A Bayesian approach to the g-formula

Characterizing quantile-varying covariate effects under the accelerated failure time model

An important task in survival analysis is choosing a structure for the relationship between covariates of interest and the time-to-event outcome. For example, the accelerated failure time (AFT) model structures each covariate effect as a constant multiplicative shift in the outcome distribution across all survival quantiles. Though parsimonious, this structure cannot detect or capture effects that differ across quantiles of the distribution, a limitation that is analogous to only permitting proportional hazards in the Cox model. To address this, we propose a general framework for quantile-varying multiplicative effects under the AFT model. Specifically, we embed flexible regression structures within the AFT model and derive a novel formula for interpretable effects on the quantile scale. A regression standardization scheme based on the g-formula is proposed to enable the estimation of both covariate-conditional and marginal effects for an exposure of interest. We implement a user-friendly Bayesian approach for the estimation and quantification of uncertainty while accounting for left truncation and complex censoring. We emphasize the intuitive interpretation of this model through numerical and graphical tools and illustrate its performance through simulation and application to a study of Alzheimer's disease and dementia.

Covariate adjustment in Bayesian adaptive randomized controlled trials

In conventional randomized controlled trials, adjustment for baseline values of covariates known to be at least moderately associated with the outcome increases the power of the trial. Recent work has shown a particular benefit for more flexible frequentist designs, such as information adaptive and adaptive multi-arm designs. However, covariate adjustment has not been characterized within the more flexible Bayesian adaptive designs, despite their growing popularity. We focus on a subclass of these which allow for early stopping at an interim analysis given evidence of treatment superiority. We consider both collapsible and non-collapsible estimands and show how to obtain posterior samples of marginal estimands from adjusted analyses. We describe several estimands for three common outcome types. We perform a simulation study to assess the impact of covariate adjustment using a variety of adjustment models in several different scenarios. This is followed by a real-world application of the compared approaches to a COVID-19 trial with a binary endpoint. For all scenarios, it is shown that covariate adjustment increases power and the probability of stopping the trials early, and decreases the expected sample sizes as compared to unadjusted analyses.

Model-based standardization using multiple imputation

BACKGROUND

When studying the association between treatment and a clinical outcome, a parametric multivariable model of the conditional outcome expectation is often used to adjust for covariates. The treatment coefficient of the outcome model targets a conditional treatment effect. Model-based standardization is typically applied to average the model predictions over the target covariate distribution, and generate a covariate-adjusted estimate of the marginal treatment effect.

METHODS

The standard approach to model-based standardization involves maximum-likelihood estimation and use of the non-parametric bootstrap. We introduce a novel, general-purpose, model-based standardization method based on multiple imputation that is easily applicable when the outcome model is a generalized linear model. We term our proposed approach multiple imputation marginalization (MIM). MIM consists of two main stages: the generation of synthetic datasets and their analysis. MIM accommodates a Bayesian statistical framework, which naturally allows for the principled propagation of uncertainty, integrates the analysis into a probabilistic framework, and allows for the incorporation of prior evidence.

RESULTS

We conduct a simulation study to benchmark the finite-sample performance of MIM in conjunction with a parametric outcome model. The simulations provide proof-of-principle in scenarios with binary outcomes, continuous-valued covariates, a logistic outcome model and the marginal log odds ratio as the target effect measure. When parametric modeling assumptions hold, MIM yields unbiased estimation in the target covariate distribution, valid coverage rates, and similar precision and efficiency than the standard approach to model-based standardization.

CONCLUSION

We demonstrate that multiple imputation can be used to marginalize over a target covariate distribution, providing appropriate inference with a correctly specified parametric outcome model and offering statistical performance comparable to that of the standard approach to model-based standardization.

Causal decomposition maps: An exploratory tool for designing area-level interventions aimed at reducing health disparities

Methods for decomposition analyses have been developed to partition between-group differences into explained and unexplained portions. In this paper, we introduce the concept of causal decomposition maps, which allow researchers to test the effect of area-level interventions on disease maps before implementation. These maps quantify the impact of interventions that aim to reduce differences in health outcomes between groups and illustrate how the disease map might change under different interventions. We adapt a new causal decomposition analysis method for the disease mapping context. Through the specification of a Bayesian hierarchical outcome model, we obtain counterfactual small area estimates of age-adjusted rates and reliable estimates of decomposition quantities. We present two formulations of the outcome model, with the second allowing for spatial interference of the intervention. Our method is utilized to determine whether the addition of gyms in different sets of rural ZIP codes could reduce any of the rural-urban difference in age-adjusted colorectal cancer incidence rates in Iowa ZIP codes.

