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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 multi-study comparisons are challenging because of potential differences between trial populations that can affect the outcome. In this paper, two bridging estimators are considered that allow for comparisons of treatments evaluated in different trials using data fusion methods to account 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 versus four-drug antiretroviral therapy on CD4 cell counts among persons with advanced HIV. The single-span approach requires fewer identification assumptions and was more efficient in simulations and the application.

People living with HIV on antiretroviral therapy often have undetectable virus levels by standard assays, but "latent" HIV still persists in viral reservoirs. Eliminating these reservoirs is the goal of HIV cure research. The quantitative viral outgrowth assay (QVOA) is commonly used to estimate the reservoir size, i.e., the infectious units per million (IUPM) of HIV-persistent resting CD4+ T cells. A new variation of the QVOA, the Ultra Deep Sequencing Assay of the outgrowth virus (UDSA), was recently developed that further quantifies the number of viral lineages within a subset of infected wells. Performing the UDSA on a subset of wells provides additional information that can improve IUPM estimation. This paper considers statistical inference about the IUPM from combined dilution assay (QVOA) and deep viral sequencing (UDSA) data, even when some deep sequencing data are missing. The proposed methods accommodate assays with wells sequenced at multiple dilution levels and include a novel bias-corrected estimator for small samples. The proposed methods are evaluated in a simulation study, applied to data from the University of North Carolina HIV Cure Center, and implemented in the open-source R package SLDeepAssay., Comment: 12 pages, 2 figures, 2 tables, supporting information available through figshare

The U.S. Food and Drug Administration only gave emergency-use-authorization of the BNT162b2 and the mRNA-1273 SARS-CoV-2 vaccines for infants 6 months and older in June 2022. Yet, questions regarding the durability of vaccine efficacy, especially against emerging variants, in this age group remain. We demonstrated previously that a two-dose regimen of stabilized prefusion Washington SARS-CoV-2 S-2P spike (S) protein encoded by mRNA encapsulated in lipid nanoparticles (mRNA-LNP) or purified S-2P mixed with 3 M-052, a synthetic toll-like receptor (TLR) 7/8 agonist, in a squalene emulsion (Protein+3 M-052-SE) was safe and immunogenic in infant rhesus macaques. Here, we demonstrate that broadly neutralizing and spike-binding antibodies against variants of concern (VOC), as well as T cell responses, persisted for 12 months. At one year, corresponding to human toddler age, we challenged vaccinated rhesus macaques and age-matched non-vaccinated controls intranasally and intratracheally with a high-dose of heterologous SARS-CoV-2 B.1.617.2 (Delta). Seven of eight control rhesus macaques exhibited severe interstitial pneumonia and high virus replication in the upper and lower respiratory tract. In contrast, vaccinated rhesus macaques had faster viral clearance with mild to no pneumonia. Neutralizing and binding antibody responses to the B.1.617.2 variant at the day of challenge correlated with lung pathology and reduced virus replication. Overall, the Protein+3 M-052-SE vaccine provided superior protection to the mRNA-LNP vaccine, emphasizing opportunities for optimization of current vaccine platforms. Notably, the observed efficacy of both vaccines one year after vaccination supports the implementation of an early life SARS-CoV-2 vaccine.

Interference occurs when the treatment (or exposure) of a unit affects the outcome of another unit. In some settings, units may be grouped into clusters such that it is reasonable to assume that interference, if present, only occurs between individuals in the same cluster, i.e., there is clustered interference. Various causal estimands have been proposed to quantify treatment effects under clustered interference from observational data, but these estimands either entail treatment policies lacking real-world relevance or are based on parametric propensity score models. Here, we propose new causal estimands based on incremental changes to propensity scores which may be more relevant in many contexts and are not based on parametric models. Nonparametric sample splitting estimators of the new estimands are constructed, which allow for flexible data-adaptive estimation of nuisance functions and are consistent, asymptotically normal, and efficient, converging at the usual parametric rate. Simulations show the finite sample performance of the proposed estimators. The proposed methods are applied to evaluate the effect of water, sanitation, and hygiene facilities on diarrhea incidence among children in Senegal under clustered interference.

Comparisons of treatments 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/mm$^3$. Bridged treatment comparisons address questions that none of the constituent data sources could address alone, but valid fusion-based inference requires careful consideration., Comment: 20 pages, 3 figures, 5 tables

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 the weights are known and then using the so-called "robust" (Huber-White) sandwich estimator, which results in conservative standard error (SE) estimation. Here it is shown 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 conservative or anti-conservative. Thus confidence intervals of 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 two variance estimators are compared via simulation studies and in a data analysis of the effect of smoking on gene expression.

