Generalized propensity score approach to causal inference with spatial interference

Many spatial phenomena exhibit interference, where exposures at one location may affect the response at other locations. Because interference violates the stable unit treatment value assumption, standard methods for causal inference do not apply. We propose a new causal framework to recover direct and spill-over effects in the presence of spatial interference, taking into account that exposures at nearby locations are more influential than exposures at locations further apart. Under the no unmeasured confounding assumption, we show that a generalized propensity score is sufficient to remove all measured confounding. To reduce dimensionality issues, we propose a Bayesian spline-based regression model accounting for a sufficient set of variables for the generalized propensity score. A simulation study demonstrates the accuracy and coverage properties. We apply the method to estimate the causal effect of wildland fires on air pollution in the Western United States over 2005–2018.     

Assessing the Independent Contribution of Maternal Educational Expectations to Children’s Educational Attainment in Early Adulthood: A Propensity Score Matching Analysis

Background

Parental educational expectations have been associated with children’s educational attainment in a number of long-term longitudinal studies, but whether this relationship is causal has long been debated. The aims of this prospective study were twofold: 1) test whether low maternal educational expectations contributed to failure to graduate from high school; and 2) compare the results obtained using different strategies for accounting for confounding variables (i.e. multivariate regression and propensity score matching).

Methodology/Principal Findings

The study sample included 1,279 participants from the Quebec Longitudinal Study of Kindergarten Children. Maternal educational expectations were assessed when the participants were aged 12 years. High school graduation – measuring educational attainment – was determined through the Quebec Ministry of Education when the participants were aged 22–23 years. Findings show that when using the most common statistical approach (i.e. multivariate regressions to adjust for a restricted set of potential confounders) the contribution of low maternal educational expectations to failure to graduate from high school was statistically significant. However, when using propensity score matching, the contribution of maternal expectations was reduced and remained statistically significant only for males.

Conclusions/Significance

The results of this study are consistent with the possibility that the contribution of parental expectations to educational attainment is overestimated in the available literature. This may be explained by the use of a restricted range of potential confounding variables as well as the dearth of studies using appropriate statistical techniques and study designs in order to minimize confounding. Each of these techniques and designs, including propensity score matching, has its strengths and limitations: A more comprehensive understanding of the causal role of parental expectations will stem from a convergence of findings from studies using different techniques and designs.     

Ultra-high dimensional variable selection for doubly robust causal inference

Causal inference has been increasingly reliant on observational studies with rich covariate information. To build tractable causal procedures, such as the doubly robust estimators, it is imperative to first extract important features from high or even ultra-high dimensional data. In this paper, we propose causal ball screening for confounder selection from modern ultra-high dimensional data sets. Unlike the familiar task of variable selection for prediction modeling, our confounder selection procedure aims to control for confounding while improving efficiency in the resulting causal effect estimate. Previous empirical and theoretical studies suggest excluding causes of the treatment that are not confounders. Motivated by these results, our goal is to keep all the predictors of the outcome in both the propensity score and outcome regression models. A distinctive feature of our proposal is that we use an outcome model-free procedure for propensity score model selection, thereby maintaining double robustness in the resulting causal effect estimator. Our theoretical analyses show that the proposed procedure enjoys a number of properties, including model selection consistency and pointwise normality. Synthetic and real data analysis show that our proposal performs favorably with existing methods in a range of realistic settings. Data used in preparation of this paper were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database.     

Propensity score methods for time-dependent cluster confounding

In observational studies, subjects are often nested within clusters. In medical studies, patients are often treated by doctors and therefore patients are regarded as nested or clustered within doctors. A concern that arises with clustered data is that cluster-level characteristics (e.g., characteristics of the doctor) are associated with both treatment selection and patient outcomes, resulting in cluster-level confounding. Measuring and modeling cluster attributes can be difficult and statistical methods exist to control for all unmeasured cluster characteristics. An assumption of these methods however is that characteristics of the cluster and the effects of those characteristics on the outcome (as well as probability of treatment assignment when using covariate balancing methods) are constant over time. In this paper, we consider methods that relax this assumption and allow for estimation of treatment effects in the presence of unmeasured time-dependent cluster confounding. The methods are based on matching with the propensity score and incorporate unmeasured time-specific cluster effects by performing matching within clusters or using fixed- or random-cluster effects in the propensity score model. The methods are illustrated using data to compare the effectiveness of two total hip devices with respect to survival of the device and a simulation study is performed that compares the proposed methods. One method that was found to perform well is matching within surgeon clusters partitioned by time. Considerations in implementing the proposed methods are discussed.     

