The assumption of positivity or experimental treatment assignment requires that observed treatment levels vary within confounder strata. This article discusses the positivity assumption in the context of assessing model and parameter-specific identifiability of causal effects. Positivity violations occur when certain subgroups in a sample rarely or never receive some treatments of interest. The resulting sparsity in the data may increase bias with or without an increase in variance and can threaten valid inference. The parametric bootstrap is presented as a tool to assess the severity of such threats and its utility as a diagnostic is explored using simulated and real data. Several approaches for improving the identifiability of parameters in the presence of positivity violations are reviewed. Potential responses to data sparsity include restriction of the covariate adjustment set, use of an alternative projection function to define the target parameter within a marginal structural working model, restriction of the sample, and modification of the target intervention. All of these approaches can be understood as trading off proximity to the initial target of inference for identifiability; we advocate approaching this tradeoff systematically.

Many common problems in epidemiologic and clinical research involve estimating the effect of an exposure on an outcome while blocking the exposure's effect on an intermediate variable. Effects of this kind are termed direct effects. Estimation of direct effects arises frequently in research aimed at understanding mechanistic pathways by which an exposure acts to cause or prevent disease, as well as in many other settings. Although multivariable regression is commonly used to estimate direct effects, this approach requires assumptions beyond those required for the estimation of total causal effects. In addition, multivariable regression estimates a particular type of direct effect, the effect of an exposure on outcome fixing the intermediate at a specified level. Using the counterfactual framework, we distinguish this definition of a direct effect (Type 1 direct effect) from an alternative definition, in which the effect of the exposure on the intermediate is blocked, but the intermediate is otherwise allowed to vary as it would in the absence of exposure (Type 2 direct effect). When the intermediate and exposure interact to affect the outcome these two types of direct effects address distinct research questions. Relying on examples, we illustrate the difference between Type 1 and Type 2 direct effects. We propose an estimation approach for Type 2 direct effects that can be implemented using standard statistical software and illustrate its implementation using a numerical example. We also review the assumptions underlying our approach, which are less restrictive than those proposed by previous authors.

BACKGROUNDUniversal antiretroviral therapy (ART) with annual population testing and a multidisease, patient-centered strategy could reduce new human immunodeficiency virus (HIV) infections and improve community health. METHODSWe randomly assigned 32 rural communities in Uganda and Kenya to baseline HIV and multidisease testing and national guideline-restricted ART (control group) or to baseline testing plus annual testing, eligibility for universal ART, and patient-centered care (intervention group). The primary end point was the cumulative incidence of HIV infection at 3 years. Secondary end points included viral suppression, death, tuberculosis, hypertension control, and the change in the annual incidence of HIV infection (which was evaluated in the intervention group only). RESULTSA total of 150,395 persons were included in the analyses. Population-level viral suppression among 15,399 HIV-infected persons was 42% at baseline and was higher in the intervention group than in the control group at 3 years (79% vs. 68%; relative prevalence, 1.15; 95% confidence interval [CI], 1.11 to 1.20). The annual incidence of HIV infection in the intervention group decreased by 32% over 3 years (from 0.43 to 0.31 cases per 100 personyears; relative rate, 0.68; 95% CI, 0.56 to 0.84). However, the 3-year cumulative incidence (704 incident HIV infections) did not differ significantly between the intervention group and the control group (0.77% and 0.81%, respectively; relative risk, 0.95; 95% CI, 0.77 to 1.17). Among HIV-infected persons, the risk of death by year 3 was 3% in the intervention group and 4% in the control group (0.99 vs. 1.29 deaths per 100 person-years; relative risk, 0.77; 95% CI, 0.64 to 0.93). The risk of HIV-associated tuberculosis or death by year 3 among HIV-infected persons was 4% in the intervention group and 5% in the control group (1.19 vs. 1.50 events per 100 person-years; relative risk, 0.79; 95% CI, 0.67 to 0.94). At 3 years, 47% of adults with hypertension in the intervention group and 37% in the control group had hypertension control (relative prevalence, 1.26; 95% CI, 1.15 to 1.39). CONCLUSIONSUniversal HIV treatment did not result in a significantly lower incidence of HIV infection than standard care, probably owing to the availability of comprehensive baseline HIV testing and the rapid expansion of ART eligibility in the control group. (Funded by the National Institutes of Health and others; SEARCH ClinicalTrials.gov number, NCT01864603.

