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Assessing heterogeneous treatment effects (HTEs) is an essential task in epidemiology. The recent integration of machine learning into causal inference has provided a new, flexible tool for evaluating complex HTEs: causal forest. In a recent paper, Jawadekar et al (Am J Epidemiol. 2023;192(7):1155-1165) introduced this innovative approach and offered practical guidelines for applied users. Building on their work, this commentary provides additional insights and guidance to promote the understanding and application of causal forest in epidemiologic research. We start with conceptual clarifications, differentiating between honesty and cross-fitting, and exploring the interpretation of estimated conditional average treatment effects. We then delve into practical considerations not addressed by Jawadekar et al, including motivations for estimating HTEs, calibration approaches, and ways to leverage causal forest output with examples from simulated data. We conclude by outlining challenges to consider for future advancements and applications of causal forest in epidemiologic research. [ABSTRACT FROM AUTHOR]

In this paper, we present a practical approach for computing the sandwich variance estimator in 2-stage regression model settings. As a motivating example for 2-stage regression, we consider regression calibration, a popular approach for addressing covariate measurement error. The sandwich variance approach has rarely been applied in regression calibration, despite its requiring less computation time than popular resampling approaches for variance estimation, specifically the bootstrap. This is probably because it requires specialized statistical coding. Here we first outline the steps needed to compute the sandwich variance estimator. We then develop a convenient method of computation in R for sandwich variance estimation, which leverages standard regression model outputs and existing R functions and can be applied in the case of a simple random sample or complex survey design. We use a simulation study to compare the sandwich estimator to a resampling variance approach for both settings. Finally, we further compare these 2 variance estimation approaches in data examples from the Women's Health Initiative (1993–2005) and the Hispanic Community Health Study/Study of Latinos (2008–2011). In our simulations, the sandwich variance estimator typically had good numerical performance, but simple Wald bootstrap confidence intervals were unstable or overcovered in certain settings, particularly when there was high correlation between covariates or large measurement error. [ABSTRACT FROM AUTHOR]

In this paper, we consider methods for generating draws of a binary random variable whose expectation conditional on covariates follows a logistic regression model with known covariate coefficients. We examine approximations for finding a "balancing intercept," that is, a value for the intercept of the logistic model that leads to a desired marginal expectation for the binary random variable. We show that a recently proposed analytical approximation can produce inaccurate results, especially when targeting more extreme marginal expectations or when the linear predictor of the regression model has high variance. We then formulate the balancing intercept as a solution to an integral equation, implement a numerical approximation for solving the equation based on Monte Carlo methods, and show that the approximation works well in practice. Our approach to the basic problem of the balancing intercept provides an example of a broadly applicable strategy for formulating and solving problems that arise in the design of simulation studies used to evaluate or teach epidemiologic methods. [ABSTRACT FROM AUTHOR]

Recurrent events—outcomes that an individual can experience repeatedly over the course of follow-up—are common in epidemiologic and health services research. Studies involving recurrent events often focus on time to first occurrence or on event rates, which assume constant hazards over time. In this paper, we contextualize recurrent event parameters of interest using counterfactual theory in a causal inference framework and describe an approach for estimating a target parameter referred to as the mean cumulative count. This approach leverages inverse probability weights to control measured confounding with an existing (and underutilized) nonparametric estimator of recurrent event burden first proposed by Dong et al. in 2015. We use simulations to demonstrate the unbiased estimation of the mean cumulative count using the weighted Dong-Yasui estimator in a variety of scenarios. The weighted Dong-Yasui estimator for the mean cumulative count allows researchers to use observational data to flexibly estimate and contrast the expected number of cumulative events experienced per individual by a given time point under different exposure regimens. We provide code to ease application of this method. [ABSTRACT FROM AUTHOR]

"Fusion" study designs combine data from different sources to answer questions that could not be answered (as well) by subsets of the data. Studies that augment main study data with validation data, as in measurement-error correction studies or generalizability studies, are examples of fusion designs. Fusion estimators, here solutions to stacked estimating functions, produce consistent answers to identified research questions using data from fusion designs. In this paper, we describe a pair of examples of fusion designs and estimators, one where we generalize a proportion to a target population and one where we correct measurement error in a proportion. For each case, we present an example motivated by human immunodeficiency virus research and summarize results from simulation studies. Simulations demonstrate that the fusion estimators provide approximately unbiased results with appropriate 95% confidence interval coverage. Fusion estimators can be used to appropriately combine data in answering important questions that benefit from multiple sources of information. [ABSTRACT FROM AUTHOR]

The development of tools for power and sample-size calculations for mediation analysis has lagged far behind the development of methods. The accompanying paper by Rudolph et al. (Am J Epidemiol. 2020;189(12):1559–1567) is a helpful contribution in using simulations as a tool for power calculations for more complex methods and settings. Much work remains to be done in the development of easy-to-use packages and simple online websites for carrying out power and sample-size calculations for mediation analysis. Much remains to be learned with respect to the relative power of different methods in different settings. There will likely be feedback between these 2 important frontiers of the tools we have available and of our understanding of power when conducting mediation analysis. [ABSTRACT FROM AUTHOR]

Measurement error is pervasive in epidemiologic research. Epidemiologists often assume that mismeasurement of study variables is nondifferential with respect to other analytical variables and then rely on the heuristic that "nondifferential misclassification will bias estimates towards the null." However, there are many exceptions to the heuristic for which bias towards the null cannot be assumed. In this paper, we compile and characterize 7 exceptions to this rule and encourage analysts to take a more critical and nuanced approach to evaluating and discussing bias from nondifferential mismeasurement. [ABSTRACT FROM AUTHOR]