Marginal structural models fit via inverse probability of treatment weighting are commonly used to control for confounding when estimating causal effects from observational data. When planning a study that will be analyzed with marginal structural modeling, determining the required sample size for a given level of statistical power is challenging because of the effect of weighting on the variance of the estimated causal means. This paper considers the utility of the design effect to quantify the effect of weighting on the precision of causal estimates. The design effect is defined as the ratio of the variance of the causal mean estimator divided by the variance of a naive estimator if, counter to fact, no confounding had been present and weights were not needed. A simple, closed-form approximation of the design effect is derived that is outcome invariant and can be estimated during the study design phase. Once the design effect is approximated for each treatment group, sample size calculations are conducted as for a randomized trial, but with variances inflated by the design effects to account for weighting. Simulations demonstrate the accuracy of the design effect approximation, and practical considerations are discussed.

Cluster-randomized trials are often conducted to assess vaccine effects. Defining estimands of interest before conducting a trial is integral to the alignment between a study's objectives and the data to be collected and analyzed. This paper considers estimands and estimators for overall, indirect, and total vaccine effects in trials where clusters of individuals are randomized to vaccine or control. The scenario is considered where individuals self-select whether to participate in the trial and the outcome of interest is measured on all individuals in each cluster. Unlike the overall, indirect, and total effects, the direct effect of vaccination is shown in general not to be estimable without further assumptions, such as no unmeasured confounding. An illustrative example motivated by a cluster-randomized typhoid vaccine trial is provided., Comment: 14 pages, 1 figure

Accurate power calculations are essential in small studies containing expensive experimental units or high-stakes exposures. Herein, exact power of the Wilcoxon Mann-Whitney rank-sum test of a continuous variable is formulated using a Monte Carlo approach and defining P(X < Y) = p as a measure of effect size, where X and Y denote random observations from two distributions hypothesized to be equal under the null. Effect size p fosters productive communications because researchers understand p = 0.5 is analogous to a fair coin toss, and p near 0 or 1 represents a large effect. This approach is feasible even without background data. Simulations were conducted comparing the exact power approach to existing approaches by Rosner & Glynn (2009), Shieh et al. (2006), Noether (1987), and O'Brien-Castelloe (2006). Approximations by Noether and O'Brien-Castelloe are shown to be inaccurate for small sample sizes. The Rosner & Glynn and Shieh et al. approaches performed well in many small sample scenarios, though both are restricted to location-shift alternatives and neither approach is theoretically justified for small samples. The exact method is recommended and available in the R package wmwpow. KEYWORDS: Mann-Whitney test, Monte Carlo simulation, non-parametric, power analysis, Wilcoxon rank-sum test

Estimating population-level effects of a vaccine is challenging because there may be interference, i.e., the outcome of one individual may depend on the vaccination status of another individual. Partial interference occurs when individuals can be partitioned into groups such that interference occurs only within groups. In the absence of interference, inverse probability weighted (IPW) estimators are commonly used to draw inference about causal effects of an exposure or treatment. Tchetgen Tchetgen and VanderWeele (2012) proposed a modified IPW estimator for causal effects in the presence of partial interference. Motivated by a cholera vaccine study in Bangladesh, this paper considers an extension of the Tchetgen Tchetgen and VanderWeele IPW estimator to the setting where the outcome is subject to right censoring using inverse probability of censoring weights (IPCW). Censoring weights are estimated using proportional hazards frailty models. The large sample properties of the IPCW estimators are derived, and simulation studies are presented demonstrating the estimators' performance in finite samples. The methods are then used to analyze data from the cholera vaccine study.

High-dimensional low sample size (HDLSS) data sets emerge frequently in many biomedical applications. A common task for analyzing HDLSS data is to assign data to the correct class using a classifier. Classifiers which use two labels and a linear combination of features are known as binary linear classifiers. The direction-projection-permutation (DiProPerm) test was developed for testing the difference of two high-dimensional distributions induced by a binary linear classifier. This paper discusses the key components of the DiProPerm test, introduces the diproperm R package, and demonstrates the package on a real-world data set., Comment: Package located at https://github.com/allmondrew/diproperm

While the HVTN 505 trial showed no overall efficacy of the tested vaccine to prevent HIV infection over placebo, previous studies, biological theories, and the finding that immune response markers strongly correlated with infection in vaccine recipients generated the hypothesis that a qualitative interaction occurred. This hypothesis can be assessed with statistical methods for studying treatment effect modification by an intermediate response variable (i.e., principal stratification effect modification (PSEM) methods). However, available PSEM methods make untestable structural risk assumptions, such that assumption-lean versions of PSEM methods are needed in order to surpass the high bar of evidence to demonstrate a qualitative interaction. Fortunately, the survivor average causal effect (SACE) literature is replete with assumption-lean methods that can be readily adapted to the PSEM application for the special case of a binary intermediate response variable. We map this adaptation, opening up a host of new PSEM methods for a binary intermediate variable measured via two-phase sampling, for a dichotomous or failure time final outcome and including or excluding the SACE monotonicity assumption. The new methods support that the vaccine partially protected vaccine recipients with a high polyfunctional CD8+ T cell response, an important new insight for the HIV vaccine field.

