Propensity scores with misclassified treatment assignment: a likelihood-based adjustment

Differential recall bias in estimating treatment effects in observational studies

Observational studies are frequently used to estimate the effect of an exposure or treatment on an outcome. To obtain an unbiased estimate of the treatment effect, it is crucial to measure the exposure accurately. A common type of exposure misclassification is recall bias, which occurs in retrospective cohort studies when study subjects may inaccurately recall their past exposure. Particularly challenging is differential recall bias in the context of self-reported binary exposures, where the bias may be directional rather than random and its extent varies according to the outcomes experienced. This paper makes several contributions: (1) it establishes bounds for the average treatment effect even when a validation study is not available; (2) it proposes multiple estimation methods across various strategies predicated on different assumptions; and (3) it suggests a sensitivity analysis technique to assess the robustness of the causal conclusion, incorporating insights from prior research. The effectiveness of these methods is demonstrated through simulation studies that explore various model misspecification scenarios. These approaches are then applied to investigate the effect of childhood physical abuse on mental health in adulthood.

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.

Assessing Adverse Health Effects of Long-Term Exposure to Low Levels of Ambient Air Pollution: Implementation of Causal Inference Methods

This report provides a final summary of the principal findings and key conclusions of a study supported by an HEI grant aimed at "Assessing Adverse Health Effects of Long-Term Exposure to Low Levels of Ambient Air Pollution." It is the second and final report on this topic. The study was designed to advance four critical areas of inquiry and methods development. First, it focused on predicting short- and long-term exposures to ambient fine particulate matter (PM2.5), nitrogen dioxide (NO2), and ozone (O3) at high spatial resolution (1 km × 1 km) for the continental United States over the period 2000-2016 and linking these predictions to health data. Second, it developed new causal inference methods for estimating exposure-response (ER) curves (ERCs) and adjusting for measured confounders. Third, it applied these methods to claims data from Medicare and Medicaid beneficiaries to estimate health effects associated with short- and long-term exposure to low levels of ambient air pollution. Finally, it developed pipelines for reproducible research, including approaches for data sharing, record linkage, and statistical software. Our HEI-funded work has supported an extensive portfolio of analyses and the development of statistical methods that can be used to robustly understand the health effects of short- and long-term exposure to low levels of ambient air pollution. Our Phase 1 report (Dominici et al. 2019) provided a high-level overview of our statistical methods, data analysis, and key findings, grouped into the following five areas: (1) exposure prediction, (2) epidemiological studies of ambient exposures to air pollution at low levels, (3) sensitivity analysis, (4) methodological contributions in causal inference, and (5) an open access research data platform. The current, final report includes a comprehensive overview of the entire research project.

Considering our (1) massive study population, (2) numerous sensitivity analyses, and (3) transparent assessment of covariate balance indicating the quality of causal inference for simulating randomized experiments, we conclude that conditionally on the required assumptions for causal inference, our results collectively indicate that long-term PM2.5 exposure is likely to be causally related to mortality. This conclusion assumes that the causal inference assumptions hold and, more specifically, that we accounted adequately for confounding bias. We explored various modeling approaches, conducted extensive sensitivity analyses, and found that our results were robust across approaches and models. This work relied on publicly available data, and we have provided code that allows for reproducibility of our analyses.

Our work provides comprehensive evidence of associations between exposures to PM2.5, NO2, and O3 and various health outcomes. In the current report, we report more specific results on the causal link between long-term exposure to PM2.5 and mortality, even at PM2.5 levels below or equal to 12 μg/m3, and mortality among Medicare beneficiaries (ages 65 and older). This work relies on newly developed causal inference methods for continuous exposure.

For the period 2000-2016, we found that all statistical approaches led to consistent results: a 10-μg/m3 decrease in PM2.5 led to a statistically significant decrease in mortality rate ranging between 6% and 7% (= 1 - 1/hazard ratio [HR]) (HR estimates 1.06 [95% CI, 1.05 to 1.08] to 1.08 [95% CI, 1.07 to 1.09]). The estimated HRs were larger when studying the cohort of Medicare beneficiaries that were always exposed to PM2.5 levels lower than 12 μg/m3 (1.23 [95% CI, 1.18 to 1.28] to 1.37 [95% CI, 1.34 to 1.40]).

Comparing the results from multiple and single pollutant models, we found that adjusting for the other two pollutants slightly attenuated the causal effects of PM2.5 and slightly elevated the causal effects of NO2 exposure on all-cause mortality. The results for O3 remained almost unchanged.

We found evidence of a harmful causal relationship between mortality and long-term PM2.5 exposures adjusted for NO2 and O3 across the range of annual averages between 2.77 and 17.16 μg/m3 (included >98% of observations) in the entire cohort of Medicare beneficiaries across the continental United States from 2000 to 2016. Our results are consistent with recent epidemiological studies reporting a strong association between long-term exposure to PM2.5 and adverse health outcomes at low exposure levels. Importantly, the curve was almost linear at exposure levels lower than the current national standards, indicating aggravated harmful effects at exposure levels even below these standards.

There is, in general, a harmful causal impact of long-term NO2 exposures to mortality adjusted for PM2.5 and O3 across the range of annual averages between 3.4 and 80 ppb (included >98% of observations). Yet within low levels (annual mean ≤53 ppb) below the current national standards, the causal impacts of NO2 exposures on all-cause mortality are nonlinear with statistical uncertainty.

The ERCs of long-term O3 exposures on all-cause mortality adjusted for PM2.5 and NO2 are almost flat below 45 ppb, which shows no statistically significant effect. Yet we observed an increased hazard when the O3 exposures were higher than 45 ppb, and the HR was approximately 1.10 when comparing Medicare beneficiaries with annual mean O3 exposures of 50 ppb versus those with 30 ppb.

institutions, including those that support the Health Effects Institute; therefore, it may not reflect the views or policies of these parties, and no endorsement by them should be inferred.

