networks. Such interventions are often made in the absence of sound evidence on resulting outcomes. Cycling superhighways were promoted as a sustainable and healthy travel mode, one of the aims of which was to reduce traffic congestion. Estimating the impacts that cycle superhighways have on congestion is complicated due to the non-random assignment of such intervention over the transport network. In this paper, we analyse the causal effect of cycle superhighways utilising pre-intervention and post-i…
In this chapter, we review the class of causal effects based on incremental propensity scores interventions proposed by Kennedy [2019]. The aim of incremental propensity score interventions is to estimate the effect of increasing or decreasing subjects' odds of receiving treatment; this differs from the average treatment effect, where the aim is to estimate the effect of everyone deterministically receiving versus not receiving treatment. We first present incremental causal effects for the case when there is a single binary treatment, such that it can be compared to average treatment effects a…
Evaluating air quality interventions is confronted with the challenge of interference since interventions at a particular pollution source likely impact air quality and health at distant locations and air quality and health at any given location are likely impacted by interventions at many sources. The structure of interference in this context is dictated by complex atmospheric processes governing how pollution emitted from a particular source is transformed and transported across space, and can be cast with a bipartite structure reflecting the two distinct types of units: 1) interventional un…
Inverse probability of treatment weighting (IPTW), which has been used to estimate sample average treatment effects (SATE) using observational data, tenuously relies on the positivity assumption and the correct specification of the treatment assignment model, both of which are problematic assumptions in many observational studies. Various methods have been proposed to overcome these challenges, including truncation, covariate-balancing propensity scores, and stable balancing weights. Motivated by an observational study in spine surgery, in which positivity is violated and the true treatment as…
Uplift is a particular case of individual treatment effect modeling. Such models deal with cause-and-effect inference for a specific factor, such as a marketing intervention. In practice, these models are built on customer data who purchased products or services to improve product marketing. Uplift is estimated using either i) conditional mean regression or ii) transformed outcome regression. Most existing approaches are adaptations of classification and regression trees for the uplift case. However, in practice, these conventional approaches are prone to overfitting. Here we propose a new met…
Estimating average causal effect (ACE) is useful whenever we want to know the effect of an intervention on a given outcome. In the absence of a randomized experiment, many methods such as stratification and inverse propensity weighting have been proposed to estimate ACE. However, it is hard to know which method is optimal for a given dataset or which hyperparameters to use for a chosen method. To this end, we provide a framework to characterize the loss of a causal inference method against the true ACE, by framing causal inference as a representation learning problem. We show that many popular…
The methodological development of this paper is motivated by the need to address the following scientific question: does the issuance of heat alerts prevent adverse health effects? Our goal is to address this question within a causal inference framework in the context of time series data. A key challenge is that causal inference methods require the overlap assumption to hold: each unit (i.e., a day) must have a positive probability of receiving the treatment (i.e., issuing a heat alert on that day). In our motivating example, the overlap assumption is often violated: the probability of issuing…
Causal inference has numerous real-world applications in many domains, such as health care, marketing, political science, and online advertising. Treatment effect estimation, a fundamental problem in causal inference, has been extensively studied in statistics for decades. However, traditional treatment effect estimation methods may not well handle large-scale and high-dimensional heterogeneous data. In recent years, an emerging research direction has attracted increasing attention in the broad artificial intelligence field, which combines the advantages of traditional treatment effect estimat…
Conformal Convolution and Monte Carlo Meta-learners for Predictive Inference of Individual Treatment Effects
IDLab Department of Electronics and Information Systems Ghent University, Belgium（IDLab电子与信息系统系根特大学，比利时）；IDLab Department of Electronics and Information Systems Ghent University - imec, Belgium（IDLab电子与信息系统系根特大学-imec，比利时）；Biometrics Research Group Department of Morphology, Imaging, Orthopedics, Rehabilitation and Nutrition Ghent University, Belgium（生物医学研究组形态学、成像、骨科、康复与营养系根特大学，比利时）
