Estimating a Causal Exposure Response Function with a Continuous Error-Prone Exposure: A Study of Fine Particulate Matter and All-Cause Mortality.

Numerous studies have examined the associations between long-term exposure to fine particulate matter (PM2.5) and adverse health outcomes. Recently, many of these studies have begun to employ high-resolution predicted PM2.5 concentrations, which are subject to measurement error. Previous approaches for exposure measurement error correction have either been applied in non-causal settings or have only considered a categorical exposure. Moreover, most procedures have failed to account for uncertainty induced by error correction when fitting an exposure-response function (ERF). To remedy these deficiencies, we develop a multiple imputation framework that combines regression calibration and Bayesian techniques to estimate a causal ERF. We demonstrate how the output of the measurement error correction steps can be seamlessly integrated into a Bayesian additive regression trees (BART) estimator of the causal ERF. We also demonstrate how locally-weighted smoothing of the posterior samples from BART can be used to create a more accurate ERF estimate. Our proposed approach also properly propagates the exposure measurement error uncertainty to yield accurate standard error estimates. We assess the robustness of our proposed approach in an extensive simulation study. We then apply our methodology to estimate the effects of PM2.5 on all-cause mortality among Medicare enrollees in New England from 2000-2012.

Air Pollution and Mortality at the Intersection of Race and Social Class.

BACKGROUND: Black Americans are exposed to higher annual levels of air pollution containing fine particulate matter (particles with an aerodynamic diameter of ≤2.5 µm [PM2.5]) than White Americans and may be more susceptible to its health effects. Low-income Americans may also be more susceptible to PM2.5 pollution than high-income Americans. Because information is lacking on exposure-response curves for PM2.5 exposure and mortality among marginalized subpopulations categorized according to both race and socioeconomic position, the Environmental Protection Agency lacks important evidence to inform its regulatory rulemaking for PM2.5 standards. METHODS: We analyzed 623 million person-years of Medicare data from 73 million persons 65 years of age or older from 2000 through 2016 to estimate associations between annual PM2.5 exposure and mortality in subpopulations defined simultaneously by racial identity (Black vs. White) and income level (Medicaid eligible vs. ineligible). RESULTS: Lower PM2.5 exposure was associated with lower mortality in the full population, but marginalized subpopulations appeared to benefit more as PM2.5 levels decreased. For example, the hazard ratio associated with decreasing PM2.5 from 12 µg per cubic meter to 8 µg per cubic meter for the White higher-income subpopulation was 0.963 (95% confidence interval [CI], 0.955 to 0.970), whereas equivalent hazard ratios for marginalized subpopulations were lower: 0.931 (95% CI, 0.909 to 0.953) for the Black higher-income subpopulation, 0.940 (95% CI, 0.931 to 0.948) for the White low-income subpopulation, and 0.939 (95% CI, 0.921 to 0.957) for the Black low-income subpopulation. CONCLUSIONS: Higher-income Black persons, low-income White persons, and low-income Black persons may benefit more from lower PM2.5 levels than higher-income White persons. These findings underscore the importance of considering racial identity and income together when assessing health inequities. (Funded by the National Institutes of Health and the Alfred P. Sloan Foundation.).

Power for balanced linear mixed models with complex missing data processes.

When designing repeated measures studies, both the amount and the pattern of missing outcome data can affect power. The chance that an observation is missing may vary across measurements, and missingness may be correlated across measurements. For example, in a physiotherapy study of patients with Parkinson's disease, increasing intermittent dropout over time yielded missing measurements of physical function. In this example, we assume data are missing completely at random, since the chance that a data point was missing appears to be unrelated to either outcomes or covariates. For data missing completely at random, we propose noncentral F power approximations for the Wald test for balanced linear mixed models with Gaussian responses. The power approximations are based on moments of missing data summary statistics. The moments were derived assuming a conditional linear missingness process. The approach provides approximate power for both complete-case analyses, which include independent sampling units where all measurements are present, and observed-case analyses, which include all independent sampling units with at least one measurement. Monte Carlo simulations demonstrate the accuracy of the method in small samples. We illustrate the utility of the method by computing power for proposed replications of the Parkinson's study.

Transportability Methods for Time-to-Event Outcomes: Application in Adjuvant Colon Cancer Trials.