An increasing number of recent studies have suggested that doubly robust estimators with cross-fitting should be used when estimating causal effects with machine learning methods. However, not all existing programs that implement doubly robust estimators support machine learning methods and cross-fitting, or provide estimates on multiplicative scales. To address these needs, we developed AIPW , a software package implementing augmented inverse probability weighting (AIPW) estimation of average causal effects in R (R Foundation for Statistical Computing, Vienna, Austria). Key features of the AIPW package include cross-fitting and flexible covariate adjustment for observational studies and randomized controlled trials (RCTs). In this paper, we use a simulated RCT to illustrate implementation of the AIPW estimator. We also perform a simulation study to evaluate the performance of the AIPW package compared with other doubly robust implementations, including CausalGAM , npcausal , tmle , and tmle3. Our simulation showed that the AIPW package yields performance comparable to that of other programs. Furthermore, we also found that cross-fitting substantively decreases the bias and improves the confidence interval coverage for doubly robust estimators fitted with machine learning algorithms. Our findings suggest that the AIPW package can be a useful tool for estimating average causal effects with machine learning methods in RCTs and observational studies. [ABSTRACT FROM AUTHOR]

A letter to the editor is presented in response to an article by J. Santaella-Tenorio et all wherein they repeated that they provided a summary of results from studies where researchers investigated the impact of various gun control laws on crime rates.

In this paper, we evaluate 11 measures of inequality, d (p 1, p 2), between 2 proportions p 1 and p 2, some of which are new to the health disparities literature. These measures are selected because they are continuous, nonnegative, equal to 0 if and only if | p 1 − p 2| = 0, and maximal when | p 1 − p 2| = 1. They are also symmetrical [ d (p 1, p 2) =  d (p 2, p 1)] and complement-invariant [ d (p 1, p 2) =  d (1 − p 2, 1 − p 1)]. To study intermeasure agreement, 5 of the 11 measures, including the absolute difference, are retained, because they remain finite and are maximal if and only if | p 1 − p 2| = 1. Even when the 2 proportions are assumed to be drawn at random from a shared distribution—interpreted as the absence of an avoidable difference—the expected value of d (p 1, p 2) depends on the shape of the distribution (and the choice of d) and can be quite large. To allow for direct comparisons among measures, we propose a standard measurement unit akin to a z score. For skewed underlying beta distributions, 4 of the 5 retained measures, once standardized, offer more conservative assessments of the magnitude of inequality than the absolute difference. We conclude that, even for measures that share the highlighted mathematical properties, magnitude comparisons are most usefully assessed relative to an elicited or estimated underlying distribution for the 2 proportions. [ABSTRACT FROM AUTHOR]

Epidemiologists often compare the observed number of deaths in a cohort with the expected number of deaths, obtained by multiplying person-time accrued in the cohort by mortality rates for a reference population (ideally, a reference that represents the mortality rate in the cohort in the absence of exposure). However, if exposure is hazardous (or salutary), this calculation will not consistently estimate the number of deaths expected in the absence of exposure because exposure will have affected the distribution of person-time observed in the study cohort. While problems with interpretation of this standard calculation of expected counts were discussed more than 2 decades ago, these discussions had little impact on epidemiologic practice. The logic of counterfactuals may help clarify this topic as we revisit these issues. In this paper, we describe a simple way to consistently estimate the expected number of deaths in such settings, and we illustrate the approach using data from a cohort study of mortality among underground miners. [ABSTRACT FROM AUTHOR]

Sequences of treatments that adapt to a patient's changing condition over time are often needed for the management of chronic diseases. An adaptive treatment strategy (ATS) consists of personalized treatment rules to be applied through the course of a disease that input the patient's characteristics at the time of decision-making and output a recommended treatment. An optimal ATS is the sequence of tailored treatments that yields the best clinical outcome for patients sharing similar characteristics. Methods for estimating optimal adaptive treatment strategies, which must disentangle short- and long-term treatment effects, can be theoretically involved and hard to explain to clinicians, especially when the outcome to be optimized is a survival time subject to right-censoring. In this paper, we describe dynamic weighted survival modeling, a method for estimating an optimal ATS with survival outcomes. Using data from the Clinical Practice Research Datalink, a large primary-care database, we illustrate how it can answer an important clinical question about the treatment of type 2 diabetes. We identify an ATS pertaining to which drug add-ons to recommend when metformin in monotherapy does not achieve the therapeutic goals. [ABSTRACT FROM AUTHOR]

The National Cancer Institute developed the Health Disparities Calculator (HD*Calc) to facilitate research on health disparities. HD*Calc calculates multiple measures of health disparities using data collected from population-based disease surveillance systems, such as cancer registries. In this paper, we extend the use of HD*Calc to complex survey data by developing plug-in point estimators and Taylor linearization variance estimators that consider complex designs: stratification, multistage clustering, and differential weighting. Our simulation indicates that the plug-in estimators are approximately unbiased and the Taylor linearization variance estimators are accurate. Using 2011–2016 data from the National Health and Nutrition Examination Survey, we demonstrate the use of these estimators in evaluating socioeconomic disparities in the prevalence of child and adolescent (ages 2–18 years) obesity in the United States. Statistical software has been developed for ease of disparity analyses using complex survey data. [ABSTRACT FROM AUTHOR]