We examine the effect of the Philadelphia LandCare (PLC) vacant lot greening initiative on crime and the extent to which surrounding land uses and business types moderate this intervention. We rely on a propensity score matching analysis to account for substantial differences in demographic, economic, land use, and business characteristics between greened and ungreened vacant lots. We estimate larger and more significant crime reductions around vacant lots that are greened in our matched pairs analysis compared to unmatched analyses. The effects of vacant lot greening on crime are larger in ar…
Although review papers on causal inference methods are now available, there is a lack of introductory overviews on what they can render and on the guiding criteria for choosing one particular method. This tutorial gives an overview in situations where an exposure of interest is set at a chosen baseline (`point exposure') and the target outcome arises at a later time point. We first phrase relevant causal questions and make a case for being specific about the possible exposure levels involved and the populations for which the question is relevant. Using the potential outcomes framework, we desc…
University of South Australia（南澳大学）；School of Computer and Information, Hefei University of Science and Technology（合肥理工大学计算机与信息学院）
In many applications, there is a need to predict the effect of an intervention on different individuals from data. For example, which customers are persuadable by a product promotion? which patients should be treated with a certain type of treatment? These are typical causal questions involving the effect or the change in outcomes made by an intervention. The questions cannot be answered with traditional classification methods as they only use associations to predict outcomes. For personalised marketing, these questions are often answered with uplift modelling. The objective of uplift modellin…
Orthogonal Uplift Learning with Permutation-Invariant Representations for Combinatorial Treatments
Didi Chuxing（滴滴出行）；School of Statistics, East China Normal University（华东师范大学统计学院）；School of Mathematics and Statistics, Beijing Jiaotong University（北京交通大学数学与统计学院）；School of Statistics and Data Science, Shanghai University of Finance and Economics（上海财经大学统计与数据科学学院）；Institute of Data Science and Statistics, Shanghai University of Finance and Economics（上海财经大学数据科学与统计研究院）
This paper quantifies the effect of speed cameras on road traffic collisions using an approximate Bayesian doubly-robust (DR) causal inference estimation method. Previous empirical work on this topic, which shows a diverse range of estimated effects, is based largely on outcome regression (OR) models using the Empirical Bayes approach or on simple before and after comparisons. Issues of causality and confounding have received little formal attention. A causal DR approach combines propensity score (PS) and OR models to give an average treatment effect (ATE) estimator that is consistent and asym…
Policy evaluation studies, which intend to assess the effect of an intervention, face some statistical challenges: in real-world settings treatments are not randomly assigned and the analysis might be further complicated by the presence of interference between units. Researchers have started to develop novel methods that allow to manage spillover mechanisms in observational studies; recent works focus primarily on binary treatments. However, many policy evaluation studies deal with more complex interventions. For instance, in political science, evaluating the impact of policies implemented by …
Institute for Analytical Sociology（分析社会学研究所）；Linköping University（林雪平大学）；Chalmers University of Technology（查尔姆斯理工大学）
Observational studies of causal effects require adjustment for confounding factors. In the tabular setting, where these factors are well-defined, separate random variables, the effect of confounding is well understood. However, in public policy, ecology, and in medicine, decisions are often made in non-tabular settings, informed by patterns or objects detected in images (e.g., maps, satellite or tomography imagery). Using such imagery for causal inference presents an opportunity because objects in the image may be related to the treatment and outcome of interest. In these cases, we rely on the…
The weighted average treatment effect (WATE) is a causal measure for the comparison of interventions in a specific target population, which may be different from the population where data are sampled from. For instance, when the goal is to introduce a new treatment to a target population, the question is what efficacy (or effectiveness) can be gained by switching patients from a standard of care (control) to this new treatment, for which the average treatment effect for the control (ATC) estimand can be applied. In this paper, we propose two estimators based on augmented inverse probability we…