A list of abbreviations and other terms appears at the end of this volume.

Exposure misclassification in propensity score-based time-to-event data analysis

In epidemiology, identifying the effect of exposure variables in relation to a time-to-event outcome is a classical research area of practical importance. Incorporating propensity score in the Cox regression model, as a measure to control for confounding, has certain advantages when outcome is rare. However, in situations involving exposure measured with moderate to substantial error, identifying the exposure effect using propensity score in Cox models remains a challenging yet unresolved problem. In this paper, we propose an estimating equation method to correct for the exposure misclassification-caused bias in the estimation of exposure-outcome associations. We also discuss the asymptotic properties and derive the asymptotic variances of the proposed estimators. We conduct a simulation study to evaluate the performance of the proposed estimators in various settings. As an illustration, we apply our method to correct for the misclassification-caused bias in estimating the association of PM2.5 level with lung cancer mortality using a nationwide prospective cohort, the Nurses' Health Study. The proposed methodology can be applied using our user-friendly R program published online.

A weighting method for simultaneous adjustment for confounding and joint exposure-outcome misclassifications

Joint misclassification of exposure and outcome variables can lead to considerable bias in epidemiological studies of causal exposure-outcome effects. In this paper, we present a new maximum likelihood based estimator for marginal causal effects that simultaneously adjusts for confounding and several forms of joint misclassification of the exposure and outcome variables. The proposed method relies on validation data for the construction of weights that account for both sources of bias. The weighting estimator, which is an extension of the outcome misclassification weighting estimator proposed by Gravel and Platt (Weighted estimation for confounded binary outcomes subject to misclassification. Stat Med 2018; 37: 425–436), is applied to reinfarction data. Simulation studies were carried out to study its finite sample properties and compare it with methods that do not account for confounding or misclassification. The new estimator showed favourable large sample properties in the simulations. Further research is needed to study the sensitivity of the proposed method and that of alternatives to violations of their assumptions. The implementation of the estimator is facilitated by a new R function (ipwm) in an existing R package (mecor).

Evaluating the impact of long-term exposure to fine particulate matter on mortality among the elderly

Many studies link long-term fine particle (PM2.5) exposure to mortality, even at levels below current U.S. air quality standards (12 micrograms per cubic meter). These findings have been disputed with claims that the use of traditional statistical approaches does not guarantee causality. Leveraging 16 years of data-68.5 million Medicare enrollees-we provide strong evidence of the causal link between long-term PM2.5 exposure and mortality under a set of causal inference assumptions. Using five distinct approaches, we found that a decrease in PM2.5 (by 10 micrograms per cubic meter) leads to a statistically significant 6 to 7% decrease in mortality risk. Based on these models, lowering the air quality standard to 10 micrograms per cubic meter would save 143,257 lives (95% confidence interval, 115,581 to 170,645) in one decade. Our study provides the most comprehensive evidence to date of the link between long-term PM2.5 exposure and mortality, even at levels below current standards.

Causal inference with noisy data: Bias analysis and estimation approaches to simultaneously addressing missingness and misclassification in binary outcomes

Causal inference has been widely conducted in various fields and many methods have been proposed for different settings. However, for noisy data with both mismeasurements and missing observations, those methods often break down. In this paper, we consider a problem that binary outcomes are subject to both missingness and misclassification, when the interest is in estimation of the average treatment effects (ATE). We examine the asymptotic biases caused by ignoring missingness and/or misclassification and establish the intrinsic connections between missingness effects and misclassification effects on the estimation of ATE. We develop valid weighted estimation methods to simultaneously correct for missingness and misclassification effects. To provide protection against model misspecification, we further propose a doubly robust correction method which yields consistent estimators when either the treatment model or the outcome model is misspecified. Simulation studies are conducted to assess the performance of the proposed methods. An application to smoking cessation data is reported to illustrate the use of the proposed methods.

CAUSAL INFERENCE IN THE CONTEXT OF AN ERROR PRONE EXPOSURE: AIR POLLUTION AND MORTALITY

We propose a new approach for estimating causal effects when the exposure is measured with error and confounding adjustment is performed via a generalized propensity score (GPS). Using validation data, we propose a regression calibration (RC)-based adjustment for a continuous error-prone exposure combined with GPS to adjust for confounding (RC-GPS). The outcome analysis is conducted after transforming the corrected continuous exposure into a categorical exposure. We consider confounding adjustment in the context of GPS subclassification, inverse probability treatment weighting (IPTW) and matching. In simulations with varying degrees of exposure error and confounding bias, RC-GPS eliminates bias from exposure error and confounding compared to standard approaches that rely on the error-prone exposure. We applied RC-GPS to a rich data platform to estimate the causal effect of long-term exposure to fine particles (PM2.5) on mortality in New England for the period from 2000 to 2012. The main study consists of 2202 zip codes covered by 217,660 1 km × 1 km grid cells with yearly mortality rates, yearly PM2.5 averages estimated from a spatio-temporal model (error-prone exposure) and several potential confounders. The internal validation study includes a subset of 83 1 km × 1 km grid cells within 75 zip codes from the main study with error-free yearly PM2.5 exposures obtained from monitor stations. Under assumptions of noninterference and weak unconfoundedness, using matching we found that exposure to moderate levels of PM2.5 (8 < PM2.5 ≤ 10 μg/m3) causes a 2.8% (95% CI: 0.6%, 3.6%) increase in all-cause mortality compared to low exposure (PM2.5 ≤ 8 μg/m3).