Semiparametric g-computation for survival outcomes with time-fixed exposures: An illustration.

PURPOSE: Generalized (g-) computation is a useful tool for causal inference in epidemiology. However, in settings when the outcome is a survival time subject to right censoring, the standard pooled logistic regression approach to g-computation requires arbitrary discretization of time, parametric modeling of the baseline hazard function, and the need to expand one's dataset. We illustrate a semiparametric Breslow estimator for g-computation with time-fixed treatments and survival outcomes that is not subject to these limitations. METHODS: We compare performance of the Breslow g-computation estimator to the pooled logistic g-computation estimator in simulations and illustrate both approaches to estimate the effect of a 3-drug vs 2-drug antiretroviral therapy regimen among people with HIV. RESULTS: In simulations, both approaches performed well at the end of follow-up. The pooled logistic approach was biased at times between the endpoints of the discrete time intervals used, while the Breslow approach was not. In the example, both approaches estimated a 1-year risk difference of about 6 % in favor of the 3-drug regimen, but the shape of the survival curves differed. CONCLUSIONS: The Breslow g-computation estimator of counterfactual risk functions does not rely on strong parametric assumptions about the time-to-event distribution or onerous dataset expansions.

Invited Commentary: Mixing multiple imputation and bootstrapping for variance estimation.

In 2023, Martinez et al. examined trends in the inclusion, conceptualization, operationalization and analysis of race and ethnicity among studies published in US epidemiology journals. Based on a random sample of papers (N=1,050) published from 1995-2018, the authors describe the treatment of race, ethnicity, and ethnorace in the analytic sample (N=414, 39% of baseline sample) over time. Between 32% and 19% of studies in each time stratum lacked race data; 61% to 34% lacked ethnicity data. The review supplies stark evidence of the routine omission and variability of measures of race and ethnicity in epidemiologic research. Informed by public health critical race praxis (PHCRP), this commentary discusses the implications of four problems the findings suggest pervade epidemiology: 1) a general lack of clarity about what race and ethnicity are; 2) the limited use of critical race or other theory; 3) an ironic lack of rigor in measuring race and ethnicity; and, 4) the ordinariness of racism and white supremacy in epidemiology. The identified practices reflect neither current publication guidelines nor the state of the knowledge on race, ethnicity and racism; therefore, we conclude by offering recommendations to move epidemiology toward more rigorous research in an increasingly diverse society.

M-estimation for common epidemiological measures: introduction and applied examples.

M-estimation is a statistical procedure that is particularly advantageous for some comon epidemiological analyses, including approaches to estimate an adjusted marginal risk contrast (i.e. inverse probability weighting and g-computation) and data fusion. In such settings, maximum likelihood variance estimates are not consistent. Thus, epidemiologists often resort to bootstrap to estimate the variance. In contrast, M-estimation allows for consistent variance estimates in these settings without requiring the computational complexity of the bootstrap. In this paper, we introduce M-estimation and provide four illustrative examples of implementation along with software code in multiple languages. M-estimation is a flexible and computationally efficient estimation procedure that is a powerful addition to the epidemiologist's toolbox.

Higher-order evidence.

Higher-order evidence is evidence about evidence. Epidemiologic examples of higher-order evidence include the settings where the study data constitute first-order evidence and estimates of misclassification comprise the second-order evidence (e.g., sensitivity, specificity) of a binary exposure or outcome collected in the main study. While sampling variability in higher-order evidence is typically acknowledged, higher-order evidence is often assumed to be free of measurement error (e.g., gold standard measures). Here we provide two examples, each with multiple scenarios where second-order evidence is imperfectly measured, and this measurement error can either amplify or attenuate standard corrections to first-order evidence. We propose a way to account for such imperfections that requires third-order evidence. Further illustrations and exploration of how higher-order evidence impacts results of epidemiologic studies is warranted.

HIV Prevention Among Men Who Have Sex With Men: Tenofovir Alafenamide Combination Preexposure Prophylaxis Versus Placebo.