Sensitivity analysis for causal inference using inverse probability weighting

Evaluation of impact of potential uncontrolled confounding is an important component for causal inference based on observational studies. In this article, we introduce a general framework of sensitivity analysis that is based on inverse probability weighting. We propose a general methodology that allows both non‐parametric and parametric analyses, which are driven by two parameters that govern the magnitude of the variation of the multiplicative errors of the propensity score and their correlations with the potential outcomes. We also introduce a specific parametric model that offers a mechanistic view on how the uncontrolled confounding may bias the inference through these parameters. Our method can be readily applied to both binary and continuous outcomes and depends on the covariates only through the propensity score that can be estimated by any parametric or non‐parametric method. We illustrate our method with two medical data sets.     

Sensitivity analyses comparing outcomes only existing in a subset selected post-randomization, conditional on covariates, with application to HIV vaccine trials

In many experiments, researchers would like to compare between treatments and outcome that only exists in a subset of participants selected after randomization. For example, in preventive HIV vaccine efficacy trials it is of interest to determine whether randomization to vaccine causes lower HIV viral load, a quantity that only exists in participants who acquire HIV. To make a causal comparison and account for potential selection bias we propose a sensitivity analysis following the principal stratification framework set forth by Frangakis and Rubin (2002, Biometrics58, 21-29). Our goal is to assess the average causal effect of treatment assignment on viral load at a given baseline covariate level in the always infected principal stratum (those who would have been infected whether they had been assigned to vaccine or placebo). We assume stable unit treatment values (SUTVA), randomization, and that subjects randomized to the vaccine arm who became infected would also have become infected if randomized to the placebo arm (monotonicity). It is not known which of those subjects infected in the placebo arm are in the always infected principal stratum, but this can be modeled conditional on covariates, the observed viral load, and a specified sensitivity parameter. Under parametric regression models for viral load, we obtain maximum likelihood estimates of the average causal effect conditional on covariates and the sensitivity parameter. We apply our methods to the world's first phase III HIV vaccine trial.     

Evaluating Propensity Score Methods in a Quasi-Experimental Study of the Impact of Menu-Labeling

Background

Quasi-experimental studies of menu labeling have found mixed results for improving diet. Differences between experimental groups can hinder interpretation. Propensity scores are an increasingly common method to improve covariate balance, but multiple methods exist and the improvements associated with each method have rarely been compared. In this re-analysis of the impact of menu labeling, we compare multiple propensity score methods to determine which methods optimize balance between experimental groups.

Methods

Study participants included adult customers who visited full-service restaurants with menu labeling (treatment) and without (control). We compared the balance between treatment groups obtained by four propensity score methods: 1) 1:1 nearest neighbor matching (NN), 2) augmented 1:1 NN (using caliper of 0.2 and an exact match on an imbalanced covariate), 3) full matching, and 4) inverse probability weighting (IPW). We then evaluated the treatment effect on differences in nutrients purchased across the different methods.

Results

1:1 NN resulted in worse balance than the original unmatched sample (average standardized absolute mean distance [ASAM]: 0.185 compared to 0.171). Augmented 1:1 NN improved balance (ASAM: 0.038) but resulted in a large reduction in sample size. Full matching and IPW improved balance over the unmatched sample without a reduction in sample size (ASAM: 0.049 and 0.031, respectively). Menu labeling was associated with decreased calories, fat, sodium and carbohydrates in the unmatched analysis. Results were qualitatively similar in the propensity score matched/weighted models.

Conclusions

While propensity scores offer an increasingly popular tool to improve causal inference, choosing the correct method can be challenging. Our results emphasize the benefit of examining multiple methods to ensure results are consistent, and considering approaches beyond the most popular method of 1:1 NN matching.     