Combining parametric and nonparametric models to estimate treatment effects in observational studies

Performing causal inference in observational studies requires we assume confounding variables are correctly adjusted for. In settings with few discrete-valued confounders, standard models can be employed. However, as the number of confounders increases these models become less feasible as there are fewer observations available for each unique combination of confounding variables. In this paper, we propose a new model for estimating treatment effects in observational studies that incorporates both parametric and nonparametric outcome models. By conceptually splitting the data, we can combine these models while maintaining a conjugate framework, allowing us to avoid the use of Markov chain Monte Carlo (MCMC) methods. Approximations using the central limit theorem and random sampling allow our method to be scaled to high-dimensional confounders. Through simulation studies we show our method can be competitive with benchmark models while maintaining efficient computation, and illustrate the method on a large epidemiological health survey.

Outcome trajectory estimation for optimal dynamic treatment regimes with repeated measures

In recent sequential multiple assignment randomized trials, outcomes were assessed multiple times to evaluate longer-term impacts of the dynamic treatment regimes (DTRs). Q-learning requires a scalar response to identify the optimal DTR. Inverse probability weighting may be used to estimate the optimal outcome trajectory, but it is inefficient, susceptible to model mis-specification, and unable to characterize how treatment effects manifest over time. We propose modified Q-learning with generalized estimating equations to address these limitations and apply it to the M-bridge trial, which evaluates adaptive interventions to prevent problematic drinking among college freshmen. Simulation studies demonstrate our proposed method improves efficiency and robustness.

BayesGmed: An R-package for Bayesian causal mediation analysis

BACKGROUND

The past decade has seen an explosion of research in causal mediation analysis. However, most analytic tools developed so far rely on frequentist methods which may not be robust in the case of small sample sizes. In this paper, we propose a Bayesian approach for causal mediation analysis based on Bayesian g-formula, which will overcome the limitations of the frequentist methods.

METHODS

We created BayesGmed, an R-package for fitting Bayesian mediation models in R. The application of the methodology (and software tool) is demonstrated by a secondary analysis of data collected as part of the MUSICIAN study, a randomised controlled trial of remotely delivered cognitive behavioural therapy (tCBT) for people with chronic pain. We tested the hypothesis that the effect of tCBT would be mediated by improvements in active coping, passive coping, fear of movement and sleep problems. We then demonstrate the use of informative priors to conduct probabilistic sensitivity analysis around violations of causal identification assumptions.

RESULT

The analysis of MUSICIAN data shows that tCBT has better-improved patients' self-perceived change in health status compared to treatment as usual (TAU). The adjusted log-odds of tCBT compared to TAU range from 1.491 (95% CI: 0.452-2.612) when adjusted for sleep problems to 2.264 (95% CI: 1.063-3.610) when adjusted for fear of movement. Higher scores of fear of movement (log-odds, -0.141 [95% CI: -0.245, -0.048]), passive coping (log-odds, -0.217 [95% CI: -0.351, -0.104]), and sleep problem (log-odds, -0.179 [95% CI: -0.291, -0.078]) leads to lower odds of a positive self-perceived change in health status. The result of BayesGmed, however, shows that none of the mediated effects are statistically significant. We compared BayesGmed with the mediation R- package, and the results were comparable. Finally, our sensitivity analysis using the BayesGmed tool shows that the direct and total effect of tCBT persists even for a large departure in the assumption of no unmeasured confounding.

CONCLUSION

This paper comprehensively overviews causal mediation analysis and provides an open-source software package to fit Bayesian causal mediation models.

Long-term impacts of an urban sanitation intervention on enteric pathogens in children in Maputo city, Mozambique: study protocol for a cross-sectional follow-up to the Maputo Sanitation (MapSan) trial 5 years postintervention

INTRODUCTION

We previously assessed the effect of an onsite sanitation intervention in informal neighbourhoods of urban Maputo, Mozambique on enteric pathogen detection in children after 2 years of follow-up (Maputo Sanitation (MapSan) trial, ClinicalTrials.gov: NCT02362932). We found significant reductions in Shigella and Trichuris prevalence but only among children born after the intervention was delivered. In this study, we assess the health impacts of the sanitation intervention after 5 years among children born into study households postintervention.

