Long-term exposure to ambient PM2.5 and population health: evidence from linked census data.

Particulate matter suspended in the air that is comprised of microscopic particles with a diameter of 2.5µm or less (PM2.5) is among the most impactful pollutants globally. Extensive evidence shows exposure to ambient PM2.5 is associated with a wide range of poor health outcomes. However, few studies examine long-run pollution exposures in nationally representative data. This study exploits Census data for Northern Ireland, linked to average PM2.5 concentrations at the 1x1km grid-square level during the period 2002-2010. We combine outcome measures in 2011 with data on complete residential histories. Before adjusting for other covariates, we show strong relationships between PM2.5 exposure, self-rated general health, disability, and all available (eleven) domain-specific health measures in the data. Associations with poor general health, chronic illness, breathing difficulties, mobility difficulties, and deafness are robust to extensive conditioning and to further analysis designed to examine sensitivity to unobserved confounders.

Association between low health literacy and adverse health behaviors in North Carolina, 2016.

Introduction: Health literacy (HL) is an urgent public health challenge facing the U.S. HL is a critical factor in health inequities and exacerbates underlying social determinants of health. Purpose: This study assesses the association between low HL (LHL) and adverse health behaviors, which contribute to poor health. Methods: Researchers used North Carolina's 2016 Behavioral Risk Factor Surveillance System data, namely, the Health Literacy optional module which asks respondents to rate how difficult it is for them to get health-related advice or to understand medical information (verbal or written). Health behaviors analyzed were excessive alcohol consumption, lack of adequate exercise and sleep, and irregular medical and dental check-ups. The sample was divided into four age categories (18-49, 50-64, and 65-75, and 76 and older) for statistical comparisons. Stata 15 and a user-written Stata command, - psacalc-, were used to examine the relationships by addressing omitted variable bias in OLS regressions. Results: Findings indicate that LHL has a direct robust relationship with not exercising, inadequate sleep, irregular health and dental checkup, and health screenings across different age groups. Among women, LHL is associated with getting a Pap test in 3 years as opposed to more than 3 years. Implications: The adverse behaviors can explain the mechanisms underlying the link between LHL and adverse health outcomes. Further research on the causal relationship between LHL and adverse health behaviors using longitudinal data on a broader geographic region is warranted.

Modified interactive Q-learning for attenuating the impact of model misspecification with treatment effect heterogeneity.

A sequential multiple assignment randomized trial, which incorporates multiple stages of randomization, is a popular approach for collecting data to inform personalized and adaptive treatments. There is an extensive literature on statistical methods to analyze data collected in sequential multiple assignment randomized trials and estimate the optimal dynamic treatment regime. Q-learning with linear regression is widely used for this purpose due to its ease of implementation. However, model misspecification is a common problem with this approach, and little attention has been given to the impact of model misspecification when treatment effects are heterogeneous across subjects. This article describes the integrative impact of two possible types of model misspecification related to treatment effect heterogeneity: omitted early-stage treatment effects in late-stage main effect model, and violated linearity assumption between pseudo-outcomes and predictors despite non-linearity arising from the optimization operation. The proposed method, aiming to deal with both types of misspecification concomitantly, builds interactive models into modified parametric Q-learning with Murphy's regret function. Simulations show that the proposed method is robust to both sources of model misspecification. The proposed method is applied to a two-stage sequential multiple assignment randomized trial with embedded tailoring aimed at reducing binge drinking in first-year college students.

Tuning Random Forests for Causal Inference under Cluster-Level Unmeasured Confounding.

Recently, there has been growing interest in using machine learning methods for causal inference due to their automatic and flexible ability to model the propensity score and the outcome model. However, almost all the machine learning methods for causal inference have been studied under the assumption of no unmeasured confounding and there is little work on handling omitted/unmeasured variable bias. This paper focuses on a machine learning method based on random forests known as Causal Forests and presents five simple modifications for tuning Causal Forests so that they are robust to cluster-level unmeasured confounding. Our simulation study finds that adjusting the default tuning procedure with the propensity score from fixed effects logistic regression or using variables that are centered to their cluster means produces estimates that are more robust to cluster-level unmeasured confounding. Also, when these parametric propensity score models are mis-specified, our modified machine learning methods remain robust to bias from cluster-level unmeasured confounders compared to existing parametric approaches based on propensity score weighting. We conclude by demonstrating our proposals in a real data study concerning the effect of taking an eighth-grade algebra course on math achievement scores from the Early Childhood Longitudinal Study.