Correction of confounding bias in non-randomized studies by appropriate weighting

In non-randomized studies, the assessment of a causal effect of treatment or exposure on outcome is hampered by possible confounding. Applying multiple regression models including the effects of treatment and covariates on outcome is the well-known classical approach to adjust for confounding. In recent years other approaches have been promoted. One of them is based on the propensity score and considers the effect of possible confounders on treatment as a relevant criterion for adjustment. Another proposal is based on using an instrumental variable. Here inference relies on a factor, the instrument, which affects treatment but is thought to be otherwise unrelated to outcome, so that it mimics randomization. Each of these approaches can basically be interpreted as a simple reweighting scheme, designed to address confounding. The procedures will be compared with respect to their fundamental properties, namely, which bias they aim to eliminate, which effect they aim to estimate, and which parameter is modelled. We will expand our overview of methods for analysis of non-randomized studies to methods for analysis of randomized controlled trials and show that analyses of both study types may target different effects and different parameters. The considerations will be illustrated using a breast cancer study with a so-called Comprehensive Cohort Study design, including a randomized controlled trial and a non-randomized study in the same patient population as sub-cohorts. This design offers ideal opportunities to discuss and illustrate the properties of the different approaches.     

Bias-reduced estimators of conditional odds ratios in matched case-control studies with unmatched confounding

We study bias-reduced estimators of exponentially transformed parameters in general linear models (GLMs) and show how they can be used to obtain bias-reduced conditional (or unconditional) odds ratios in matched case-control studies. Two options are considered and compared: the explicit approach and the implicit approach. The implicit approach is based on the modified score function where bias-reduced estimates are obtained by using iterative procedures to solve the modified score equations. The explicit approach is shown to be a one-step approximation of this iterative procedure. To apply these approaches for the conditional analysis of matched case-control studies, with potentially unmatched confounding and with several exposures, we utilize the relation between the conditional likelihood and the likelihood of the unconditional logit binomial GLM for matched pairs and Cox partial likelihood for matched sets with appropriately setup data. The properties of the estimators are evaluated by using a large Monte Carlo simulation study and an illustration of a real dataset is shown. Researchers reporting the results on the exponentiated scale should use bias-reduced estimators since otherwise the effects can be under or overestimated, where the magnitude of the bias is especially large in studies with smaller sample sizes.     

Estimation of causal effects of a time-varying exposure at multiple time points through multivariable mendelian randomization

Mendelian Randomisation (MR) is a powerful tool in epidemiology that can be used to estimate the causal effect of an exposure on an outcome in the presence of unobserved confounding, by utilising genetic variants as instrumental variables (IVs) for the exposure. The effect estimates obtained from MR studies are often interpreted as the lifetime effect of the exposure in question. However, the causal effects of some exposures are thought to vary throughout an individual’s lifetime with periods during which an exposure has a greater effect on a particular outcome. Multivariable MR (MVMR) is an extension of MR that allows for multiple, potentially highly related, exposures to be included in an MR estimation. MVMR estimates the direct effect of each exposure on the outcome conditional on all the other exposures included in the estimation. We explore the use of MVMR to estimate the direct effect of a single exposure at different time points in an individual’s lifetime on an outcome. We use simulations to illustrate the interpretation of the results from such analyses and the key assumptions required. We show that causal effects at different time periods can be estimated through MVMR when the association between the genetic variants used as instruments and the exposure measured at those time periods varies. However, this estimation will not necessarily identify exact time periods over which an exposure has the most effect on the outcome. Prior knowledge regarding the biological basis of exposure trajectories can help interpretation. We illustrate the method through estimation of the causal effects of childhood and adult BMI on C-Reactive protein and smoking behaviour.     

Bayesian propensity scores for high‐dimensional causal inference: A comparison of drug‐eluting to bare‐metal coronary stents

High‐dimensional data provide many potential confounders that may bolster the plausibility of the ignorability assumption in causal inference problems. Propensity score methods are powerful causal inference tools, which are popular in health care research and are particularly useful for high‐dimensional data. Recent interest has surrounded a Bayesian treatment of propensity scores in order to flexibly model the treatment assignment mechanism and summarize posterior quantities while incorporating variance from the treatment model. We discuss methods for Bayesian propensity score analysis of binary treatments, focusing on modern methods for high‐dimensional Bayesian regression and the propagation of uncertainty. We introduce a novel and simple estimator for the average treatment effect that capitalizes on conjugacy of the beta and binomial distributions. Through simulations, we show the utility of horseshoe priors and Bayesian additive regression trees paired with our new estimator, while demonstrating the importance of including variance from the treatment regression model. An application to cardiac stent data with almost 500 confounders and 9000 patients illustrates approaches and facilitates comparison with existing alternatives. As measured by a falsifiability endpoint, we improved confounder adjustment compared with past observational research of the same problem.     