METHODS AND ANALYSIS

We are conducting a cross-sectional household study of enteric pathogen detection in child stool and the environment at compounds (household clusters sharing sanitation and outdoor living space) that received the pour-flush toilet and septic tank intervention at least 5 years prior or meet the original criteria for trial control sites. We are enrolling at least 400 children (ages 29 days to 60 months) in each treatment arm. Our primary outcome is the prevalence of 22 bacterial, protozoan, and soil transmitted helminth enteric pathogens in child stool using the pooled prevalence ratio across the outcome set to assess the overall intervention effect. Secondary outcomes include the individual pathogen detection prevalence and gene copy density of 27 enteric pathogens (including viruses); mean height-for-age, weight-for-age, and weight-for-height z-scores; prevalence of stunting, underweight, and wasting; and the 7-day period prevalence of caregiver-reported diarrhoea. All analyses are adjusted for prespecified covariates and examined for effect measure modification by age. Environmental samples from study households and the public domain are assessed for pathogens and faecal indicators to explore environmental exposures and monitor disease transmission.

ETHICS AND DISSEMINATION

Study protocols have been reviewed and approved by human subjects review boards at the Ministry of Health, Republic of Mozambique and the University of North Carolina at Chapel Hill. Deidentified study data will be deposited at https://osf.io/e7pvk/.

TRIAL REGISTRATION NUMBER

ISRCTN86084138.

Estimating Causal Effects of Interventions on Early-life Environmental Exposures Using Observational Data

PURPOSE OF REVIEW

We discuss how epidemiologic studies have used observational data to estimate the effects of potential interventions on early-life environmental exposures. We summarize the value of posing questions about interventions, how a group of techniques known as "g-methods" can provide advantages for estimating intervention effects, and how investigators have grappled with the strong assumptions required for causal inference.

RECENT FINDINGS

We identified nine studies that estimated health effects of hypothetical interventions on early-life environmental exposures. Of these, six examined air pollution. Interventions evaluated by these studies included setting exposure levels at a specific value, shifting exposure distributions, and limiting exposure levels to less than a threshold value. Only one study linked exposure contrasts to a specific intervention on an exposure source, however. There is growing interest in estimating intervention effects of early-life environmental exposures, in part because intervention effects are directly related to possible public health actions. Future studies can build on existing work by linking research questions to specific hypothetical interventions that could reduce exposure levels. We discuss how framing questions around interventions can help overcome some of the barriers to causal inference and how advances related to machine learning may strengthen studies by sidestepping the overly restrictive assumptions of parametric regression models. By leveraging advancements in causal inference and exposure science, an intervention framework for environmental epidemiology can guide actionable solutions to improve children's environmental health.

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.

Metabolic Signatures of Youth Exposure to Mixtures of Per- and Polyfluoroalkyl Substances: A Multi-Cohort Study

BACKGROUND

Exposure to per- and polyfluoroalkyl substances (PFAS) is ubiquitous and has been associated with an increased risk of several cardiometabolic diseases. However, the metabolic pathways linking PFAS exposure and human disease are unclear.

OBJECTIVE

We examined associations of PFAS mixtures with alterations in metabolic pathways in independent cohorts of adolescents and young adults.

METHODS

Three hundred twelve overweight/obese adolescents from the Study of Latino Adolescents at Risk (SOLAR) and 137 young adults from the Southern California Children's Health Study (CHS) were included in the analysis. Plasma PFAS and the metabolome were determined using liquid-chromatography/high-resolution mass spectrometry. A metabolome-wide association study was performed on log-transformed metabolites using Bayesian regression with a g-prior specification and g-computation for modeling exposure mixtures to estimate the impact of exposure to a mixture of six ubiquitous PFAS (PFOS, PFHxS, PFHpS, PFOA, PFNA, and PFDA). Pathway enrichment analysis was performed using Mummichog and Gene Set Enrichment Analysis. Significance across cohorts was determined using weighted Z -tests.