In this paper, we propose a structural framework for population-based cancer epidemiology and evaluate the performance of double-robust estimators for a binary exposure in cancer mortality. We conduct numerical analyses to study the bias and efficiency of these estimators. Furthermore, we compare 2 different model selection strategies based on 1) Akaike's Information Criterion and the Bayesian Information Criterion and 2) machine learning algorithms, and we illustrate double-robust estimators' performance in a real-world setting. In simulations with correctly specified models and near-positivity violations, all but the naive estimators had relatively good performance. However, the augmented inverse-probability-of-treatment weighting estimator showed the largest relative bias. Under dual model misspecification and near-positivity violations, all double-robust estimators were biased. Nevertheless, the targeted maximum likelihood estimator showed the best bias-variance trade-off, more precise estimates, and appropriate 95% confidence interval coverage, supporting the use of the data-adaptive model selection strategies based on machine learning algorithms. We applied these methods to estimate adjusted 1-year mortality risk differences in 183,426 lung cancer patients diagnosed after admittance to an emergency department versus persons with a nonemergency cancer diagnosis in England (2006-2013). The adjusted mortality risk (for patients diagnosed with lung cancer after admittance to an emergency department) was 16% higher in men and 18% higher in women, suggesting the importance of interventions targeting early detection of lung cancer signs and symptoms. [ABSTRACT FROM AUTHOR]

There have been recent proposals advocating the use of additive gene-environment interaction instead of the widely used multiplicative scale, as a more relevant public health measure. Using gene-environment independence enhances statistical power for testing multiplicative interaction in case-control studies. However, under departure from this assumption, substantial bias in the estimates and inflated type I error in the corresponding tests can occur. In this paper, we extend the empirical Bayes (EB) approach previously developed for multiplicative interaction, which trades off between bias and efficiency in a data-adaptive way, to the additive scale. An EB estimator of the relative excess risk due to interaction is derived, and the corresponding Wald test is proposed with a general regression setting under a retrospective likelihood framework. We study the impact of gene-environment association on the resultant test with case-control data. Our simulation studies suggest that the EB approach uses the gene-environment independence assumption in a data-adaptive way and provides a gain in power compared with the standard logistic regression analysis and better control of type I error when compared with the analysis assuming gene-environment independence. We illustrate themethods with data from the Ovarian Cancer Association Consortium. [ABSTRACT FROM AUTHOR]

Recently, many new approaches, study designs, and statistical and analytical methods have emerged for studying gene-environment interactions (GxEs) in large-scale studies of human populations. There are opportunities in this field, particularly with respect to the incorporation of -omics and next-generation sequencing data and continual improvement in measures of environmental exposures implicated in complex disease outcomes. In a workshop called "Current Challenges and New Opportunities for Gene-Environment Interaction Studies of Complex Diseases," held October 17-18, 2014, by the National Institute of Environmental Health Sciences and the National Cancer Institute in conjunction with the annual American Society of Human Genetics meeting, participants explored new approaches and tools that have been developed in recent years for GxE discovery. This paper highlights current and critical issues and themes in GxE research that need additional consideration, including the improved data analytical methods, environmental exposure assessment, and incorporation of functional data and annotations. [ABSTRACT FROM AUTHOR]

The analysis of gene-environment interaction (GxE) may hold the key for further understanding the etiology of many complex traits. The current availability of high-volume genetic data, the wide range in types of environmental data that can be measured, and the formation of consortiums of multiple studies provide new opportunities to identify GxE but also new analytical challenges. In this article, we summarize several statistical approaches that can be used to test for GxE in a genome-wide association study. These include traditional models of GxE in a case-control or quantitative trait study as well as alternative approaches that can provide substantially greater power. The latest methods for analyzing GxE with gene sets and with data in a consortium setting are summarized, as are issues that arise due to the complexity of environmental data. We provide some speculation on why detecting GxE in a genome-wide association study has thus far been difficult. We conclude with a description of software programs that can be used to implement most of the methods described in the paper. [ABSTRACT FROM AUTHOR]

There is no complete solution for the problem of abuse of statistics, but methodological training needs to cover cognitive biases and other psychosocial factors affecting inferences. The present paper discusses 3 common cognitive distortions: 1) dichotomania, the compulsion to perceive quantities as dichotomous even when dichotomization is unnecessary and misleading, as in inferences based on whether a P value is "statistically significant"; 2) nullism, the tendency to privilege the hypothesis of no difference or no effect when there is no scientific basis for doing so, as when testing only the null hypothesis; and 3) statistical reification, treating hypothetical data distributions and statistical models as if they reflect known physical laws rather than speculative assumptions for thought experiments. As commonly misused, null-hypothesis significance testing combines these cognitive problems to produce highly distorted interpretation and reporting of study results. Interval estimation has so far proven to be an inadequate solution because it involves dichotomization, an avenue for nullism. Sensitivity and bias analyses have been proposed to address reproducibility problems (Am J Epidemiol. 2017;186(6):646--647); these methods can indeed address reification, but they can also introduce new distortions via misleading specifications for bias parameters. P values can be reframed to lessen distortions by presenting them without reference to a cutoff, providing them for relevant alternatives to the null, and recognizing their dependence on all assumptions used in their computation; they nonetheless require rescaling for measuring evidence. I conclude that methodological development and training should go beyond coverage of mechanistic biases (e.g., confounding, selection bias, measurement error) to cover distortions of conclusions produced by statistical methods and psychosocial forces. [ABSTRACT FROM AUTHOR]