Mendelian randomization in health research: Using appropriate genetic variants and avoiding biased estimates

Mendelian randomization methods, which use genetic variants as instrumental variables for exposures of interest to overcome problems of confounding and reverse causality, are becoming widespread for assessing causal relationships in epidemiological studies. The main purpose of this paper is to demonstrate how results can be biased if researchers select genetic variants on the basis of their association with the exposure in their own dataset, as often happens in candidate gene analyses. This can lead to estimates that indicate apparent “causal” relationships, despite there being no true effect of the exposure. In addition, we discuss the potential bias in estimates of magnitudes of effect from Mendelian randomization analyses when the measured exposure is a poor proxy for the true underlying exposure. We illustrate these points with specific reference to tobacco research.     

Estimating treatment effects with partially observed covariates using outcome regression with missing indicators

Missing data is a common issue in research using observational studies to investigate the effect of treatments on health outcomes. When missingness occurs only in the covariates, a simple approach is to use missing indicators to handle the partially observed covariates. The missing indicator approach has been criticized for giving biased results in outcome regression. However, recent papers have suggested that the missing indicator approach can provide unbiased results in propensity score analysis under certain assumptions. We consider assumptions under which the missing indicator approach can provide valid inferences, namely, (1) no unmeasured confounding within missingness patterns; either (2a) covariate values of patients with missing data were conditionally independent of treatment or (2b) these values were conditionally independent of outcome; and (3) the outcome model is correctly specified: specifically, the true outcome model does not include interactions between missing indicators and fully observed covariates. We prove that, under the assumptions above, the missing indicator approach with outcome regression can provide unbiased estimates of the average treatment effect. We use a simulation study to investigate the extent of bias in estimates of the treatment effect when the assumptions are violated and we illustrate our findings using data from electronic health records. In conclusion, the missing indicator approach can provide valid inferences for outcome regression, but the plausibility of its assumptions must first be considered carefully.     

A Propensity Score-Enhanced Sequential Analytic Method for Comparative Drug Safety Surveillance

We introduce a new sequential monitoring approach to facilitate the use of observational electronic healthcare utilization databases in comparative drug safety surveillance studies comparing the safety between two approved medical products. The new approach enhances the confounder adjustment capabilities of the conditional sequential sampling procedure (CSSP), an existing group sequential method for sequentially monitoring excess risks of adverse events following the introduction of a new medical product. It applies to a prospective cohort setting where information for both treatment and comparison groups accumulates concurrently over time. CSSP adjusts for covariates through stratification and thus it may have limited capacity to control for confounding as it can only accommodate a few categorical covariates. To address this issue, we propose the propensity score (PS)-stratified CSSP, in which we construct strata based on selected percentiles of the estimated PSs. The PS is defined as the conditional probability of being treated given measured baseline covariates and is commonly used in epidemiological studies to adjust for confounding bias. The PS-stratified CSSP approach integrates this more flexible confounding adjustment, PS-stratification, with the sequential analytic approach, CSSP, thus inheriting CSSP’s attractive features: (i) it accommodates varying amounts of person follow-up time, (ii) it uses exact conditional inference, which can be important when studying rare safety outcomes, and (iii) it allows for a large number of interim tests. Further, it overcomes CSSP’s difficulty with adjusting for multiple categorical and continuous confounders.     

Model misspecification and bias for inverse probability weighting estimators of average causal effects

Commonly used semiparametric estimators of causal effects specify parametric models for the propensity score (PS) and the conditional outcome. An example is an augmented inverse probability weighting (IPW) estimator, frequently referred to as a doubly robust estimator, because it is consistent if at least one of the two models is correctly specified. However, in many observational studies, the role of the parametric models is often not to provide a representation of the data-generating process but rather to facilitate the adjustment for confounding, making the assumption of at least one true model unlikely to hold. In this paper, we propose a crude analytical approach to study the large-sample bias of estimators when the models are assumed to be approximations of the data-generating process, namely, when all models are misspecified. We apply our approach to three prototypical estimators of the average causal effect, two IPW estimators, using a misspecified PS model, and an augmented IPW (AIPW) estimator, using misspecified models for the outcome regression (OR) and the PS. For the two IPW estimators, we show that normalization, in addition to having a smaller variance, also offers some protection against bias due to model misspecification. To analyze the question of when the use of two misspecified models is better than one we derive necessary and sufficient conditions for when the AIPW estimator has a smaller bias than a simple IPW estimator and when it has a smaller bias than an IPW estimator with normalized weights. If the misspecification of the outcome model is moderate, the comparisons of the biases of the IPW and AIPW estimators show that the AIPW estimator has a smaller bias than the IPW estimators. However, all biases include a scaling with the PS-model error and we suggest caution in modeling the PS whenever such a model is involved. For numerical and finite sample illustrations, we include three simulation studies and corresponding approximations of the large-sample biases. In a dataset from the National Health and Nutrition Examination Survey, we estimate the effect of smoking on blood lead levels.     