BACKGROUND: While noninferiority of tenofovir alafenamide and emtricitabine (TAF/FTC) as preexposure prophylaxis (PrEP) for the prevention of human immunodeficiency virus (HIV) has been shown, interest remains in its efficacy relative to placebo. We estimate the efficacy of TAF/FTC PrEP versus placebo for the prevention of HIV infection. METHODS: We used data from the DISCOVER and iPrEx trials to compare TAF/FTC to placebo. DISCOVER was a noninferiority trial conducted from 2016 to 2017. iPrEx was a placebo-controlled trial conducted from 2007 to 2009. Inverse probability weights were used to standardize the iPrEx participants to the distribution of demographics and risk factors in the DISCOVER trial. To check the comparison, we evaluated whether risk of HIV infection in the shared tenofovir disoproxil fumarate and emtricitabine (TDF/FTC) arms was similar. RESULTS: Notable differences in demographics and risk factors occurred between trials. After standardization, the difference in risk of HIV infection between the TDF/FTC arms was near zero. The risk of HIV with TAF/FTC was 5.8 percentage points lower (95% confidence interval [CI], -2.0% to -9.6%) or 12.5-fold lower (95% CI, .02 to .31) than placebo standardized to the DISCOVER population. CONCLUSIONS: There was a reduction in HIV infection with TAF/FTC versus placebo across 96 weeks of follow-up. CLINICAL TRIALS REGISTRATION: NCT02842086 and NCT00458393.

Leveraging External Validation Data: The Challenges of Transporting Measurement Error Parameters.

Approaches to address measurement error frequently rely on validation data to estimate measurement error parameters (e.g., sensitivity and specificity). Acquisition of validation data can be costly, thus secondary use of existing data for validation is attractive. To use these external validation data, however, we may need to address systematic differences between these data and the main study sample. Here, we derive estimators of the risk and the risk difference that leverage external validation data to account for outcome misclassification. If misclassification is differential with respect to covariates that themselves are differentially distributed in the validation and study samples, the misclassification parameters are not immediately transportable. We introduce two ways to account for such covariates: (1) standardize by these covariates or (2) iteratively model the outcome. If conditioning on a covariate for transporting the misclassification parameters induces bias of the causal effect (e.g., M-bias), the former but not the latter approach is biased. We provide proof of identification, describe estimation using parametric models, and assess performance in simulations. We also illustrate implementation to estimate the risk of preterm birth and the effect of maternal HIV infection on preterm birth. Measurement error should not be ignored and it can be addressed using external validation data via transportability methods.

Transportability Without Positivity: A Synthesis of Statistical and Simulation Modeling.

Studies designed to estimate the effect of an action in a randomized or observational setting often do not represent a random sample of the desired target population. Instead, estimates from that study can be transported to the target population. However, transportability methods generally rely on a positivity assumption, such that all relevant covariate patterns in the target population are also observed in the study sample. Strict eligibility criteria, particularly in the context of randomized trials, may lead to violations of this assumption. Two common approaches to address positivity violations are restricting the target population and restricting the relevant covariate set. As neither of these restrictions is ideal, we instead propose a synthesis of statistical and simulation models to address positivity violations. We propose corresponding g-computation and inverse probability weighting estimators. The restriction and synthesis approaches to addressing positivity violations are contrasted with a simulation experiment and an illustrative example in the context of sexually transmitted infection testing uptake. In both cases, the proposed synthesis approach accurately addressed the original research question when paired with a thoughtfully selected simulation model. Neither of the restriction approaches was able to accurately address the motivating question. As public health decisions must often be made with imperfect target population information, model synthesis is a viable approach given a combination of empirical data and external information based on the best available knowledge.

Fusing trial data for treatment comparisons: Single vs multi-span bridging.