RESULTS

In the SOLAR and CHS cohorts, PFAS exposure was associated with alterations in tyrosine metabolism (meta-analysis p = 0.00002 ) and de novo fatty acid biosynthesis (p = 0.03 ), among others. For example, when increasing all PFAS in the mixture from low (∼ 30 th percentile) to high (∼ 70 th percentile), thyroxine (T4), a thyroid hormone related to tyrosine metabolism, increased by 0.72 standard deviations (SDs; equivalent to a standardized mean difference) in the SOLAR cohort (95% Bayesian credible interval (BCI): 0.00, 1.20) and 1.60 SD in the CHS cohort (95% BCI: 0.39, 2.80). Similarly, when going from low to high PFAS exposure, arachidonic acid increased by 0.81 SD in the SOLAR cohort (95% BCI: 0.37, 1.30) and 0.67 SD in the CHS cohort (95% BCI: 0.00, 1.50). In general, no individual PFAS appeared to drive the observed associations.

DISCUSSION

Exposure to PFAS is associated with alterations in amino acid metabolism and lipid metabolism in adolescents and young adults. https://doi.org/10.1289/EHP11372.

Parametric G-computation for compatible indirect treatment comparisons with limited individual patient data

Population adjustment methods such as matching-adjusted indirect comparison (MAIC) are increasingly used to compare marginal treatment effects when there are cross-trial differences in effect modifiers and limited patient-level data. MAIC is based on propensity score weighting, which is sensitive to poor covariate overlap and cannot extrapolate beyond the observed covariate space. Current outcome regression-based alternatives can extrapolate but target a conditional treatment effect that is incompatible in the indirect comparison. When adjusting for covariates, one must integrate or average the conditional estimate over the relevant population to recover a compatible marginal treatment effect. We propose a marginalization method based on parametric G-computation that can be easily applied where the outcome regression is a generalized linear model or a Cox model. The approach views the covariate adjustment regression as a nuisance model and separates its estimation from the evaluation of the marginal treatment effect of interest. The method can accommodate a Bayesian statistical framework, which naturally integrates the analysis into a probabilistic framework. A simulation study provides proof-of-principle and benchmarks the method's performance against MAIC and the conventional outcome regression. Parametric G-computation achieves more precise and more accurate estimates than MAIC, particularly when covariate overlap is poor, and yields unbiased marginal treatment effect estimates under no failures of assumptions. Furthermore, the marginalized regression-adjusted estimates provide greater precision and accuracy than the conditional estimates produced by the conventional outcome regression, which are systematically biased because the measure of effect is non-collapsible.

Bayesian G-Computation for Estimating Impacts of Interventions on Exposure Mixtures: Demonstration With Metals From Coal-Fired Power Plants and Birth Weight

The importance of studying the health impacts of exposure mixtures is increasingly being recognized, but such research presents many methodological and interpretation difficulties. We used Bayesian g-computation to estimate effects of a simulated public health action on exposure mixtures and birth weights in Milwaukee, Wisconsin, in 2011-2013. We linked data from birth records with census-tract-level air toxics data from the Environmental Protection Agency's National Air Toxics Assessment model. We estimated the difference between observed and expected birth weights that theoretically would have followed a hypothetical intervention to reduce exposure to 6 airborne metals by decommissioning 3 coal-fired power plants in Milwaukee County prior to 2010. Using Bayesian g-computation, we estimated a 68-g (95% credible interval: 25, 135) increase in birth weight following this hypothetical intervention. This example demonstrates the utility of our approach for using observational data to evaluate and contrast possible public health actions. Additionally, Bayesian g-computation offers a flexible strategy for estimating the effects of highly correlated exposures, addressing statistical issues such as variance inflation, and addressing conceptual issues such as the lack of interpretability of independent effects.

A Bayesian approach to comparing common models of life-course epidemiology

BACKGROUND

Life-course epidemiology studies people's health over long periods, treating repeated measures of their experiences (usually risk factors) as predictors or causes of subsequent morbidity and mortality. Three hypotheses or models often guide the analyst in assessing these sequential risks: the accumulation model (all measurement occasions are equally important for predicting the outcome), the critical period model (only one occasion is important) and the sensitive periods model (a catch-all model for any other pattern of temporal dependence).

METHODS

We propose a Bayesian omnibus test of these three composite models, as well as post hoc decompositions that identify their best respective sub-models. We test the approach via simulations, before presenting an empirical example that relates five sequential measurements of body weight to an RNAseq measure of colorectal-cancer disposition.

