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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]

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]

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.

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]

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]

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]

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.