Meta-analysis under imbalance in measurement of confounders in cohort studies using only summary-level data.

BACKGROUND: Cohort collaborations often require meta-analysis of exposure-outcome association estimates across cohorts as an alternative to pooling individual-level data that requires a laborious process of data harmonization on individual-level data. However, it is likely that important confounders are not all measured uniformly across the cohorts due to differences in study protocols. This imbalance in measurement of confounders leads to association estimates that are not comparable across cohorts and impedes the meta-analysis of results. METHODS: In this article, we empirically show some asymptotic relations between fully adjusted and unadjusted exposure-outcome effect estimates, and provide theoretical justification for the same. We leverage these results to obtain fully adjusted estimates for the cohorts with no information on confounders by borrowing information from cohorts with complete measurement on confounders. We implement this novel method in CIMBAL (confounder imbalance), which additionally provides a meta-analyzed estimate that appropriately accounts for the dependence between estimates arising due to borrowing of information across cohorts. We perform extensive simulation experiments to study CIMBAL's statistical properties. We illustrate CIMBAL using National Children's Study (NCS) data to estimate association of maternal education and low birth weight in infants, adjusting for maternal age at delivery, race/ethnicity, marital status, and income. RESULTS: Our simulation studies indicate that estimates of exposure-outcome association from CIMBAL are closer to the truth than those from commonly-used approaches for meta-analyzing cohorts with disparate confounder measurements. CIMBAL is not too sensitive to heterogeneity in underlying joint distributions of exposure, outcome and confounders but is very sensitive to heterogeneity of confounding bias across cohorts. Application of CIMBAL to NCS data for a proof-of-concept analysis further illustrates the utility and advantages of CIMBAL. CONCLUSIONS: CIMBAL provides a practical approach for meta-analyzing cohorts with imbalance in measurement of confounders under a weak assumption that the cohorts are independently sampled from populations with the same confounding bias.

Estimating the effect of friction on crash risk: Reducing the effect of omitted variable bias that results from spatial correlation.

Omitted variable bias is one of the main factors that lead to incorrect estimates of the effect of a variable on the expected number of crashes using regression modeling. We propose to use differencing of the (spatially adjacent) variables to reduce the effect of omitted variable bias. Differencing is a linear transformation that preserves the structure of the (generalized) linear model but can often result in significantly reducing the correlation between the variables. It is special case of (generalized) partial linear model regression which itself is a special case of a generalized additive model (GAM). In the spatial context used in this paper, differencing is similar to the well-known approach of including a spatial correlation structure (spatial error term) in the analysis of crash data. It is generally not clear how to interpret the results of models that include a spatial correlation structure and whether and how the added spatial correlation structure reduces the bias in the estimated regression parameters. However, for the case of differencing, it becomes clear how the effect of omitted variable bias is reduced by reducing the correlation between the variable of interest and the omitted variables. The order of differencing determines the dominant spatial scales of the variables considered in the model which affect how much the correlation is reduced. This reveals that omitted variable bias can be reduced when there are spatial scales at which the covariate of interest varies but the omitted variables either 1) are relatively homogeneous or 2) have variations that are not correlated to those of the variable of interest.

Robust Machine Learning for Treatment Effects in Multilevel Observational Studies Under Cluster-level Unmeasured Confounding.

Recently, machine learning (ML) methods have been used in causal inference to estimate treatment effects in order to reduce concerns for model mis-specification. However, many ML methods require that all confounders are measured to consistently estimate treatment effects. In this paper, we propose a family of ML methods that estimate treatment effects in the presence of cluster-level unmeasured confounders, a type of unmeasured confounders that are shared within each cluster and are common in multilevel observational studies. We show through simulation studies that our proposed methods are robust from biases from unmeasured cluster-level confounders in a variety of multilevel observational studies. We also examine the effect of taking an algebra course on math achievement scores from the Early Childhood Longitudinal Study, a multilevel observational educational study, using our methods. The proposed methods are available in the CURobustML R package.

Childhood Mistreatment, PTSD, and Substance Use in Latinx: The Role of Discrimination in an Omitted-Variable Bias.