RESULTS

The approach correctly identifies the life-course model under which the data were simulated. Our empirical cohort study indicated with >90% probability that colorectal-cancer disposition reflected a sensitive process, with current weight being most important but prior body weight also playing a role.

CONCLUSIONS

The Bayesian methods we present allow precise inferences about the probability of life-course models given the data and are applicable in realistic scenarios involving causal analysis and missing data.

Effect of preschool childcare on school-aged children's adiposity in Quebec, Canada

BACKGROUND

Regulated public childcare must follow nutrition and physical activity guidelines, but the impact of public childcare on childhood adiposity is unclear.

OBJECTIVES

To estimate the effects of universal preschool childcare on children's BMI in elementary school in Quebec, Canada, and whether the effects differed in children from more or less advantaged families.

METHODS

For 1657 children enrolled in the Quebec Longitudinal Study of Child Development (1998-2010), BMI z-scores (BMIz) from 6 to 13 years were regressed on the childcare used from 2 to 5 years, adjusted for pre-childcare variables. Average treatment effects were estimated using the Bayesian multilevel linear regression and g-computation for four childcare profiles: 1) parental care or full-time care (35 hours/week) in a 2) centre-based, 3) regulated home-based or 4) unregulated home-based arrangement.

RESULTS

Had all participants attended centre-based care, mean BMIz in kindergarten would have been 0.38 (95% credible interval [CrI] 0.23, 0.52), which was 0.40 (95% CrI 0.14, 0.65) SD higher than regulated home-based, 0.20 (95% CrI -0.04, 0.43) SD higher than unregulated home-based and 0.36 (95% CrI 0.11, 0.60) SD higher than parental care. By 12 years, mean BMIz had increased for all childcare profiles, but differences between childcare profiles had diminished.

CONCLUSIONS

Although centre-based childcare was associated with an earlier rise in BMI, compared with informal care, it had no large, enduring effect, overall, or for less advantaged children, in particular.

Effects of gestational exposures to chemical mixtures on birth weight using Bayesian factor analysis in the Health Outcome and Measures of Environment (HOME) Study

Studying the effects of gestational exposures to chemical mixtures on infant birth weight is inconclusive due to several challenges. One of the challenges is which statistical methods to rely on. Bayesian factor analysis (BFA), which has not been utilized for chemical mixtures, has advantages in variance reduction and model interpretation.

METHODS

We analyzed data from a cohort of 384 pregnant women and their newborns using urinary biomarkers of phthalates, phenols, and organophosphate pesticides (OPs) and serum biomarkers of polychlorinated biphenyls (PCBs), polybrominated diphenyl ethers (PBDEs), perfluoroalkyl substances (PFAS), and organochlorine pesticides (OCPs). We examined the association between exposure to chemical mixtures and birth weight using BFA and compared with multiple linear regression (MLR) and Bayesian kernel regression models (BKMR).

RESULTS

For BFA, a 10-fold increase in the concentrations of PCB and PFAS mixtures was associated with an 81 g (95% confidence intervals [CI] = -132 to -31 g) and 57 g (95% CI = -105 to -10 g) reduction in birth weight, respectively. BKMR results confirmed the direction of effect. However, the 95% credible intervals all contained the null. For single-pollutant MLR, a 10-fold increases in the concentrations of multiple chemicals were associated with reduced birth weight, yet the 95% CI all contained the null. Variance inflation from MLR was apparent for models that adjusted for copollutants, resulting in less precise confidence intervals.

CONCLUSION

We demonstrated the merits of BFA on mixture analysis in terms of precision and interpretation compared with MLR and BKMR. We also identified the association between exposure to PCBs and PFAS and lower birth weight.

Bayesian data fusion: Probabilistic sensitivity analysis for unmeasured confounding using informative priors based on secondary data

Bayesian causal inference offers a principled approach to policy evaluation of proposed interventions on mediators or time-varying exposures. Building on the Bayesian g-formula method introduced by Keil et al., we outline a general approach for the estimation of population-level causal quantities involving dynamic and stochastic treatment regimes, including regimes related to mediation estimands such as natural direct and indirect effects. We further extend this approach to propose a Bayesian data fusion (BDF), an algorithm for performing probabilistic sensitivity analysis when a confounder unmeasured in a primary data set is available in an external data source. When the relevant relationships are causally transportable between the two source populations, BDF corrects confounding bias and supports causal inference and decision-making within the main study population without sharing of the individual-level external data set. We present results from a simulation study comparing BDF to two common frequentist correction methods for unmeasured mediator-outcome confounding bias in the mediation setting. We use these methods to analyze data on the role of stage at cancer diagnosis in contributing to Black-White colorectal cancer survival disparities.