PURPOSE: Differences in the benefits of treatment on 5-year overall survival have been observed in 12 randomized phase III colon cancer adjuvant clinical trials from the ACCENT group. We investigated the reasons for these differences by incorporating the distribution of the observed covariates from each trial. MATERIALS AND METHODS: We applied state-of-the-art transportability methods on the basis of causal inference, and compared them with a conventional meta-analysis approach to predict the treatment effect for the target population. Prediction errors were defined to evaluate whether the identifiability conditions necessary for causal inference were satisfied among the 12 trials, and to measure the performance of each method. RESULTS: In the one-trial-at-a-time transportability analysis, the ranks of prediction errors for the target population were mostly consistent with the discrepancy in treatment effects among the 12 trials across the three models. The overall prediction errors between the leave-one-trial-out transportability method and the conventional individual participant data meta-analysis approach were very similar, and more than 40% lower than the overall prediction errors from the one-trial-at-a-time transportability method. CONCLUSION: The discrepancy in treatment effects among the 12 trials is unlikely to arise from the choice of model specification or distribution of observed covariates but from the distribution of unobserved covariates or study-level features. The ability to quantify heterogeneity among the 12 trials was greatly reduced in both the leave-one-trial-out transportability method and the conventional meta-analysis approach compared with the one-trial-at-a-time transportability method.

A calibration approach to transportability and data-fusion with observational data.

Two important considerations in clinical research studies are proper evaluations of internal and external validity. While randomized clinical trials can overcome several threats to internal validity, they may be prone to poor external validity. Conversely, large prospective observational studies sampled from a broadly generalizable population may be externally valid, yet susceptible to threats to internal validity, particularly confounding. Thus, methods that address confounding and enhance transportability of study results across populations are essential for internally and externally valid causal inference, respectively. These issues persist for another problem closely related to transportability known as data-fusion. We develop a calibration method to generate balancing weights that address confounding and sampling bias, thereby enabling valid estimation of the target population average treatment effect. We compare the calibration approach to two additional doubly robust methods that estimate the effect of an intervention on an outcome within a second, possibly unrelated target population. The proposed methodologies can be extended to resolve data-fusion problems that seek to evaluate the effects of an intervention using data from two related studies sampled from different populations. A simulation study is conducted to demonstrate the advantages and similarities of the different techniques. We also test the performance of the calibration approach in a motivating real data example comparing whether the effect of biguanides vs sulfonylureas-the two most common oral diabetes medication classes for initial treatment-on all-cause mortality described in a historical cohort applies to a contemporary cohort of US Veterans with diabetes.

Transporting experimental results with entropy balancing.

We show how entropy balancing can be used for transporting experimental treatment effects from a trial population onto a target population. This method is doubly robust in the sense that if either the outcome model or the probability of trial participation is correctly specified, then the estimate of the target population average treatment effect is consistent. Furthermore, we only require the sample moments of the effect modifiers drawn from the target population to consistently estimate the target population average treatment effect. We compared the finite-sample performance of entropy balancing with several alternative methods for transporting treatment effects between populations. Entropy balancing techniques are efficient and robust to violations of model misspecification. We also examine the results of our proposed method in an applied analysis of the Action to Control Cardiovascular Risk in Diabetes Blood Pressure trial transported to a sample of US adults with diabetes taken from the National Health and Nutrition Examination Survey cohort.

Risk of obstructive coronary artery disease and major adverse cardiac events in patients with noncoronary atherosclerosis: Insights from the Veterans Affairs Clinical Assessment, Reporting, and Tracking (CART) Program.

We sought to determine the risk of obstructive coronary artery disease (oCAD) associated with noncoronary atherosclerosis (cerebrovascular disease [CVD] or peripheral arterial disease [PAD]) and major adverse cardiac events following percutaneous coronary intervention (PCI). METHODS: Rates of the angiographic end point of oCAD were compared among patients with and without noncoronary atherosclerosis undergoing coronary angiography within the Veterans Health Administration between October 2007 and August 2015. The primary angiographic end point of oCAD was defined as left main stenosis ≥50% or any stenosis ≥70% in 1, 2, or 3 vessels. In patients who proceeded to PCI, the rate of the composite clinical end point of death, myocardial infarction, or stroke was compared among those with concomitant noncoronary atherosclerosis (CVD, PAD, or CVD + PAD) versus isolated CAD. RESULTS: Among 233,353 patients undergoing angiography, 9.6% had CVD, 12.4% had PAD, and 6.1% had CVD + PAD. Rates of oCAD were 57.9% for neither CVD nor PAD, 66.4% for CVD, 73.6% for PAD, and 80.9% for CVD + PAD. Compared with patients without noncoronary atherosclerosis, the adjusted risk of oCAD with CVD, PAD, or CVD + PAD was 1.03 (95% CI 1.02-1.04), 1.10 (95% CI 1.09-1.11), and 1.12 (95% CI 1.11-1.13), respectively. In patients who underwent PCI, the adjusted hazard for death, myocardial infarction, or stroke among those with CVD, PAD, or CVD + PAD was 1.36 (95% CI 1.26-1.45), 1.53 (95% CI 1.45-1.62), and 1.72 (95% CI 1.59-1.86), respectively. CONCLUSIONS: In patients undergoing coronary angiography, noncoronary atherosclerosis was associated with increased burden of oCAD and adverse events post-PCI.