arXiv subjects

Elizabeth A. Stuart

Publications and source records attributed to Elizabeth A. Stuart.

49 records · Page 3Linked to original sources

arXiv2020

Partially Pooled Propensity Score Models for Average Treatment Effect Estimation with Multilevel Data

Causal inference analyses often use existing observational data, which in many cases has some clustering of individuals. In this paper we discuss propensity score weighting methods in a multilevel setting where within clusters individuals share unmeasured confounders that are related to treatment assignment and the potential outcomes. We focus in particular on settings where models with fixed cluster effects are either not feasible or not useful due to the presence of a large number of small clusters. We found, both through numerical experiments and theoretical derivations, that a strategy of grouping clusters with similar treatment prevalence and estimating propensity scores within such cluster groups is effective in reducing bias from unmeasured cluster-level covariates under mild conditions on the outcome model. We apply our proposed method in evaluating the effectiveness of center-based pre-school program participation on children's achievement at kindergarten, using the Early Childhood Longitudinal Study, Kindergarten data.

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arXiv2020

Sensitivity analyses for effect modifiers not observed in the target population when generalizing treatment effects from a randomized controlled trial: Assumptions, models, effect scales, data scenarios, and implementation details

Background: Randomized controlled trials are often used to inform policy and practice for broad populations. The average treatment effect (ATE) for a target population, however, may be different from the ATE observed in a trial if there are effect modifiers whose distribution in the target population is different that from that in the trial. Methods exist to use trial data to estimate the target population ATE, provided the distributions of treatment effect modifiers are observed in both the trial and target population -- an assumption that may not hold in practice. Methods: The proposed sensitivity analyses address the situation where a treatment effect modifier is observed in the trial but not the target population. These methods are based on an outcome model or the combination of such a model and weighting adjustment for observed differences between the trial sample and target population. They accommodate several types of outcome models: linear models (including single time outcome and pre- and post-treatment outcomes) for additive effects, and models with log or logit link for multiplicative effects. We clarify the methods' assumptions and provide detailed implementation instructions. Illustration: We illustrate the methods using an example generalizing the effects of an HIV treatment regimen from a randomized trial to a relevant target population. Conclusion: These methods allow researchers and decision-makers to have more appropriate confidence when drawing conclusions about target population effects.

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arXiv2020

A trial emulation approach for policy evaluations with group-level longitudinal data

To limit the spread of the novel coronavirus, governments across the world implemented extraordinary physical distancing policies, such as stay-at-home orders, and numerous studies aim to estimate their effects. Many statistical and econometric methods, such as difference-in-differences, leverage repeated measurements and variation in timing to estimate policy effects, including in the COVID-19 context. While these methods are less common in epidemiology, epidemiologic researchers are well accustomed to handling similar complexities in studies of individual-level interventions. "Target trial emulation" emphasizes the need to carefully design a non-experimental study in terms of inclusion and exclusion criteria, covariates, exposure definition, and outcome measurement -- and the timing of those variables. We argue that policy evaluations using group-level longitudinal ("panel") data need to take a similar careful approach to study design, which we refer to as "policy trial emulation." This is especially important when intervention timing varies across jurisdictions; the main idea is to construct target trials separately for each "treatment cohort" (states that implement the policy at the same time) and then aggregate. We present a stylized analysis of the impact of state-level stay-at-home orders on total coronavirus cases. We argue that estimates from panel methods -- with the right data and careful modeling and diagnostics -- can help add to our understanding of many policies, though doing so is often challenging.

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arXiv2020

Clarifying causal mediation analysis for the applied researcher: Defining effects based on what we want to learn

The incorporation of causal inference in mediation analysis has led to theoretical and methodological advancements -- effect definitions with causal interpretation, clarification of assumptions required for effect identification, and an expanding array of options for effect estimation. However, the literature on these results is fast-growing and complex, which may be confusing to researchers unfamiliar with causal inference or unfamiliar with mediation. The goal of this paper is to help ease the understanding and adoption of causal mediation analysis. It starts by highlighting a key difference between the causal inference and traditional approaches to mediation analysis and making a case for the need for explicit causal thinking and the causal inference approach in mediation analysis. It then explains in as-plain-as-possible language existing effect types, paying special attention to motivating these effects with different types of research questions, and using concrete examples for illustration. This presentation differentiates two perspectives (or purposes of analysis): the explanatory perspective (aiming to explain the total effect) and the interventional perspective (asking questions about hypothetical interventions on the exposure and mediator, or hypothetically modified exposures). For the latter perspective, the paper proposes tapping into a general class of interventional effects that contains as special cases most of the usual effect types -- interventional direct and indirect effects, controlled direct effects and also a generalized interventional direct effect type, as well as the total effect and overall effect. This general class allows flexible effect definitions which better match many research questions than the standard interventional direct and indirect effects.