Researchers conducting observational studies need to consider 3 types of biases: selection bias, information bias, and confounding bias. A whole arsenal of statistical tools can be used to deal with information and confounding biases. However, methods for addressing selection bias and unmeasured confounding are less developed. In this paper, we propose general bounding formulas for bias, including selection bias and unmeasured confounding. This should help researchers make more prudent interpretations of their (potentially biased) results. [ABSTRACT FROM AUTHOR]

In cohort mortality studies, there often is interest in associations between an exposure of primary interest and mortality due to a range of different causes. A standard approach to such analyses involves fitting a separate regression model for each type of outcome. However, the statistical precision of some estimated associations may be poor because of sparse data. In this paper, we describe a hierarchical regression model for estimation of parameters describing outcome-specific relative rate functions and associated credible intervals. The proposed model uses background stratification to provide flexible control for the outcome-specific associations of potential confounders, and it employs a hierarchical “shrinkage” approach to stabilize estimates of an exposure’s associations with mortality due to different causes of death. The approach is illustrated in analyses of cancer mortality in 2 cohorts: a cohort of dioxin-exposed US chemical workers and a cohort of radiation-exposed Japanese atomic bomb survivors. Compared with standard regression estimates of associations, hierarchical regression yielded estimates with improved precision that tended to have less extreme values. The hierarchical regression approach also allowed the fitting of models with effect-measure modification. The proposed hierarchical approach can yield estimates of association that are more precise than conventional estimates when one wishes to estimate associations with multiple outcomes. [ABSTRACT FROM AUTHOR]

The authors offer a response to A. R. Cartus and B. D. L. Marshall's commentary on their study on choosing medication type for patients with opioid use disorder (OUD). Topics include the interesting set of issues raised by Cartus and Marshall regarding the potential trade-offs between investing in technical sophistication and public health considerations and their agreement with Cartus and Marshall on the need to focus on OUD patient-centered outcomes.

As pellagra reached epidemic proportions in the United States in the early 20th century, 2 teams of investigators assessed its incidence in cotton mill villages in South Carolina. The first, the Thompson-McFadden Commission, concluded that pellagra was likely infectious. The second, a Public Health Service investigation led by Joseph Goldberger, concluded that pellagra was caused by a dietary deficiency. In this paper, we recount the history of the 2 investigations and consider how the differences between the 2 studies' designs, measurements, analyses, and interpretations led to different conclusions. Because the novel dietary assessment strategy was a key feature of the Public Health Service's study design, we incorporated simulated measurement error in a reanalysis of the Public Health Service's data to assess whether this specific difference affected the divergent conclusions. [ABSTRACT FROM PUBLISHER]

Mixed evidence exists of associations between mobility data and coronavirus disease 2019 (COVID-19) case rates. We aimed to evaluate the county-level impact of reducing mobility on new COVID-19 cases in summer/fall of 2020 in the United States and to demonstrate modified treatment policies to define causal effects with continuous exposures. Specifically, we investigated the impact of shifting the distribution of 10 mobility indexes on the number of newly reported cases per 100,000 residents 2 weeks ahead. Primary analyses used targeted minimum loss-based estimation with Super Learner to avoid parametric modeling assumptions during statistical estimation and flexibly adjust for a wide range of confounders, including recent case rates. We also implemented unadjusted analyses. For most weeks, unadjusted analyses suggested strong associations between mobility indexes and subsequent new case rates. However, after confounder adjustment, none of the indexes showed consistent associations under mobility reduction. Our analysis demonstrates the utility of this novel distribution-shift approach to defining and estimating causal effects with continuous exposures in epidemiology and public health. [ABSTRACT FROM AUTHOR]

The coronavirus disease 2019 (COVID-19) pandemic has underscored the importance of observational studies of real-world vaccine effectiveness (VE) to help answer urgent public health questions. One approach to rapidly answering questions about real-world VE relies on linking data from a population-based registry of vaccinations with a population-based registry of health outcomes. Here we consider some potential sources of bias in linked registry studies, including incomplete reporting to the registries, errors in linking individuals between registries, and errors in the assumed population size of the catchment area of the registries. We show that the direction of the bias resulting from one source of error by itself is predictable. However, if multiple sources of error are present, the direction of the bias can be either upward or downward. The biases can be so strong as to make harmful vaccines appear effective. We provide explicit formulas with which to quantify and adjust for multiple biases in estimates of VE which could be used in sensitivity analyses. While this work was motivated by COVID-19 vaccine questions, the results are generally applicable to studies that link population-based exposure registries with population-based case registries to estimate relative risks of exposures. [ABSTRACT FROM AUTHOR]