BackgroundThe high burden of undiagnosed HIV in sub-Saharan Africa limits treatment and prevention efforts. Community-based HIV testing campaigns can address this challenge and provide an untapped opportunity to identify non-communicable diseases (NCDs). We tested the feasibility and diagnostic yield of integrating NCD and communicable diseases into a rapid HIV testing and referral campaign for all residents of a rural Ugandan parish.MethodsA five-day, multi-disease campaign, offering diagnostic, preventive, treatment and referral services, was performed in May 2011. Services included point-of-care screening for HIV, malaria, TB, hypertension and diabetes. Finger-prick diagnostics eliminated the need for phlebotomy. HIV-infected adults met clinic staff and peer counselors on-site; those with CD4≤100/µL underwent intensive counseling and rapid referral for antiretroviral therapy (ART). Community participation, case-finding yield, and linkage to care three months post-campaign were analyzed.ResultsOf 6,300 residents, 2,323/3,150 (74%) adults and 2,020/3,150 (69%) children participated. An estimated 95% and 52% of adult female and male residents participated respectively. Adult HIV prevalence was 7.8%, with 46% of HIV-infected adults newly diagnosed. Thirty-nine percent of new HIV diagnoses linked to care. In a pilot subgroup with CD4≤100, 83% linked and started ART within 10 days. Malaria was identified in 10% of children, and hypertension and diabetes in 28% and 3.5% of adults screened, respectively. Sixty-five percent of hypertensives and 23% of diabetics were new diagnoses, of which 43% and 61% linked to care, respectively. Screening identified suspected TB in 87% of HIV-infected and 19% of HIV-uninfected adults; 52% percent of HIV-uninfected TB suspects linked to care.ConclusionsIn an integrated campaign engaging 74% of adult residents, we identified a high burden of undiagnosed HIV, hypertension and diabetes. Improving male attendance and optimizing linkage to care require new approaches. The campaign demonstrates the feasibility of integrating hypertension, diabetes and communicable diseases into HIV initiatives.

Background Despite large investments in HIV testing, only 45% of HIV-infected persons in sub-Saharan Africa are estimated to know their status. Optimal methods for maximizing population-level testing remain unknown. We sought to demonstrate the effectiveness at achieving population-wide testing coverage of a hybrid mobile HIV testing approach. Methods From 2013–2014, we enumerated 168,772 adult (≥15 years) residents of 32 communities in Uganda (N=20), and Kenya (N=12) using a door-to-door census. “Stable” residence was defined as living in community for ≥6 months over the past year. In each community we performed 2-week multi-disease community health campaigns (CHC) that included HIV testing, counseling, and referral to care if HIV-infected; CHC non-participants were approached for home-based testing (HBT) over 1–2 months. We determined population HIV testing coverage, and predictors of testing via HBT (vs. CHC) and non-testing. Findings HIV testing was achieved in 89% of stable adult residents (131,307/146,906). HIV prevalence was 9.6% (13,043/136,033 stable and non-stable adults); median CD4+ T-cell count was 514 cells/μL (IQR: 355–703). Among stable adults tested, 43% (56,106/131,307) reported no prior testing. Among HIV-infected adults, 38% (4,932/13,043) were unaware of their status. Among stable CHC attendees, 99.5% (104,635/105,170) accepted HIV testing. Of stable adults tested, 80% (104,635/131,307, range: 60–93%) tested via CHCs. In multivariable analyses of stable adults, predictors of non-testing included male gender (risk ratio [RR]: 1.52, 95% CI: 1.48–1.56), single marital status (RR: 1.70, 95% CI: 1.66–1.75), Kenyan residence (RR: 1.46, 95% CI: 1.41–1.50, vs. Ugandan), and out-of-community migration for ≥1 month in past year (RR: 1.60, 95% CI: 1.53–1.68). Testing was more common among farmers (RR: 0.73, 95% CI: 0.67–0.79) and adults with primary education (RR: 0.84, 95% CI: 0.80–0.89). Interpretation High HIV testing coverage was achieved in rural Ugandan and Kenyan communities using a hybrid, mobile approach of multi-disease CHCs followed by HBT. This approach allowed for flexibility at the community and individual level in reaching testing coverage goals. Men and mobile populations remain challenges for universal testing.