BACKGROUND: Childhood mistreatment (CM) has been associated with adult posttraumatic disorder (PTSD) and substance use disorders (SUDs) in the general population. Few studies have examined the role of PTSD in the CM-SUD association among Latinx. This cross-sectional study evaluated a theory-driven conceptual model with a specific focus on the impact of perceived discrimination, which may interfere with these associations. METHOD: Using a nationally representative sample and structural equation modeling (SEM), the study evaluated the mediation of PTSD in the CM-SUD link, adjusting for or omitting discrimination and other sociodemographic variables that are known predictors of Latinx behavioral health. Multi-subsample analyses were then conducted to review nativity differences (US-born = 924.43% and immigrant = 1630.57%). RESULTS: The fully specified final model (model 1, covariates adjusted) failed to show a significant mediation of PTSD in the tested link, but a direct detrimental effect group of discrimination, for all Latinx. The mediation was only supported, when treating discrimination and other covariates as omitted variables (model 5), which also showed additional direct and indirect effect of CM on SUD. In subsample analyses, models of US-born and immigrant-Latinx subpopulations were identical but showed nativity differences when omitting covariates. CONCLUSION: When discrimination and other covariates were fully adjusted, Latinx exposed to trauma were more likely to develop SUD in adulthood, regardless of when traumatic exposure occurred. This unexpected finding challenges theories explaining the CM-SUD connection, suggesting possible model misspecifications of parametric SES; namely, omitting the unique impact of perceived discrimination in Latinx can lead to biased results. From a clinical standpoint, both trauma and discrimination must be addressed when assessing Latinx behavioral health.

Statistical methods for the estimation of contagion effects in human disease and health networks.

Contagion effects, sometimes referred to as spillover or influence effects, have long been central to the study of human disease and health networks. Accurate estimation and identification of contagion effects are important in terms of understanding the spread of human disease and health behavior, and they also have various implications for designing effective public health interventions. However, many challenges remain in estimating contagion effects and it is often unclear when it is difficult to correctly estimate contagion effects, or why a particular method would need to be applied. In this review I explain the challenges in estimating contagion effects, and how they can be framed as an omitted variable bias problem. I then discuss how such challenges have been addressed in randomized experiments and traditional statistical analyses, as well as several state-of-the-art statistical methods. Finally, I conclude by summarizing recent advancements and noting remaining challenges, as well as appropriate next steps.

The Mechanics of Omitted Variable Bias: Bias Amplification and Cancellation of Offsetting Biases.

Causal inference with observational data frequently requires researchers to estimate treatment effects conditional on a set of observed covariates, hoping that they remove or at least reduce the confounding bias. Using a simple linear (regression) setting with two confounders - one observed (X), the other unobserved (U) - we demonstrate that conditioning on the observed confounder X does not necessarily imply that the confounding bias decreases, even if X is highly correlated with U. That is, adjusting for X may increase instead of reduce the omitted variable bias (OVB). Two phenomena can cause an increasing OVB: (i) bias amplification and (ii) cancellation of offsetting biases. Bias amplification occurs because conditioning on X amplifies any remaining bias due to the omitted confounder U. Cancellation of offsetting biases is an issue whenever X and U induce biases in opposite directions such that they perfectly or partially offset each other, in which case adjusting for X inadvertently cancels the bias-offsetting effect. In this article we discuss the conditions under which adjusting for X increases OVB, and demonstrate that conditioning on X increases the imbalance in U, which turns U into an even stronger confounder. We also show that conditioning on an unreliably measured confounder can remove more bias than the corresponding reliable measure. Practical implications for causal inference will be discussed.

The effect of unmeasured confounders on the ability to estimate a true performance or selection gradient (and other partial regression coefficients).

Multiple regression of observational data is frequently used to infer causal effects. Partial regression coefficients are biased estimates of causal effects if unmeasured confounders are not in the regression model. The sensitivity of partial regression coefficients to omitted confounders is investigated with a Monte-Carlo simulation. A subset of causal traits is "measured" and their effects are estimated using ordinary least squares regression and compared to their expected values. Three major results are: (1) the error due to confounding is much larger than that due to sampling, especially with large samples, (2) confounding error shrinks trivially with sample size, and (3) small true effects are frequently estimated as large effects. Consequently, confidence intervals from regression are poor guides to the true intervals, especially with large sample sizes. The addition of a confounder to the model improves estimates only 55% of the time. Results are improved with complete knowledge of the rank order of causal effects but even with this omniscience, measured intervals are poor proxies for true intervals if there are many unmeasured confounders. The results suggest that only under very limited conditions can we have much confidence in the magnitude of partial regression coefficients as estimates of causal effects.