A Quantile-Based g-Computation Approach to Addressing the Effects of Exposure Mixtures

BACKGROUND

Exposure mixtures frequently occur in data across many domains, particularly in the fields of environmental and nutritional epidemiology. Various strategies have arisen to answer questions about exposure mixtures, including methods such as weighted quantile sum (WQS) regression that estimate a joint effect of the mixture components.

OBJECTIVES

We demonstrate a new approach to estimating the joint effects of a mixture: quantile g-computation. This approach combines the inferential simplicity of WQS regression with the flexibility of g-computation, a method of causal effect estimation. We use simulations to examine whether quantile g-computation and WQS regression can accurately and precisely estimate the effects of mixtures in a variety of common scenarios.

METHODS

We examine the bias, confidence interval (CI) coverage, and bias-variance tradeoff of quantile g-computation and WQS regression and how these quantities are impacted by the presence of noncausal exposures, exposure correlation, unmeasured confounding, and nonlinearity of exposure effects.

RESULTS

Quantile g-computation, unlike WQS regression, allows inference on mixture effects that is unbiased with appropriate CI coverage at sample sizes typically encountered in epidemiologic studies and when the assumptions of WQS regression are not met. Further, WQS regression can magnify bias from unmeasured confounding that might occur if important components of the mixture are omitted from the analysis.

DISCUSSION

Unlike inferential approaches that examine the effects of individual exposures while holding other exposures constant, methods like quantile g-computation that can estimate the effect of a mixture are essential for understanding the effects of potential public health actions that act on exposure sources. Our approach may serve to help bridge gaps between epidemiologic analysis and interventions such as regulations on industrial emissions or mining processes, dietary changes, or consumer behavioral changes that act on multiple exposures simultaneously. https://doi.org/10.1289/EHP5838.

A Bayesian nonparametric model for zero-inflated outcomes: Prediction, clustering, and causal estimation

Researchers are often interested in predicting outcomes, detecting distinct subgroups of their data, or estimating causal treatment effects. Pathological data distributions that exhibit skewness and zero-inflation complicate these tasks-requiring highly flexible, data-adaptive modeling. In this paper, we present a multipurpose Bayesian nonparametric model for continuous, zero-inflated outcomes that simultaneously predicts structural zeros, captures skewness, and clusters patients with similar joint data distributions. The flexibility of our approach yields predictions that capture the joint data distribution better than commonly used zero-inflated methods. Moreover, we demonstrate that our model can be coherently incorporated into a standardization procedure for computing causal effect estimates that are robust to such data pathologies. Uncertainty at all levels of this model flow through to the causal effect estimates of interest-allowing easy point estimation, interval estimation, and posterior predictive checks verifying positivity, a required causal identification assumption. Our simulation results show point estimates to have low bias and interval estimates to have close to nominal coverage under complicated data settings. Under simpler settings, these results hold while incurring lower efficiency loss than comparator methods. We use our proposed method to analyze zero-inflated inpatient medical costs among endometrial cancer patients receiving either chemotherapy or radiation therapy in the SEER-Medicare database.

Bayesian estimation of the average treatment effect on the treated using inverse weighting

We develop a Bayesian approach to estimate the average treatment effect on the treated in the presence of confounding. The approach builds on developments proposed by Saarela et al in the context of marginal structural models, using importance sampling weights to adjust for confounding and estimate a causal effect. The Bayesian bootstrap is adopted to approximate posterior distributions of interest and avoid the issue of feedback that arises in Bayesian causal estimation relying on a joint likelihood. We present results from simulation studies to estimate the average treatment effect on the treated, evaluating the impact of sample size and the strength of confounding on estimation. We illustrate our approach using the classic Right Heart Catheterization data set and find a negative causal effect of the exposure on 30-day survival, in accordance with previous analyses of these data. We also apply our approach to the data set of the National Center for Health Statistics Birth Data and obtain a negative effect of maternal smoking during pregnancy on birth weight.