Overdose Good Samaritan laws (GSLs) aim to reduce mortality by providing limited legal protections when a bystander to a possible drug overdose summons help. Most research into the impact of these laws is dated or potentially confounded by coenacted naloxone access laws. Lack of awareness and trust in GSL protections, as well as fear of police involvement and legal repercussions, remain key deterrents to help-seeking. These barriers may be unequally distributed by race/ethnicity due to racist policing and drug policies, potentially producing racial/ethnic disparities in the effectiveness of GSLs for reducing overdose mortality. We used 2015–2019 vital statistics data to estimate the effect of recent GSLs on overdose mortality, overall (8 states) and by Black/White race/ethnicity (4 states). Given GSLs' near ubiquity, few unexposed states were available for comparison. Therefore, we generated an "inverted" synthetic control method (SCM) to compare overdose mortality in new-GSL states with that in states that had GSLs throughout the analytical period. The estimated relationships between GSLs and overdose mortality, both overall and stratified by Black/White race/ethnicity, were consistent with chance. An absence of effect could result from insufficient protection provided by the laws, insufficient awareness of them, and/or reticence to summon help not addressable by legal protections. The inverted SCM may be useful for evaluating other widespread policies. [ABSTRACT FROM AUTHOR]

Inverse probability weighting (IPW) and targeted maximum likelihood estimation (TMLE) are methodologies that can adjust for confounding and selection bias and are often used for causal inference. Both estimators rely on the positivity assumption that within strata of confounders there is a positive probability of receiving treatment at all levels under consideration. Practical applications of IPW require finite inverse probability (IP) weights. TMLE requires that propensity scores (PS) be bounded away from 0 and 1. Although truncation can improve variance and finite sample bias, this artificial distortion of the IP weights and PS distribution introduces asymptotic bias. As sample size grows, truncation-induced bias eventually swamps variance, rendering nominal confidence interval coverage and hypothesis tests invalid. We present a simple truncation strategy based on the sample size, n , that sets the upper bound on IP weights at |$\sqrt{\textit{n}}$| ln  n /5. For TMLE, the lower bound on the PS should be set to 5/(⁠|$\sqrt{\textit{n}}$| ln  n /5). Our strategy was designed to optimize the mean squared error of the parameter estimate. It naturally extends to data structures with missing outcomes. Simulation studies and a data analysis demonstrate our strategy's ability to minimize both bias and mean squared error in comparison with other common strategies, including the popular but flawed quantile-based heuristic. [ABSTRACT FROM AUTHOR]

In this article, I provide a perspective on the tobacco epidemic and epidemiology, describing the impact of the tobacco-caused disease epidemic on the field of epidemiology. Although there is an enormous body of epidemiologic evidence on the associations of smoking with health, little systematic attention has been given to how decades of research have affected epidemiology and its practice. I address the many advances that resulted from epidemiologic research on smoking and health, such as demonstration of the utility of observational designs and important parameters (the odds ratio and the population attributable risk), guidelines for causal inference, and systematic review approaches. I also cover unintended and adverse consequences for the field, including the strategy of doubt creation and the recruitment of epidemiologists by the tobacco industry to serve its mission. The paradigm of evidence-based action for addressing noncommunicable diseases began with the need to address the epidemic of tobacco-caused disease, an imperative for action documented by epidemiologic research. [ABSTRACT FROM AUTHOR]

In the accompanying article (Am J Epidemiol. 2017;186(6):646-647), Dr. Timothy Lash makes a forceful case that the problems with reproducibility in science stem from our "culture" of null hypothesis significance testing. He notes that when attention is selectively given to statistically significant findings, the estimated effects will be systematically biased away from the null. Here I revisit the recent history of genetic epidemiology and argue for retaining statistical testing as an important part of the tool kit. Particularly when many factors are considered in an agnostic way, in what Lash calls "innovative" research, investigators need a selection strategy to identify which findings are most likely to be genuine, and hence worthy of further study. [ABSTRACT FROM AUTHOR]

Perfluoroalkyl and polyfluoroalkyl substances (PFAS) have been associated with earlier natural menopause; however, the underlying mechanisms are not well understood, particularly the extent to which this relationship is mediated by sex hormones. We analyzed data (1999–2017) on 1,120 premenopausal women from the Study of Women's Health Across the Nation (SWAN). Causal mediation analysis was applied to quantify the degree to which follicle-stimulating hormone (FSH) and estradiol levels could mediate the associations between PFAS and incident natural menopause. Participants with higher PFAS concentrations had shorter times to natural menopause, with a relative survival of 0.82 (95% confidence interval (CI): 0.69, 0.96) for linear perfluorooctane sulfonate (n-PFOS), 0.84 (95% CI: 0.69, 1.00) for sum of branched-chain perfluorooctane sulfonate (Sm-PFOS), 0.79 (95% CI: 0.66, 0.93) for linear-chain perfluorooctanoate (n-PFOA), and 0.84 (95% CI: 0.71, 0.97) for perfluorononanoate (PFNA), comparing the highest tertile of PFAS concentrations with the lowest. The proportion of the effect mediated through FSH was 8.5% (95% CI: −11.7, 24.0) for n-PFOS, 13.2% (95% CI: 0.0, 24.5) for Sm-PFOS, 26.9% (95% CI: 15.6, 38.4) for n-PFOA, and 21.7% (6.8, 37.0) for PFNA. No significant mediation by estradiol was observed. The effect of PFAS on natural menopause may be partially explained by variations in FSH concentrations. [ABSTRACT FROM AUTHOR]

In the analysis of observational studies, inverse probability weighting (IPW) is commonly used to consistently estimate the average treatment effect (ATE) or the average treatment effect in the treated (ATT). The variance of the IPW ATE estimator is often estimated by assuming that the weights are known and then using the so-called "robust" (Huber-White) sandwich estimator, which results in conservative standard errors (SEs). Here we show that using such an approach when estimating the variance of the IPW ATT estimator does not necessarily result in conservative SE estimates. That is, assuming the weights are known, the robust sandwich estimator may be either conservative or anticonservative. Thus, confidence intervals for the ATT using the robust SE estimate will not be valid, in general. Instead, stacked estimating equations which account for the weight estimation can be used to compute a consistent, closed-form variance estimator for the IPW ATT estimator. The 2 variance estimators are compared via simulation studies and in a data analysis of the association between smoking and gene expression. [ABSTRACT FROM AUTHOR]

A letter to the editor is presented in response to a commentary by OA Panagiotou and S. Wacholder on an article by MC Turner et al where the former discussed the estimation of population attributable risks (PARs) or population attributable fractions when multiple risk factors are involved.