The United States Environmental Protection Agency considers nutrient pollution in stream ecosystems one of the U.S. most pressing environmental challenges. But limited independent replicates, lack of experimental randomization, and space- and time-varying confounding handicap causal inference on effects of nutrient pollution. In this paper the causal g-methods developed by Robins and colleagues are extended to allow for exposures to vary in time and space in order to assess the effects of nutrient pollution on chlorophyll a, a proxy for algal production. Publicly available data from the North Carolina Cape Fear River and a simulation study are used to show how causal effects of upstream nutrient concentrations on downstream chlorophyll a levels may be estimated from typical water quality monitoring data. Estimates obtained from the parametric g-formula, a marginal structural model, and a structural nested model indicate that chlorophyll a concentrations at Lock and Dam 1 were influenced by nitrate concentrations measured 86 to 109 km upstream, an area where four major industrial and municipal point sources discharge wastewater.

A fundamental assumption usually made in causal inference is that of no interference between individuals (or units); that is, the potential outcomes of one individual are assumed to be unaffected by the treatment assignment of other individuals. However, in many settings, this assumption obviously does not hold. For example, in the dependent happenings of infectious diseases, whether one person becomes infected depends on who else in the population is vaccinated. In this article, we consider a population of groups of individuals where interference is possible between individuals within the same group. We propose estimands for direct, indirect, total, and overall causal effects of treatment strategies in this setting. Relations among the estimands are established; for example, the total causal effect is shown to equal the sum of direct and indirect causal effects. Using an experimental design with a two-stage randomization procedure (first at the group level, then at the individual level within groups), unbiased estimators of the proposed estimands are presented. Variances of the estimators are also developed. The methodology is illustrated in two different settings where interference is likely: assessing causal effects of housing vouchers and of vaccines.

The effects of vaccine on postinfection outcomes, such as disease, death, and secondary transmission to others, are important scientific and public health aspects of prophylactic vaccination. As a result, evaluation of many vaccine effects condition on being infected. Conditioning on an event that occurs posttreatment (in our case, infection subsequent to assignment to vaccine or control) can result in selection bias. Moreover, because the set of individuals who would become infected if vaccinated is likely not identical to the set of those who would become infected if given control, comparisons that condition on infection do not have a causal interpretation. In this article we consider identifiability and estimation of causal vaccine effects on binary postinfection outcomes. Using the principal stratification framework, we define a postinfection causal vaccine efficacy estimand in individuals who would be infected regardless of treatment assignment. The estimand is shown to be not identifiable under the standard assumptions of the stable unit treatment value, monotonicity, and independence of treatment assignment. Thus selection models are proposed that identify the causal estimand. Closed-form maximum likelihood estimators (MLEs) are then derived under these models, including those assuming maximum possible levels of positive and negative selection bias. These results show the relations between the MLE of the causal estimand and two commonly used estimators for vaccine effects on postinfection outcomes. For example, the usual intent-to-treat estimator is shown to be an upper bound on the postinfection causal vaccine effect provided that the magnitude of protection against infection is not too large. The methods are used to evaluate postinfection vaccine effects in a clinical trial of a rotavirus vaccine candidate and in a field study of a pertussis vaccine. Our results show that pertussis vaccination has a significant causal effect in reducing disease severity.

BACKGROUND Male circumcision reduces the risk of human immunodeficiency virus infection in men. We assessed the effect of male circumcision on the incidence and natural history of human papillomavirus (HPV) in a randomized clinical trial in Kisumu, Kenya. METHODS Sexually active, 18- to 24-year-old men provided penile exfoliated cells for HPV DNA testing every 6 months for 2 years. HPV DNA was detected via GP5+/6+ PCR in glans/coronal sulcus and in shaft samples. HPV incidence and persistence were assessed by intent-to-treat analyses. RESULTS A total of 2,193 men participated (1,096 randomized to circumcision; 1,097 controls). HPV prevalence was 50% at baseline for both groups and dropped to 23.7% at 24 months in the circumcision group, and 41.0% in control group. Incident infection of any HPV type over 24 months was lower among men in the circumcision group than in the control group [HR = 0.61; 95% confidence interval (CI), 0.52-0.72]. Clearance rate of any HPV infection over 24 months was higher in the circumcision group than in the control group (HR = 1.87; 95% CI, 1.49-2.34). Lower HPV point-prevalence, lower HPV incidence, and higher HPV clearance in the circumcision group were observed in glans but not in shaft samples. CONCLUSION Male circumcision reduced the risk of HPV acquisition and reinfection, and increased HPV clearance in the glans. IMPACT Providing voluntary, safe, and affordable male circumcision should help reduce HPV infections in men, and consequently, HPV-associated disease in their partners.