While randomized controlled trials (RCTs) are critical for establishing the efficacy of new therapies, there are limitations regarding what comparisons can be made directly from trial data. RCTs are limited to a small number of comparator arms and often compare a new therapeutic to a standard of care which has already proven efficacious. It is sometimes of interest to estimate the efficacy of the new therapy relative to a treatment that was not evaluated in the same trial, such as a placebo or an alternative therapy that was evaluated in a different trial. Such dual-study comparisons are challenging because of potential differences between trial populations that can affect the outcome. In this article, two bridging estimators are considered that allow for comparisons of treatments evaluated in different trials, accounting for measured differences in trial populations. A "multi-span" estimator leverages a shared arm between two trials, while a "single-span" estimator does not require a shared arm. A diagnostic statistic that compares the outcome in the standardized shared arms is provided. The two estimators are compared in simulations, where both estimators demonstrate minimal empirical bias and nominal confidence interval coverage when the identification assumptions are met. The estimators are applied to data from the AIDS Clinical Trials Group 320 and 388 to compare the efficacy of two-drug vs four-drug antiretroviral therapy on CD4 cell counts among persons with advanced HIV. The single-span approach requires weaker identification assumptions and was more efficient in simulations and the application.

Reducing Bias in Estimates of Per Protocol Treatment Effects: A Secondary Analysis of a Randomized Clinical Trial.

This secondary analysis of a randomized clinical trial evaluates ways of reducing bias in estimates of per protocol treatment effects.

Sensitivity Analyses for Means or Proportions with Missing Outcome Data.

We describe an approach to sensitivity analysis introduced by Robins et al (1999), for the setting where the outcome is missing for some observations. This flexible approach focuses on the relationship between the outcomes and missingness, where data can be missing completely at random, missing at random given observed data, or missing not at random. We provide examples from HIV that include the sensitivity of the estimation of a mean and proportion under different missingness mechanisms. The approach illustrated provides a method for examining how the results of epidemiologic studies might shift as a function of bias due to missing data.

Identifying and estimating effects of sustained interventions under parallel trends assumptions.

Many research questions in public health and medicine concern sustained interventions in populations defined by substantive priorities. Existing methods to answer such questions typically require a measured covariate set sufficient to control confounding, which can be questionable in observational studies. Differences-in-differences rely instead on the parallel trends assumption, allowing for some types of time-invariant unmeasured confounding. However, most existing difference-in-differences implementations are limited to point treatments in restricted subpopulations. We derive identification results for population effects of sustained treatments under parallel trends assumptions. In particular, in settings where all individuals begin follow-up with exposure status consistent with the treatment plan of interest but may deviate at later times, a version of Robins' g-formula identifies the intervention-specific mean under stable unit treatment value assumption, positivity, and parallel trends. We develop consistent asymptotically normal estimators based on inverse-probability weighting, outcome regression, and a double robust estimator based on targeted maximum likelihood. Simulation studies confirm theoretical results and support the use of the proposed estimators at realistic sample sizes. As an example, the methods are used to estimate the effect of a hypothetical federal stay-at-home order on all-cause mortality during the COVID-19 pandemic in spring 2020 in the United States.

When Does Differential Outcome Misclassification Matter for Estimating Prevalence?

BACKGROUND: When accounting for misclassification, investigators make assumptions about whether misclassification is "differential" or "nondifferential." Most guidance on differential misclassification considers settings where outcome misclassification varies across levels of exposure, or vice versa. Here, we examine when covariate-differential misclassification must be considered when estimating overall outcome prevalence. METHODS: We generated datasets with outcome misclassification under five data generating mechanisms. In each, we estimated prevalence using estimators that (a) ignored misclassification, (b) assumed misclassification was nondifferential, and (c) allowed misclassification to vary across levels of a covariate. We compared bias and precision in estimated prevalence in the study sample and an external target population using different sources of validation data to account for misclassification. We illustrated use of each approach to estimate HIV prevalence using self-reported HIV status among people in East Africa cross-border areas. RESULTS: The estimator that allowed misclassification to vary across levels of the covariate produced results with little bias for both populations in all scenarios but had higher variability when the validation study contained sparse strata. Estimators that assumed nondifferential misclassification produced results with little bias when the covariate distribution in the validation data matched the covariate distribution in the target population; otherwise estimates assuming nondifferential misclassification were biased. CONCLUSIONS: If validation data are a simple random sample from the target population, assuming nondifferential outcome misclassification will yield prevalence estimates with little bias regardless of whether misclassification varies across covariates. Otherwise, obtaining valid prevalence estimates requires incorporating covariates into the estimators used to account for misclassification.