A review of time scale fundamentals in the g-formula and insidious selection bias

PURPOSE OF REVIEW

We review recent examples of data analysis with the g-formula, a powerful tool for analyzing longitudinal data and survival analysis. Specifically, we focus on the common choices of time scale and review inferential issues that may arise.

RECENT FINDINGS

Researchers are increasingly engaged with questions that require time scales subject to left-truncation and right-censoring. The assumptions necessary for allowing right-censoring are well defined in the literature, whereas similar assumptions for left-truncation are not well defined. Policy and biologic considerations sometimes dictate that observational data must be analyzed on time scales that are subject to left-truncation, such as age.

SUMMARY

Further consideration of left-truncation is needed, especially when biologic or policy considerations dictate that age is the relevant time scale of interest. Methodologic development is needed to reduce potential for bias when left-truncation may occur.

Estimating the Impact of Changes to Occupational Standards for Silica Exposure on Lung Cancer Mortality

BACKGROUND

Respiratory exposure to silica is associated with the risk of death owing to malignant and nonmalignant disease. 2.3 million US workers are exposed to silica. Occupational exposure limits for silica are derived from a number of lines of evidence, including observational studies. Observational studies may be subject to healthy worker survivor bias, which could result in underestimates of silica's impact on worker mortality and, in turn, bias risk estimates for occupational exposure limits.

METHODS

Using data on 65,999 workers pooled across multiple industries, we estimate the impacts of several hypothetical occupational exposure limits on silica exposure on lung cancer and all-cause mortality. We use the parametric g-formula, which can account for healthy worker survivor bias.

RESULTS

Assuming we could eliminate occupational exposure, we estimate that there would be 20.7 fewer deaths per 1,000 workers in our pooled study by age 80 (95% confidence interval = 14.5, 26.8), including 3.91 fewer deaths owing to lung cancer (95% CI = 1.53, 6.30). Less restrictive interventions demonstrated smaller but still substantial risk reductions.

CONCLUSIONS

Our results suggest that occupational exposure limits for silica can be further strengthened to reduce silica-associated mortality and illustrate how current risk analysis for occupational limits can be improved.

Sensitivity Analyses for Misclassification of Cause of Death in the Parametric G-Formula

Cause-specific mortality is an important outcome in studies of interventions to improve survival, yet causes of death can be misclassified. Here, we present an approach to performing sensitivity analyses for misclassification of cause of death in the parametric g-formula. The g-formula is a useful method to estimate effects of interventions in epidemiologic research because it appropriately accounts for time-varying confounding affected by prior treatment and can estimate risk under dynamic treatment plans. We illustrate our approach using an example comparing acquired immune deficiency syndrome (AIDS)-related mortality under immediate and delayed treatment strategies in a cohort of therapy-naive adults entering care for human immunodeficiency virus infection in the United States. In the standard g-formula approach, 10-year risk of AIDS-related mortality under delayed treatment was 1.73 (95% CI: 1.17, 2.54) times the risk under immediate treatment. In a sensitivity analysis assuming that AIDS-related death was measured with sensitivity of 95% and specificity of 90%, the 10-year risk ratio comparing AIDS-related mortality between treatment plans was 1.89 (95% CI: 1.13, 3.14). When sensitivity and specificity are unknown, this approach can be used to estimate the effects of dynamic treatment plans under a range of plausible values of sensitivity and specificity of the recorded event type.

Environmental exposure mixtures: questions and methods to address them

PURPOSE OF THIS REVIEW

This review provides a summary of statistical approaches that researchers can use to study environmental exposure mixtures. Two primary considerations are the form of the research question and the statistical tools best suited to address that question. Because the choice of statistical tools is not rigid, we make recommendations about when each tool may be most useful.

RECENT FINDINGS

When dimensionality is relatively low, some statistical tools yield easily interpretable estimates of effect (e.g., risk ratio, odds ratio) or intervention impacts. When dimensionality increases, it is often necessary to compromise this interpretablity in favor of identifying interesting statistical signals from noise; this requires applying statistical tools that are oriented more heavily towards dimension reduction via shrinkage and/or variable selection.

SUMMARY

The study of complex exposure mixtures has prompted development of novel statistical methods. We suggest that further validation work would aid practicing researchers in choosing among existing and emerging statistical tools for studying exposure mixtures.