The article discusses the binary outcome formula, using counterfactual framework, to account for exposure-mediator interaction in mediation analysis. Topics discussed include effects on longitudinal settings in the presence of time-varying exposure, the marginal structural model approach for continuous outcomes to the setting of binary formula, and the effect of the mediator on the outcome. Also discussed is the effect of the exposure on the mediator.

Ambitious World Health Organization targets for disease elimination require monitoring of epidemics using routine health data in settings of decreasing and low incidence. We evaluated 2 methods commonly applied to routine testing results to estimate incidence rates that assume a uniform probability of infection between consecutive negative and positive tests based on 1) the midpoint of this interval and 2) a randomly selected point in this interval. We compared these with an approximation of the Poisson binomial distribution, which assigns partial incidence to time periods based on the uniform probability of occurrence in these intervals. We assessed bias, variance, and convergence of estimates using simulations of Weibull-distributed failure times with systematically varied baseline incidence and varying trend. We considered results for quarterly, half-yearly, and yearly incidence estimation frequencies. We applied the methods to assess human immunodeficiency virus (HIV) incidence in HIV-negative patients from the Treatment With Antiretrovirals and Their Impact on Positive and Negative Men (TAIPAN) Study, an Australian study of HIV incidence in men who have sex with men, between 2012 and 2018. The Poisson binomial method had reduced bias and variance at low levels of incidence and for increased estimation frequency, with increased consistency of estimation. Application of methods to real-world assessment of HIV incidence found decreased variance in Poisson binomial model estimates, with observed incidence declining to levels where simulation results had indicated bias in midpoint and random-point methods. [ABSTRACT FROM AUTHOR]

This primer describes the statistical uncertainty in mechanistic models and provides R code to quantify it. We begin with an overview of mechanistic models for infectious disease, and then describe the sources of statistical uncertainty in the context of a case study on severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). We describe the statistical uncertainty as belonging to 3 categories: data uncertainty, stochastic uncertainty, and structural uncertainty. We demonstrate how to account for each of these via statistical uncertainty measures and sensitivity analyses broadly, as well as in a specific case study on estimating the basic reproductive number, |${R}_0$|⁠ , for SARS-CoV-2. [ABSTRACT FROM AUTHOR]

The article offers insights on a study on the quantification of human microbiome stability and its implications for epidemiological studies. Topics discussed include the intra-class correlation coefficient (ICC) values for the Human Microbiome Project data; changes in the ICC values after centered log-ratio (CLR) transformation; and evaluation of the temporal-instability power loss in relation to the ICC metrics.

A growing number of studies use data before and after treatment initiation in groups exposed to different treatment strategies to estimate "causal effects" using a ratio measure called the prior event rate ratio (PERR). Here, we offer a causal interpretation for PERR and its additive scale analog, the prior event rate difference (PERD). We show that causal interpretation of these measures requires untestable rate-change assumptions about the relationship between 1) the change of the counterfactual rate before and after treatment initiation in the treated group under hypothetical intervention to implement the control strategy; and 2) the change of the factual rate before and after treatment initiation in the control group. The rate-change assumption is on the multiplicative scale for PERR but on the additive scale for PERD; the 2 assumptions hold simultaneously under testable, but unlikely, conditions. Even if investigators can pick the most appropriate scale, the relevant rate-change assumption might not hold exactly, so we describe sensitivity analysis methods to examine how assumption violations of different magnitudes would affect study results. We illustrate the methods using data from a published study of proton pump inhibitors and pneumonia. [ABSTRACT FROM AUTHOR]

In observational studies using routinely collected data, a variable with a high level of missingness or misclassification may determine whether an observation is included in the analysis. In settings where inclusion criteria are assessed after imputation, the popular multiple-imputation variance estimator proposed by Rubin ("Rubin's rules" (RR)) is biased due to incompatibility between imputation and analysis models. While alternative approaches exist, most analysts are not familiar with them. Using partially validated data from a human immunodeficiency virus cohort, we illustrate the calculation of an imputation variance estimator proposed by Robins and Wang (RW) in a scenario where the study exclusion criteria are based on a variable that must be imputed. In this motivating example, the corresponding imputation variance estimate for the log odds was 29% smaller using the RW estimator than using the RR estimator. We further compared these 2 variance estimators with a simulation study which showed that coverage probabilities of 95% confidence intervals based on the RR estimator were too high and became worse as more observations were imputed and more subjects were excluded from the analysis. The RW imputation variance estimator performed much better and should be employed when there is incompatibility between imputation and analysis models. We provide analysis code to aid future analysts in implementing this method. [ABSTRACT FROM AUTHOR]