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arXiv2020

Transportability of Outcome Measurement Error Correction: from Validation Studies to Intervention Trials

Many lifestyle intervention trials depend on collecting self-reported outcomes, like dietary intake, to assess the intervention's effectiveness. Self-reported outcome measures are subject to measurement error, which could impact treatment effect estimation. External validation studies measure both self-reported outcomes and an accompanying biomarker, and can therefore be used for measurement error correction. Most validation data, though, are only relevant for outcomes under control conditions. Statistical methods have been developed to use external validation data to correct for outcome measurement error under control, and then conduct sensitivity analyses around the error under treatment to obtain estimates of the corrected average treatment effect. However, an assumption underlying this approach is that the measurement error structure of the outcome is the same in both the validation sample and the intervention trial, so that the error correction is transportable to the trial. This may not always be a valid assumption to make. In this paper, we propose an approach that adjusts the validation sample to better resemble the trial sample and thus leads to more transportable measurement error corrections. We also formally investigate when bias due to poor transportability may arise. Lastly, we examine the method performance using simulation, and illustrate them using PREMIER, a multi-arm lifestyle intervention trial measuring self-reported sodium intake as an outcome, and OPEN, a validation study that measures both self-reported diet and urinary biomarkers.

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arXiv2020

Generalizing Randomized Trial Findings to a Target Population using Complex Survey Population Data

Randomized trials are considered the gold standard for estimating causal effects. Trial findings are often used to inform policy and programming efforts, yet their results may not generalize well to a relevant target population due to potential differences in effect moderators between the trial and population. Statistical methods have been developed to improve generalizability by combining trials and population data, and weighting the trial to resemble the population on baseline covariates.Large-scale surveys in fields such as health and education with complex survey designs are a logical source for population data; however, there is currently no best practice for incorporating survey weights when generalizing trial findings to a complex survey. We propose and investigate ways to incorporate survey weights in this context. We examine the performance of our proposed estimator in simulations by comparing its performance to estimators that ignore the complex survey design.We then apply the methods to generalize findings from two trials - a lifestyle intervention for blood pressure reduction and a web-based intervention to treat substance use disorders - to their respective target populations using population data from complex surveys. The work highlights the importance in properly accounting for the complex survey design when generalizing trial findings to a population represented by a complex survey sample.

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arXiv2020

Propensity score analysis with latent covariates: Measurement error bias correction using the covariate's posterior mean, aka the inclusive factor score

We address measurement error bias in propensity score (PS) analysis due to covariates that are latent variables. In the setting where latent covariate $X$ is measured via multiple error-prone items $\mathbf{W}$, PS analysis using several proxies for $X$ -- the $\mathbf{W}$ items themselves, a summary score (mean/sum of the items), or the conventional factor score (cFS , i.e., predicted value of $X$ based on the measurement model) -- often results in biased estimation of the causal effect, because balancing the proxy (between exposure conditions) does not balance $X$. We propose an improved proxy: the conditional mean of $X$ given the combination of $\mathbf{W}$, the observed covariates $Z$, and exposure $A$, denoted $X_{WZA}$. The theoretical support, which applies whether $X$ is latent or not (but is unobserved), is that balancing $X_{WZA}$ (e.g., via weighting or matching) implies balancing the mean of $X$. For a latent $X$, we estimate $X_{WZA}$ by the inclusive factor score (iFS) -- predicted value of $X$ from a structural equation model that captures the joint distribution of $(X,\mathbf{W},A)$ given $Z$. Simulation shows that PS analysis using the iFS substantially improves balance on the first five moments of $X$ and reduces bias in the estimated causal effect. Hence, within the proxy variables approach, we recommend this proxy over existing ones. We connect this proxy method to known results about weighting/matching functions (Lockwood & McCaffrey, 2016; McCaffrey, Lockwood, & Setodji, 2013). We illustrate the method in handling latent covariates when estimating the effect of out-of-school suspension on risk of later police arrests using Add Health data.

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arXiv2019

Extending inferences from a randomized trial to a new target population

When treatment effect modifiers influence the decision to participate in a randomized trial, the average treatment effect in the population represented by the randomized individuals will differ from the effect in other populations. In this tutorial, we consider methods for extending causal inferences about time-fixed treatments from a trial to a new target population of non-participants, using data from a completed randomized trial and baseline covariate data from a sample from the target population. We examine methods based on modeling the expectation of the outcome, the probability of participation, or both (doubly robust). We compare the methods in a simulation study and show how they can be implemented in software. We apply the methods to a randomized trial nested within a cohort of trial-eligible patients to compare coronary artery surgery plus medical therapy versus medical therapy alone for patients with chronic coronary artery disease. We conclude by discussing issues that arise when using the methods in applied analyses.