Marginal structural models (MSM) are an important class of models in causal inference. Given a longitudinal data structure observed on a sample of n independent and identically distributed experimental units, MSM model the counterfactual outcome distribution corresponding with a static treatment intervention, conditional on user-supplied baseline covariates. Identification of a static treatment regimen-specific outcome distribution based on observational data requires, beyond the standard sequential randomization assumption, the assumption that each experimental unit has positive probability of following the static treatment regimen. The latter assumption is called the experimental treatment assignment (ETA) assumption, and is parameter-specific. In many studies the ETA is violated because some of the static treatment interventions to be compared cannot be followed by all experimental units, due either to baseline characteristics or to the occurrence of certain events over time. For example, the development of adverse effects or contraindications can force a subject to stop an assigned treatment regimen.In this article we propose causal effect models for a user-supplied set of realistic individualized treatment rules. Realistic individualized treatment rules are defined as treatment rules which always map into the set of possible treatment options. Thus, causal effect models for realistic treatment rules do not rely on the ETA assumption and are fully identifiable from the data. Further, these models can be chosen to generalize marginal structural models for static treatment interventions. The estimating function methodology of Robins and Rotnitzky (1992) (analogue to its application in Murphy, et. al. (2001) for a single treatment rule) provides us with the corresponding locally efficient double robust inverse probability of treatment weighted estimator.In addition, we define causal effect models for "intention-to-treat" regimens. The proposed intentionto-treat interventions enforce a static intervention until the time point at which the next treatment does not belong to the set of possible treatment options, at which point the intervention is stopped. We provide locally efficient estimators of such intention-to-treat causal effects. Keywords counterfactual; causal effect; causal inference; double robust estimating function; dynamic treatment regimen; estimating function; individualized stopped treatment regimen; individualized treatment rule; inverse probability of treatment weighted estimating functions; locally efficient estimation; static treatment intervention * We thank James Robins for helpful discussions and suggestions.

This paper describes a targeted maximum likelihood estimator (TMLE) for the parameters of longitudinal static and dynamic marginal structural models. We consider a longitudinal data structure consisting of baseline covariates, time-dependent intervention nodes, intermediate timedependent covariates, and a possibly time-dependent outcome. The intervention nodes at each time point can include a binary treatment as well as a right-censoring indicator. Given a class of dynamic or static interventions, a marginal structural model is used to model the mean of the intervention-specific counterfactual outcome as a function of the intervention, time point, and possibly a subset of baseline covariates. Because the true shape of this function is rarely known, the marginal structural model is used as a working model. The causal quantity of interest is defined as the projection of the true function onto this working model. Iterated conditional expectation double robust estimators for marginal structural model parameters were previously proposed by Robins ( , 2002 and Bang and Robins (2005). Here we build on this work and present a pooled TMLE for the parameters of marginal structural working models. We compare this pooled estimator to a stratified TMLE (Schnitzer et al. 2014) that is based on estimating the intervention-specific mean separately for each intervention of interest. The performance of the pooled TMLE is compared to the performance of the stratified TMLE and the performance of Correspondence to: Maya Petersen, mayaliv@berkeley.edu. HHS Public Access

In binary classification problems, the area under the ROC curve (AUC) is commonly used to evaluate the performance of a prediction model. Often, it is combined with cross-validation in order to assess how the results will generalize to an independent data set. In order to evaluate the quality of an estimate for cross-validated AUC, we obtain an estimate of its variance. For massive data sets, the process of generating a single performance estimate can be computationally expensive. Additionally, when using a complex prediction method, the process of cross-validating a predictive model on even a relatively small data set can still require a large amount of computation time. Thus, in many practical settings, the bootstrap is a computationally intractable approach to variance estimation. As an alternative to the bootstrap, we demonstrate a computationally efficient influence curve based approach to obtaining a variance estimate for cross-validated AUC.