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.

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.

Estimating SARS-CoV-2 seroprevalence.

Governments and public health authorities use seroprevalence studies to guide responses to the COVID-19 pandemic. Seroprevalence surveys estimate the proportion of individuals who have detectable SARS-CoV-2 antibodies. However, serologic assays are prone to misclassification error, and non-probability sampling may induce selection bias. In this paper, non-parametric and parametric seroprevalence estimators are considered that address both challenges by leveraging validation data and assuming equal probabilities of sample inclusion within covariate-defined strata. Both estimators are shown to be consistent and asymptotically normal, and consistent variance estimators are derived. Simulation studies are presented comparing the estimators over a range of scenarios. The methods are used to estimate severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) seroprevalence in New York City, Belgium, and North Carolina.

HIV prevention among men who have sex with men: tenofovir alafenamide combination preexposure prophylaxis versus placebo.

BACKGROUND: While non-inferiority of tenofovir alafenamide and emtricitabine (TAF/FTC) as pre-exposure prophylaxis (PrEP) for the prevention of 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 non-inferiority 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 than (95% confidence interval: -2.0%, -9.6%) or 12.5-fold lower (95% confidence interval: 0.02, 0.31) than placebo standardized to the DISCOVER population. CONCLUSION: There was a reduction in HIV infection with TAF/FTC versus placebo across 96-weeks of follow-up.

Accounting for nonmonotone missing data using inverse probability weighting.

Inverse probability weighting can be used to correct for missing data. New estimators for the weights in the nonmonotone setting were introduced in 2018. These estimators are the unconstrained maximum likelihood estimator (UMLE) and the constrained Bayesian estimator (CBE), an alternative if UMLE fails to converge. In this work we describe and illustrate these estimators, and examine performance in simulation and in an applied example estimating the effect of anemia on spontaneous preterm birth in the Zambia Preterm Birth Prevention Study. We compare performance with multiple imputation (MI) and focus on the setting of an observational study where inverse probability of treatment weights are used to address confounding. In simulation, weighting was less statistically efficient at the smallest sample size and lowest exposure prevalence examined (n = 1500, 15% respectively) but in other scenarios statistical performance of weighting and MI was similar. Weighting had improved computational efficiency taking, on average, 0.4 and 0.05 times the time for MI in R and SAS, respectively. UMLE was easy to implement in commonly used software and convergence failure occurred just twice in >200 000 simulated cohorts making implementation of CBE unnecessary. In conclusion, weighting is an alternative to MI for nonmonotone missingness, though MI performed as well as or better in terms of bias and statistical efficiency. Weighting's superior computational efficiency may be preferred with large sample sizes or when using resampling algorithms. As validity of weighting and MI rely on correct specification of different models, both approaches could be implemented to check agreement of results.

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.

Evaluating Clinic-Based Interventions to Reduce Racial Differences in Mortality Among People With Human Immunodeficiency Virus in the United States.

BACKGROUND: Mortality remains elevated among Black versus White adults receiving human immunodeficiency virus (HIV) care in the United States. We evaluated the effects of hypothetical clinic-based interventions on this mortality gap. METHODS: We computed 3-year mortality under observed treatment patterns among >40 000 Black and >30 000 White adults entering HIV care in the United States from 1996 to 2019. We then used inverse probability weights to impose hypothetical interventions, including immediate treatment and guideline-based follow-up. We considered 2 scenarios: "universal" delivery of interventions to all patients and "focused" delivery of interventions to Black patients while White patients continued to follow observed treatment patterns. RESULTS: Under observed treatment patterns, 3-year mortality was 8% among White patients and 9% among Black patients, for a difference of 1 percentage point (95% confidence interval [CI], .5-1.4). The difference was reduced to 0.5% under universal immediate treatment (95% CI, -.4% to 1.3%) and to 0.2% under universal immediate treatment combined with guideline-based follow-up (95% CI, -1.0% to 1.4%). Under the focused delivery of both interventions to Black patients, the Black-White difference in 3-year mortality was -1.4% (95% CI, -2.3% to -.4%). CONCLUSIONS: Clinical interventions, particularly those focused on enhancing the care of Black patients, could have significantly reduced the mortality gap between Black and White patients entering HIV care from 1996 to 2019.

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.

Disparities in Fatal Occupational Injury Rates in North Carolina, 1978-2017: Comparing Nonmanagerial Employees to Managers.

BACKGROUND: We examined fatal occupational injuries among private-sector workers in North Carolina during the 40-year period 1978-2017, comparing the occurrence of fatal injuries among nonmanagerial employees to that experienced by managers. METHODS: We estimated a standardized fatal occupational injury ratio by inverse probability of exposure weighting, taking nonmanagerial workers as the target population. When this ratio measure takes a value greater than unity it signals settings in which nonmanagerial employees are not provided as safe a work environment as that provided for managers. RESULTS: Across all industries, nonmanagerial workers in North Carolina experienced fatal occupational injury rates 8.2 (95% CI = 7.0, 10.0) times the rate experienced by managers. Disparities in fatal injury rates between managers and the employees they supervise were greatest in forestry, rubber and metal manufacturing, wholesale trade, fishing and extractive industries, and construction. CONCLUSIONS: The results may help focus discussion about workplace safety between labor and management upon equity, with a goal of providing a work environment for nonmanagerial employees as safe as the one provided for managers.