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arXiv2017

Propensity score-based estimators with multiple error-prone covariates

Propensity score methods are an important tool to help reduce confounding in non-experimental studies. Most propensity score methods assume that covariates are measured without error. However, covariates are often measured with error, which leads to biased causal effect estimates if the true underlying covariates are the actual confounders. Although some studies have investigated the impact of a single mismeasured covariate on estimating a causal effect and proposed methods for handling the measurement error, almost no work exists investigating the case where multiple covariates are mismeasured. In this paper, we examine the consequences of multiple error-prone covariates when estimating causal effects using propensity score-based estimators via extensive simulation studies and real data analyses. We find that causal effect estimates are less biased when the propensity score model includes mismeasured covariates whose true underlying values are strongly correlated with each other. However, when the measurement \emph{errors} are correlated with each other, additional bias is introduced. In addition, it is beneficial to include correctly measured auxiliary variables that are correlated with confounders whose true underlying values are mismeasured in the propensity score model.

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arXiv2016

Sensitivity analysis for an unobserved moderator in RCT-to-target-population generalization of treatment effects

In the presence of treatment effect heterogeneity, the average treatment effect (ATE) in a randomized controlled trial (RCT) may differ from the average effect of the same treatment if applied to a target population of interest. If all treatment effect moderators are observed in the RCT and in a dataset representing the target population, we can obtain an estimate for the target population ATE by adjusting for the difference in the distribution of the moderators between the two samples. This paper considers sensitivity analyses for two situations: (1) where we cannot adjust for a specific moderator $V$ observed in the RCT because we do not observe it in the target population; and (2) where we are concerned that the treatment effect may be moderated by factors not observed even in the RCT, which we represent as a composite moderator $U$. In both situations, the outcome is not observed in the target population. For situation (1), we offer three sensitivity analysis methods based on (i) an outcome model, (ii) full weighting adjustment, and (iii) partial weighting combined with an outcome model. For situation (2), we offer two sensitivity analyses based on (iv) a bias formula and (v) partial weighting combined with a bias formula. We apply methods (i) and (iii) to an example where the interest is to generalize from a smoking cessation RCT conducted with participants of alcohol/illicit drug use treatment programs to the target population of people who seek treatment for alcohol/illicit drug use in the US who are also cigarette smokers. In this case a treatment effect moderator is observed in the RCT but not in the target population dataset.

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arXiv2015

Design of the Millennium Villages Project Sampling Plan: a simulation study for a multi-module survey

The Millennium Villages Project (MVP) is a ten-year integrated rural development project implemented in ten sub-Saharan African sites. At its conclusion we will conduct an evaluation of its causal effect on a variety of development outcomes, measured via household surveys in treatment and comparison areas. Outcomes are measured by six survey modules, with sample sizes for each demographic group determined by budget, logistics, and the group's vulnerability. We design a sampling plan that aims to reduce effort for survey enumerators and maximize precision for all outcomes. We propose two-stage sampling designs, sampling households at the first stage, followed by a second stage sample that differs across demographic groups. Two-stage designs are usually constructed by simple random sampling (SRS) of households and proportional within-household sampling, or probability proportional to size sampling (PPS) of households with fixed sampling within each. No measure of household size is proportional for all demographic groups, putting PPS schemes at a disadvantage. The SRS schemes have the disadvantage that multiple individuals sampled per household decreases efficiency due to intra-household correlation. We conduct a simulation study (using both design- and model-based survey inference) to understand these tradeoffs and recommend a sampling plan for the Millennium Villages Project. Similar design issues arise in other studies with surveys that target different demographic groups.

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arXiv2010

Matching Methods for Causal Inference: A Review and a Look Forward

When estimating causal effects using observational data, it is desirable to replicate a randomized experiment as closely as possible by obtaining treated and control groups with similar covariate distributions. This goal can often be achieved by choosing well-matched samples of the original treated and control groups, thereby reducing bias due to the covariates. Since the 1970s, work on matching methods has examined how to best choose treated and control subjects for comparison. Matching methods are gaining popularity in fields such as economics, epidemiology, medicine and political science. However, until now the literature and related advice has been scattered across disciplines. Researchers who are interested in using matching methods---or developing methods related to matching---do not have a single place to turn to learn about past and current research. This paper provides a structure for thinking about matching methods and guidance on their use, coalescing the existing research (both old and new) and providing a summary of where the literature on matching methods is now and where it should be headed.

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arXiv2006

Affinely invariant matching methods with discriminant mixtures of proportional ellipsoidally symmetric distributions

In observational studies designed to estimate the effects of interventions or exposures, such as cigarette smoking, it is desirable to try to control background differences between the treated group (e.g., current smokers) and the control group (e.g., never smokers) on covariates $X$ (e.g., age, education). Matched sampling attempts to effect this control by selecting subsets of the treated and control groups with similar distributions of such covariates. This paper examines the consequences of matching using affinely invariant methods when the covariate distributions are ``discriminant mixtures of proportional ellipsoidally symmetric'' (DMPES) distributions, a class herein defined, which generalizes the ellipsoidal symmetry class of Rubin and Thomas [Ann. Statist. 20 (1992) 1079--1093]. The resulting generalized results help indicate why earlier results hold quite well even when the simple assumption of ellipsoidal symmetry is not met [e.g., Biometrics 52 (1996) 249--264]. Extensions to conditionally affinely invariant matching with conditionally DMPES distributions are also discussed.

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