When estimating causal effects, careful handling of missing data is needed to avoid bias. Complete-case analysis is commonly used in epidemiologic analyses. Previous work has shown that covariate-stratified effect estimates from complete-case analysis are unbiased when missingness is independent of the outcome conditional on the exposure and covariates. Here, we assess the bias of complete-case analysis for adjusted marginal effects when confounding is present under various causal structures of missing data. We show that estimation of the marginal risk difference requires an unbiased estimate of the unconditional joint distribution of confounders and any other covariates required for conditional independence of missingness and outcome. The dependence of missing data on these covariates must be considered to obtain a valid estimate of the covariate distribution. If none of these covariates are effect-measure modifiers on the absolute scale, however, the marginal risk difference will equal the stratified risk differences and the complete-case analysis will be unbiased when the stratified effect estimates are unbiased. Estimation of unbiased marginal effects in complete-case analysis therefore requires close consideration of causal structure and effect-measure modification. [ABSTRACT FROM AUTHOR]

Mediation analyses are valuable for examining mechanisms underlying an association, investigating possible explanations for nonintuitive results, or identifying interventions that can improve health in the context of nonmanipulable exposures. However, designing a study for the purpose of answering a mediation-related research question remains challenging because sample size and power calculations for mediation analyses are typically not conducted or are crude approximations. Consequently, many studies are probably conducted without first establishing that they have the statistical power required to detect a meaningful effect, potentially resulting in wasted resources. In an effort to advance more accurate power calculations for estimating direct and indirect effects, we present a tutorial demonstrating how to conduct a flexible, simulation-based power analysis. In this tutorial, we compare power to estimate direct and indirect effects across various estimators (the Baron and Kenny estimator (J Pers Soc Psychol. 1986;51(6):1173–1182), inverse odds ratio weighting, and targeted maximum likelihood estimation) using various data structures designed to mimic important features of real data. We include step-by-step commented R code (R Foundation for Statistical Computing, Vienna, Austria) in an effort to lower implementation barriers to ultimately improving power assessment in mediation studies. [ABSTRACT FROM AUTHOR]

In the article, the authors discuss the simulation practice called the balancing intercept as an essential tool in learning and developing new methodologies in epidemiology. Topics include the basic steps when making simulation experiments, the benefits of the practice like the easier interpretation of marginal probability and validation of simulation codes, and the issues on the use of the practice in a conditional probability model.

The author reflects on the inaccuracies in two published articles about the associations among age variation, obesity status and mortality risk in the 2013 issues of the "American Journal of Public Health" (AJPH) and the "American Journal of Epidemiology" (AJE). Also cited are the letter to the editor claiming a selection bias in the articles, and the possible effects of the studies to the insurance industry.

A letter to the editor is presented in response to the article "Receiver Operating Characteristic Curve Inference From a Sample With a Limit of Detection" by N. J. Perkins and colleagues, published in a previous issue.

The Consortium of Metabolomics Studies (COMETS) was established in 2014 to facilitate large-scale collaborative research on the human metabolome and its relationship with disease etiology, diagnosis, and prognosis. COMETS comprises 47 cohorts from Asia, Europe, North America, and South America that together include more than 136,000 participants with blood metabolomics data on samples collected from 1985 to 2017. Metabolomics data were provided by 17 different platforms, with the most frequently used labs being Metabolon, Inc. (14 cohorts), the Broad Institute (15 cohorts), and Nightingale Health (11 cohorts). Participants have been followed for a median of 23 years for health outcomes including death, cancer, cardiovascular disease, diabetes, and others; many of the studies are ongoing. Available exposure-related data include common clinical measurements and behavioral factors, as well as genome-wide genotype data. Two feasibility studies were conducted to evaluate the comparability of metabolomics platforms used by COMETS cohorts. The first study showed that the overlap between any 2 different laboratories ranged from 6 to 121 metabolites at 5 leading laboratories. The second study showed that the median Spearman correlation comparing 111 overlapping metabolites captured by Metabolon and the Broad Institute was 0.79 (interquartile range, 0.56–0.89). [ABSTRACT FROM AUTHOR]

We explored the use of the E value to gauge the robustness of fields of epidemiologic inquiry to unmeasured confounding. We surveyed nutritional and air pollution studies that found statistically significant associations between exposures and incident outcomes. For 100 studies in each field, we extracted adjusted relative effect estimates and associated confidence intervals. We inverted estimates where necessary so that all effects were greater than 1. We calculated E values for both the effect estimate and the lower limit of the 95% confidence interval. Nutritional studies were smaller than air pollution studies (median participants per study, 40,652 vs. 72,460). More than 90% of nutritional studies categorized the exposure, whereas 89% of air pollution studies analyzed the exposure as a continuous variable. The median relative effect was 1.33 in nutrition and 1.16 in air pollution. The corresponding median E values for the estimates were 2.00 and 1.59, respectively. E values for the 95% confidence intervals had median values of 1.39 and 1.26, respectively. Little to moderate unmeasured confounding could explain away most observed associations. The E value is necessarily larger for smaller studies that reach statistical significance, making cross-field comparison difficult. The E value for the 95% confidence interval might be a more useful measure in reports of epidemiologic observational studies. [ABSTRACT FROM AUTHOR]