Illustration of 2 Fusion Designs and Estimators.

"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.

Missing Outcome Data in Epidemiologic Studies.

Missing data are pandemic and a central problem for epidemiology. Missing data reduce precision and can cause notable bias. There remain too few simple published examples detailing types of missing data and illustrating their possible impact on results. Here we take an example randomized trial that was not subject to missing data and induce missing data to illustrate 4 scenarios in which outcomes are 1) missing completely at random, 2) missing at random with positivity, 3) missing at random without positivity, and 4) missing not at random. We demonstrate that accounting for missing data is generally a better strategy than ignoring missing data, which unfortunately remains a standard approach in epidemiology.

Optimizing SARS-CoV-2 Pooled Testing Strategies Through Differentiated Pooling for Distinct Groups.

Pooled testing has been successfully used to expand SARS-CoV-2 testing, especially in settings requiring high volumes of screening of lower-risk individuals, but efficiency of pooling declines as prevalence rises. We propose a differentiated pooling strategy that independently optimizes pool sizes for distinct groups with different probabilities of infection to further improve the efficiency of pooled testing. We compared the efficiency (results obtained per test kit used) of the differentiated strategy with a traditional pooling strategy in which all samples are processed using uniform pool sizes under a range of scenarios. For most scenarios, differentiated pooling is more efficient than traditional pooling. In scenarios examined here, an improvement in efficiency of up to 3.94 results per test kit could be obtained through differentiated versus traditional pooling, with more likely scenarios resulting in 0.12 to 0.61 additional results per kit. Under circumstances similar to those observed in a university setting, implementation of our strategy could result in an improvement in efficiency between 0.03 to 3.21 results per test kit. Our results can help identify settings, such as universities and workplaces, where differentiated pooling can conserve critical testing resources.

Conceptualization, Operationalization, and Utilization of Race and Ethnicity in Major Epidemiology Journals, 1995-2018: A Systematic Review.

Despite repeated calls by scholars to critically engage with the concepts of race and ethnicity in US epidemiologic research, the incorporation of these social constructs in scholarship may be suboptimal. This study characterizes the conceptualization, operationalization, and utilization of race and ethnicity in US research published in leading journals whose publications shape discourse and norms around race, ethnicity, and health within the field of epidemiology. We systematically reviewed randomly selected articles from prominent epidemiology journals across 5 periods: 1995-1999, 2000-2004, 2005-2009, 2010-2014, and 2015-2018. All original human-subjects research conducted in the United States was eligible for review. Information on definitions, measurement, coding, and use in analysis was extracted. We reviewed 1,050 articles, including 414 (39%) in our analyses. Four studies explicitly defined race and/or ethnicity. Authors rarely made clear delineations between race and ethnicity, often adopting an ethnoracial construct. In the majority of studies across time periods, authors did not state how race and/or ethnicity was measured. Top coding schemes included "Black, White" (race), "Hispanic, non-Hispanic" (ethnicity), and "Black, White, Hispanic" (ethnoracial). Most often, race and ethnicity were deemed "not of interest" in analyses (e.g., control variables). Broadly, disciplinary practices have remained largely the same between 1995 and 2018 and are in need of improvement.

Targeted maximum likelihood estimation of causal effects with interference: A simulation study.

Interference, the dependency of an individual's potential outcome on the exposure of other individuals, is a common occurrence in medicine and public health. Recently, targeted maximum likelihood estimation (TMLE) has been extended to settings of interference, including in the context of estimation of the mean of an outcome under a specified distribution of exposure, referred to as a policy. This paper summarizes how TMLE for independent data is extended to general interference (network-TMLE). An extensive simulation study is presented of network-TMLE, consisting of four data generating mechanisms (unit-treatment effect only, spillover effects only, unit-treatment and spillover effects, infection transmission) in networks of varying structures. Simulations show that network-TMLE performs well across scenarios with interference, but issues manifest when policies are not well-supported by the observed data, potentially leading to poor confidence interval coverage. Guidance for practical application, freely available software, and areas of future work are provided.