Bridged Treatment Comparisons: an Illustrative Application in HIV Treatment.

Comparisons of treatments, interventions, or exposures are of central interest in epidemiology, but direct comparisons are not always possible due to practical or ethical reasons. Here, we detail a fusion approach to compare treatments across studies. The motivating example entails comparing the risk of the composite outcome of death, AIDS, or greater than a 50% CD4 cell count decline in people with HIV when assigned triple versus mono antiretroviral therapy, using data from the AIDS Clinical Trial Group (ACTG) 175 (mono versus dual therapy) and ACTG 320 (dual versus triple therapy). We review a set of identification assumptions and estimate the risk difference using an inverse probability weighting estimator that leverages the shared trial arms (dual therapy). A fusion diagnostic based on comparing the shared arms is proposed that may indicate violation of the identification assumptions. Application of the data fusion estimator and diagnostic to the ACTG trials indicates triple therapy results in a reduction in risk compared to monotherapy in individuals with baseline CD4 counts between 50 and 300 cells/mm3. Bridged treatment comparisons address questions that none of the constituent data sources could address alone, but valid fusion-based inference requires careful consideration of the underlying assumptions.

The Evolution of Selection Bias in the Recent Epidemiologic Literature-A Selective Overview.

Selection bias has long been central in methodological discussions across epidemiology and other fields. In epidemiology, the concept of selection bias has been continually evolving over time. In this issue of the Journal, Mathur and Shpitser (Am J Epidemiol. XXXX;XXX(XX):XXXX-XXXX) present simple graphical rules for using a Single World Intervention Graph (SWIG) to assess the presence of selection bias when estimating treatment effects in both the general population and a selected sample. Notably, the authors examine the setting in which the treatment affects selection, an issue not well-addressed in the existing literature on selection bias. To place the work by Mathur and Shpitser in context, we review the evolution of the concept of selection bias in epidemiology, with a primary focus on the developments in the last 20-30 years since the introduction of causal directed acyclic graphs (DAGs) to epidemiologic research.

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.