Mendelian randomization (MR) is gaining in recognition and popularity as a method for strengthening causal inference in epidemiology by utilizing genetic variants as instrumental variables. Concurrently with the explosion in empirical MR studies, there has been the steady production of new approaches for MR analysis. The recently proposed "global and individual tests for direct effects" (GLIDE) approach fits into a family of methods that aim to detect horizontal pleiotropy—at the individual single nucleotide polymorphism level and at the global level—and to adjust the analysis by removing outlying single nucleotide polymorphisms. In this commentary, we explain how existing methods can (and indeed are) being used to detect pleiotropy at the individual and global levels, although not explicitly using this terminology. By doing so, we show that the true comparator for GLIDE is not MR-Egger regression (as Dai et al. the authors of the accompanying article (Am J Epidemiol. 2018;187(12):2672–2680), claim) but rather the humble heterogeneity statistic. [ABSTRACT FROM AUTHOR]

Diagnosing pleiotropy is critical for assessing the validity of Mendelian randomization (MR) analyses. The popular MR-Egger method evaluates whether there is evidence of bias-generating pleiotropy among a set of candidate genetic instrumental variables. In this article, we propose a statistical method—global and individual tests for direct effects (GLIDE)—for systematically evaluating pleiotropy among the set of genetic variants (e.g. single nucleotide polymorphisms (SNPs)) used for MR. As a global test, simulation experiments suggest that GLIDE is nearly uniformly more powerful than the MR-Egger method. As a sensitivity analysis, GLIDE is capable of detecting outliers in individual variant-level pleiotropy, in order to obtain a refined set of genetic instrumental variables. We used GLIDE to analyze both body mass index and height for associations with colorectal cancer risk in data from the Genetics and Epidemiology of Colorectal Cancer Consortium and the Colon Cancer Family Registry (multiple studies). Among the body mass index–associated SNPs and the height-associated SNPs, several individual variants showed evidence of pleiotropy. Removal of these potentially pleiotropic SNPs resulted in attenuation of respective estimates of the causal effects. In summary, the proposed GLIDE method is useful for sensitivity analyses and improves the validity of MR. [ABSTRACT FROM AUTHOR]

With incomplete data, the "missing at random" (MAR) assumption is widely understood to enable unbiased estimation with appropriate methods. While the need to assess the plausibility of MAR and to perform sensitivity analyses considering "missing not at random" (MNAR) scenarios has been emphasized, the practical difficulty of these tasks is rarely acknowledged. With multivariable missingness, what MAR means is difficult to grasp, and in many MNAR scenarios unbiased estimation is possible using methods commonly associated with MAR. Directed acyclic graphs (DAGs) have been proposed as an alternative framework for specifying practically accessible assumptions beyond the MAR-MNAR dichotomy. However, there is currently no general algorithm for deciding how to handle the missing data given a specific DAG. Here we construct "canonical" DAGs capturing typical missingness mechanisms in epidemiologic studies with incomplete data on exposure, outcome, and confounding factors. For each DAG, we determine whether common target parameters are "recoverable," meaning that they can be expressed as functions of the available data distribution and thus estimated consistently, or whether sensitivity analyses are necessary. We investigate the performance of available-case and multiple-imputation procedures. Using data from waves 1–3 of the Longitudinal Study of Australian Children (2004–2008), we illustrate how our findings can guide the treatment of missing data in point-exposure studies. [ABSTRACT FROM AUTHOR]

Accurate interpretations and comparisons of record linkage results across jurisdictions require valid and reliable matching methods. We compared existing matching methods used by 6 US state and local health departments (Houston, Texas; Louisiana; Michigan; New York, New York; North Dakota; and Wisconsin) to link human immunodeficiency virus and viral hepatitis surveillance data with a 14-key automated, hierarchical deterministic matching method. Applicable years of study varied by disease and jurisdiction, ranging from 1979 to 2016. We calculated percentage agreement and Cohen's κ coefficient to compare the matching methods used within each jurisdiction. We calculated sensitivity, specificity, and positive predictive value for each matching method, as compared with a new standard that included manual review of discrepant cases. Agreement between the existing matching method and the deterministic matching method was 99.6% or higher in all jurisdictions; Cohen's κ values ranged from 0.87 to 0.98. The sensitivity of the deterministic matching method ranged from 97.4% to 100% in the 6 jurisdictions; specificity ranged from 99.7% to 100%; and positive predictive value ranged from 97.4% to 100%. Although no gold standard exists, prior assessments of existing methods and review of discrepant classifications suggest good accuracy and reliability of our deterministic matching method, with the advantage that our method reduces the need for manual review and allows for standard comparisons across jurisdictions when linking human immunodeficiency virus and viral hepatitis data. [ABSTRACT FROM AUTHOR]

The risk difference scale is often of primary interest when evaluating public health impacts of interventions on binary outcomes. However, few investigators report findings in terms of additive interaction, probably because the models typically used for binary outcomes implicitly measure interaction on the multiplicative scale. One measure with which to assess additive interaction from multiplicative models is the relative excess risk due to interaction (RERI). The RERI measure has been applied in many contexts, but one limitation of previous approaches is that clustering in data has rarely been considered. We evaluated the RERI metric for the setting of clustered data using both population-averaged and cluster-conditional models. In simulation studies, we found that estimation and inference for the RERI using population-averaged models was straightforward. However, frequentist implementations of cluster-conditional models including random intercepts often failed to converge or produced degenerate variance estimates. We developed a Bayesian implementation of log binomial random-intercept models, which represents an attractive alternative for estimating the RERI in cluster-conditional models. We applied the methods to an observational study of adverse birth outcomes in mothers with human immunodeficiency virus, in which mothers were clustered within clinical research sites. [ABSTRACT FROM AUTHOR]