Paul N. Zivich

The efficacy of current antiretroviral interventions for prevention of vertical HIV transmission is both a triumph and a challenge for future efficacy studies of novel agents, including long-acting antiretroviral agents. Given the effectiveness of current antiretroviral interventions, standard randomized controlled trials to assess novel interventions targeted towards further reducing vertical HIV transmission may be infeasible due to required sample sizes. To address this study design challenge, we propose a novel augmented clinical trial design, where a randomized trial with an active comparator is augmented with a concurrent observational cohort to supplement the standard-of-care arm. The proposed design and analysis can overcome sampling biases, and an associated diagnostic can evaluate potential biases from unmeasured covariates. The proposed trial design is illustrated with an example and studied further using a simulation study. In the illustrative example, an augmented trial with a 3:1 allocation ratio in the trial component yielded an unbiased treatment effect estimate, as compared to the trial component alone, and the standard error was reduced substantially. Although the total sample size of the augmented trial was larger than a similarly powered 1:1 standard trial, the sample size of the augmented trial’s trial component was half the size of the standard trial and within the range of historically similar trials, thereby providing both feasibility and potential cost advantages. Although limitations with this design remain, many of these limitations can be mitigated by careful study planning and coordination. Augmented trials provide a potentially applicable solution to studying the efficacy of long-acting antiretrovirals for infant postnatal prophylaxis against HIV.

Epidemiologists are sometimes interested in estimating multiple parameters. In this context, confidence intervals are not guaranteed to provide simultaneous coverage of more than one parameter. In other words, confidence intervals understate the uncertainty due to random error in these cases. This understated uncertainty can lead to a false sense of precision in the results, potentially leading to irreproducible results or misinformed decisions. To address this challenge, one can use confidence bands, an extension of confidence intervals to multiple parameters. We illustrate the use of confidence bands in three case studies: estimation of multiple causal effects, effect measure modification by a binary variable, and effect measure modification by a continuous variable. Each example uses publicly available data and is accompanied by SAS, R, and Python code. The type of confidence region reported by epidemiologists should depend on whether scientific interest is in one or multiple parameters. For multiple parameters, like in cases where multiple actions or outcomes, effect measure modification, dose–response, or other functions are of interest, sup-t confidence bands are preferred due to their statistical properties, computational simplicity, and ease of presentation.

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Background: Parametric g-computation with competing events typically involves fitting multiple pooled logistic regression models. We outline an alternative approach based on fitting a single pooled multinomial logistic model. Methods: Data from the Women’s Interagency HIV Study (n = 1,164) were used to estimate the marginal 2-year risk of highly active antiretroviral therapy (HAART) initiation and AIDS/death before HAART initiation with two parametric g-computation approaches: multiple pooled logistic regression and pooled multinomial logistic regression. The total effect of historical injection drug use was estimated for both event types using the multinomial approach. Results: Both g-computation implementations produced identical results. The 2-year risk difference comparing a scenario where all participants had historical injection drug use to one with no historical injection drug use was −12.5% (−18.0%, −7.0%) for HAART initiation and 13.2% (6.8%, 19.7%) for AIDS/death. Conclusions: Incorporating a pooled multinomial logit nuisance model for parametric g-computation simplifies estimation of total effects while accounting for right-censoring and competing events.

Introduction: Accounting for missing data by imputing or weighting conditional on covariates relies on the variable with missingness being observed at least some of the time for all unique covariate values. This requirement is referred to as positivity, and positivity violations can result in bias. Here, we review a novel approach to addressing positivity violations in the context of systolic blood pressure. Methods: To illustrate the proposed approach, we estimate the mean systolic blood pressure among children and adolescents aged 2–17 years old in the USA using data from the 2017–2018 National Health and Nutrition Examination Survey (NHANES). As blood pressure was not measured for those aged 2–7, there exists a positivity violation by design. Using a recently proposed synthesis of statistical and mathematical models, we integrate external information with NHANES to address our motivating question. Results: With the synthesis model, the estimated mean systolic blood pressure was 100.5 (95% CI 99.9 to 101.0), which is notably lower than either a complete-case analysis or extrapolation from a statistical model. The synthesis results were supported by a diagnostic comparing the performance of the mathematical model in the positive region. Discussion: Positivity violations pose a threat to quantitative medical research, and standard approaches to addressing non-positivity rely on restrictive untestable assumptions. Using a synthesis model, like the one detailed here, offers a viable alternative.

Background: Pooled logistic regression is a popular tool for survival analyses in epidemiology, but can face computational challenges. Commonly, these challenges are addressed through widening time intervals or using a parametric functional form for time. We propose a third option to reduce the computational burden without constraining the functional form for time. Methods: The proposed algorithm operates by restricting the long data set to rows that correspond to unique event times. However, our approach is only compatible when modeling time most flexibly with disjoint indicators. We compared the standard implementation to the proposed implementation in SAS, R, and Python using a publicly available data set. Results: For the example considered, both implementations provided the same point estimates, but the proposed implementation was between 6 and 68 times faster depending on the software. Conclusions: The proposed implementation can greatly simplify estimation of pooled logistic regression models, which is especially important when relying on the bootstrap for inference.

G-computation is a useful estimation method that can be adapted to address various biases in epidemiology. However, these adaptations may not be obvious for some complex causal structures. This challenge is an example of the much wider issue of translating a causal diagram into a novel estimation strategy. To highlight these challenges, we consider two recent cases from the selection bias literature: treatment-induced selection and co-occurrence of biases that lack a joint adjustment set. For each case study, we show how g-computation can be adapted, describe how to implement that adaptation, show some general statistical properties, and illustrate the estimator using simulation. To simplify both the theoretical study and practical application of our estimators, we express the proposed g-computation estimators as stacked estimating equations. These examples illustrate how epidemiologists can translate identification results into a g-computation estimator and study the theoretical and finite-sample properties of a novel estimator.

Background: The population attributable fraction corresponds to the reduction of the outcome had individuals (counter-to-fact) not experienced the exposure scaled by the observed incidence. Estimators proposed by Levin and Miettinen implicitly assume the study population is a random sample of the target population, which is not always the case. Methods: In our example, we estimate the reduction in AIDS or death among women diagnosed with HIV in the United States in 2008, had they not had a history of injection drug use. To transport risk estimates from 1164 women in the Women’s Interagency HIV Study to the 11,282 women diagnosed with HIV in the United States in 2008, we use the inverse probability of treatment and the inverse odds of sampling weighting. We estimate the variance of the population attributable fraction with a nonparametric bootstrap and M-estimation using the sandwich variance estimator. Results: The population attributable fraction estimated in the observed sample was 0.21 (95% confidence interval: 0.13, 0.29). After transporting the population attributable fraction to the target population, it was 0.13 (95% confidence interval: 0.065, 0.19). Conclusions: Defining the target population and identification conditions allows for a clearer interpretation of the population attributable fraction.