A randomization-based causal inference framework for uncovering environmental exposure effects on human gut microbiota

Statistical analysis of microbial genomic data within epidemiological cohort studies holds the promise to assess the influence of environmental exposures on both the host and the host-associated microbiome. However, the observational character of prospective cohort data and the intricate characteristics of microbiome data make it challenging to discover causal associations between environment and microbiome. Here, we introduce a causal inference framework based on the Rubin Causal Model that can help scientists to investigate such environment-host microbiome relationships, to capitalize on existing, possibly powerful, test statistics, and test plausible sharp null hypotheses. Using data from the German KORA cohort study, we illustrate our framework by designing two hypothetical randomized experiments with interventions of (i) air pollution reduction and (ii) smoking prevention. We study the effects of these interventions on the human gut microbiome by testing shifts in microbial diversity, changes in individual microbial abundances, and microbial network wiring between groups of matched subjects via randomization-based inference. In the smoking prevention scenario, we identify a small interconnected group of taxa worth further scrutiny, including Christensenellaceae and Ruminococcaceae genera, that have been previously associated with blood metabolite changes. These findings demonstrate that our framework may uncover potentially causal links between environmental exposure and the gut microbiome from observational data. We anticipate the present statistical framework to be a good starting point for further discoveries on the role of the gut microbiome in environmental health.     

Risk Factor Adjustment in Marginal Structural Model Estimation of Optimal Treatment Regimes

Marginal structural models (MSMs) are an increasingly popular tool, particularly in epidemiological applications, to handle the problem of time‐varying confounding by intermediate variables when studying the effect of sequences of exposures. Considerable attention has been devoted to the optimal choice of treatment model for propensity score‐based methods and, more recently, to variable selection in the treatment model for inverse weighting in MSMs. However, little attention has been paid to the modeling of the outcome of interest, particularly with respect to the best use of purely predictive, non‐confounding variables in MSMs. Four modeling approaches are investigated in the context of both static treatment sequences and optimal dynamic treatment rules with the goal of estimating a marginal effect with the least error, both in terms of bias and variability.     

Causal mediation analysis in nested case-control studies using conditional logistic regression

The paper proposes an approach to causal mediation analysis in nested case-control study designs, often incorporated with countermatching schemes using conditional likelihood, and we compare the method's performance to that of mediation analysis using the Cox model for the full cohort with a continuous or dichotomous mediator. Simulation studies are conducted to assess our proposed method and investigate the efficiency relative to the cohort. We illustrate the method using actual data from two studies of potential mediation of radiation risk conducted within the Adult Health Study cohort of atomic-bomb survivors. The performance becomes comparable to that based on the full cohort, illustrating the potential for valid mediation analysis based on the reduced data obtained through the nested case-control design.     

Optimal Caliper Width for Propensity Score Matching of Three Treatment Groups: A Monte Carlo Study

Propensity score matching is a method to reduce bias in non-randomized and observational studies. Propensity score matching is mainly applied to two treatment groups rather than multiple treatment groups, because some key issues affecting its application to multiple treatment groups remain unsolved, such as the matching distance, the assessment of balance in baseline variables, and the choice of optimal caliper width. The primary objective of this study was to compare propensity score matching methods using different calipers and to choose the optimal caliper width for use with three treatment groups. The authors used caliper widths from 0.1 to 0.8 of the pooled standard deviation of the logit of the propensity score, in increments of 0.1. The balance in baseline variables was assessed by standardized difference. The matching ratio, relative bias, and mean squared error (MSE) of the estimate between groups in different propensity score-matched samples were also reported. The results of Monte Carlo simulations indicate that matching using a caliper width of 0.2 of the pooled standard deviation of the logit of the propensity score affords superior performance in the estimation of treatment effects. This study provides practical solutions for the application of propensity score matching of three treatment groups.