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.