Optimizing Treatment for Human Immunodeficiency Virus to Improve Clinical Outcomes Using Precision Medicine.

In first-line antiretroviral therapy (ART) for human immunodeficiency virus (HIV) treatment, some subgroups of patients may respond better to an efavirenz-based regimen than an integrase strand transfer inhibitor (InSTI)-based regimen, or vice versa, due to patient characteristics modifying treatment effects. Using data based on nearly 16,000 patients from the North American AIDS Cohort Collaboration on Research and Design from 2009-2016, statistical methods for precision medicine were employed to estimate an optimal treatment rule that minimizes the 5-year risk of the composite outcome of acquired immune deficiency syndrome (AIDS)-defining illnesses, serious non-AIDS events, and all-cause mortality. The treatment rules considered were functions that recommend either an efavirenz- or InSTI-based regimen conditional on baseline patient characteristics such as demographic information, laboratory results, and health history. The estimated 5-year risk under the estimated optimal treatment rule was 10.0% (95% confidence interval (CI): 8.6, 11.3), corresponding to an absolute risk reduction of 2.3% (95% CI: 0.9, 3.8) when compared with recommending an efavirenz-based regimen for all patients and 2.6% (95% CI: 1.0, 4.2) when compared with recommending an InSTI-based regimen for all. Tailoring ART to individual patient characteristics may reduce 5-year risk of the composite outcome compared with assigning all patients the same drug regimen.

A Per-Protocol Analysis Using Inverse-Probability-of-Censoring Weights in a Randomized Trial of Initial Protease Inhibitor Versus Nonnucleoside Reverse Transcriptase Inhibitor Regimens in Children.

Protocol adherence may influence measured treatment effectiveness in randomized controlled trials. Using data from a multicenter trial (Europe and the Americas, 2002-2009) of children with human immunodeficiency virus type 1 who had been randomized to receive initial protease inhibitor (PI) versus nonnucleoside reverse transcriptase inhibitor (NNRTI) antiretroviral therapy regimens, we generated time-to-event intention-to-treat (ITT) estimates of treatment effectiveness, applied inverse-probability-of-censoring weights to generate per-protocol efficacy estimates, and compared shifts from ITT to per-protocol estimates across and within treatment arms. In ITT analyses, 263 participants experienced 4-year treatment failure probabilities of 41.3% for PIs and 39.5% for NNRTIs (risk difference = 1.8% (95% confidence interval (CI): -10.1, 13.7); hazard ratio = 1.09 (95% CI: 0.74, 1.60)). In per-protocol analyses, failure probabilities were 35.6% for PIs and 29.2% for NNRTIs (risk difference = 6.4% (95% CI: -6.7, 19.4); hazard ratio = 1.30 (95% CI: 0.80, 2.12)). Within-arm shifts in failure probabilities from ITT to per-protocol analyses were 5.7% for PIs and 10.3% for NNRTIs. Protocol nonadherence was nondifferential across arms, suggesting that possibly better NNRTI efficacy may have been masked by differences in within-arm shifts deriving from differential regimen forgiveness, residual confounding, or chance. A per-protocol approach using inverse-probability-of-censoring weights facilitated evaluation of relationships among adherence, efficacy, and forgiveness applicable to pediatric oral antiretroviral regimens.

Hypertension and one-year risk of all-cause mortality among women with treated HIV in the United States.

OBJECTIVE: Hypertension is a critical cause of cardiovascular disease, and women with HIV have a higher prevalence of hypertension than women without HIV. The relationship between hypertension and mortality has not been well characterized in women with treated HIV. Here, we estimate the effect of hypertension on 1-year risk of all-cause mortality among women with HIV on antiretroviral therapy (ART) in the United States. DESIGN: An analysis of multicenter, observational cohort data from the Women's Interagency HIV Study (WIHS) collected between 1995 and 2019. METHODS: We included women with HIV who reported ever using ART. We used parametric g-computation to estimate the effect of hypertension (SBP ≥140  mmHg, DBP ≥90 mmHg, or use of hypertensive medication) on all-cause mortality within 1 year of a WIHS visit. RESULTS: Among 2929 unique women, we included 57 034 visits with a median age of 45 (interquartile range: 39, 52) years. Women had hypertension at 34.5% of visits, and 641 deaths occurred within 1 year of a study visit. Comparing women at visits with hypertension to women at visits without hypertension, the standardized 1-year risk ratio for mortality was 1.16 [95% confidence interval (95% CI): 1.01-1.33]. The risk ratios were higher in Hispanic (risk ratio: 1.23, 95% CI: 0.86-1.77) and non-Hispanic black women (risk ratio: 1.19, 95% CI: 1.04-1.37) and lower in non-Hispanic white women (risk ratio: 0.93, 95% CI: 0.58-1.48). CONCLUSION: Among women with treated HIV, those with hypertension, compared with those without, had an increased 1-year risk of all-cause mortality.