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Many of the secondary outcomes in observational studies and randomized trials are rare. Methods for estimating causal effects and associations with rare outcomes, however, are limited, and this represents a missed opportunity for investigation. In this article, we construct a new targeted minimum loss-based estimator (TMLE) for the effect or association of an exposure on a rare outcome. We focus on the causal risk difference and statistical models incorporating bounds on the conditional mean of the outcome, given the exposure and measured confounders. By construction, the proposed estimator constrains the predicted outcomes to respect this model knowledge. Theoretically, this bounding provides stability and power to estimate the exposure effect. In finite sample simulations, the proposed estimator performed as well, if not better, than alternative estimators, including a propensity score matching estimator, inverse probability of treatment weighted (IPTW) estimator, augmented-IPTW and the standard TMLE algorithm. The new estimator yielded consistent estimates if either the conditional mean outcome or the propensity score was consistently estimated. As a substitution estimator, TMLE guaranteed the point estimates were within the parameter range. We applied the estimator to investigate the association between permissive neighborhood drunkenness norms and alcohol use disorder. Our results highlight the potential for double robust, semiparametric efficient estimation with rare events and high dimensional covariates.

The Mantel-Haenszel estimators for the common effect parameters of stratified 2×2 tables have been widely adopted in epidemiological and clinical studies for controlling the effects of confounding factors. Although the Mantel-Haenszel estimators are simple and effective estimating methods, the correctness of the common effect assumptions cannot be justified in general practices. Also then, the targeted “common effect parameters” do not exist. Under these settings, even if the Mantel-Haenszel estimators have desirable properties, it is quite uncertain what they estimate and how the estimates are interpreted. In this article, we conducted theoretical evaluations for their asymptotic behaviors when the common effect assumptions are violated. We explicitly showed that the Mantel-Haenszel estimators converge to weighted averages of stratum-specific effect parameters and they can be interpreted as intuitive summaries of the stratum-specific effect measures. Also, the Mantel-Haenszel estimators correspond to the standardized effect measures on standard distributions of stratification variables to be the total cohort, approximately. In addition, the ordinary sandwich-type variance estimators are still valid for quantifying variabilities of the Mantel-Haenszel estimators. We implemented numerical studies based on two epidemiologic studies of breast cancer and schizophrenia for evaluating empirical properties of these estimators, and confirmed general validities of these theoretical results.

Marginal Structural Models (MSMs), with the associated method of inverse probability weighting (IPW), have become increasingly popular in epidemiology to model and estimate the joint effects of a sequence of exposures. This popularity is largely related to the relative simplicity of the method, as compared to other techniques to adjust for time-varying confounding, such as g-estimation and g-computation. However, the price to pay for this simplicity can be substantial. The IPW estimators that are routinely used in applications make inefficient use of the information in the data, and are susceptible to large finite-sample bias when some confounders are strongly predictive of exposure. Moreover, the handling of continuous exposures easily becomes impractical, and the study of effect modification by time-varying covariates even impossible. In view of this, we revisit Structural Nested Mean Models (SNMMs) with the associated method of g-estimation as a useful remedy, and show how this can be implemented through standard software.

An issue that remains challenging in the field of causal inference is how to relax the assumption of no interference between units. Interference occurs when the treatment of one unit can affect the outcome of another, a situation which is likely to arise with outcomes that may depend on social interactions, such as occurrence of infectious disease. Existing methods to accommodate interference largely depend upon an assumption of “partial interference” – interference only within identifiable groups but not among them. There remains a considerable need for development of methods that allow further relaxation of the no-interference assumption. This paper focuses on an estimand that is the difference in the outcome that one would observe if the treatment were provided to all clusters compared to that outcome if treatment were provided to none – referred as the overall treatment effect. In trials of infectious disease prevention, the randomized treatment effect estimate will be attenuated relative to this overall treatment effect if a fraction of the exposures in the treatment clusters come from individuals who are outside these clusters. This source of interference – contacts sufficient for transmission that are with treated clusters – is potentially measurable. In this manuscript, we leverage epidemic models to infer the way in which a given level of interference affects the incidence of infection in clusters. This leads naturally to an estimator of the overall treatment effect that is easily implemented using existing software.

In conducting studies on an exposure of interest, a systematic roadmap should be applied for translating causal questions into statistical analyses and interpreting the results. In this paper we describe an application of one such roadmap applied to estimating the joint effect of both time to availability of a nurse-based triage system (low risk express care (LREC)) and individual enrollment in the program among HIV patients in East Africa. Our study population is comprised of 16,513 subjects found eligible for this task-shifting program within 15 clinics in Kenya between 2006 and 2009, with each clinic starting the LREC program between 2007 and 2008. After discretizing follow-up into 90-day time intervals, we targeted the population mean counterfactual outcome (i. e. counterfactual probability of either dying or being lost to follow up) at up to 450 days after initial LREC eligibility under three fixed treatment interventions. These were (i) under no program availability during the entire follow-up, (ii) under immediate program availability at initial eligibility, but non-enrollment during the entire follow-up, and (iii) under immediate program availability and enrollment at initial eligibility. We further estimated the controlled direct effect of immediate program availability compared to no program availability, under a hypothetical intervention to prevent individual enrollment in the program. Targeted minimum loss-based estimation was used to estimate the mean outcome, while Super Learning was implemented to estimate the required nuisance parameters. Analyses were conducted with the ltmle R package; analysis code is available at an online repository as an R package. Results showed that at 450 days, the probability of in-care survival for subjects with immediate availability and enrollment was 0.93 (95 % CI: 0.91, 0.95) and 0.87 (95 % CI: 0.86, 0.87) for subjects with immediate availability never enrolling. For subjects without LREC availability, it was 0.91 (95 % CI: 0.90, 0.92). Immediate program availability without individual enrollment, compared to no program availability, was estimated to slightly albeit significantly decrease survival by 4 % (95 % CI 0.03,0.06, p < 0.01). Immediately availability and enrollment resulted in a 7 % higher in-care survival compared to immediate availability with non-enrollment after 450 days (95 % CI –0.08,–0.05, p < 0.01). The results are consistent with a fairly small impact of both availability and enrollment in the LREC program on in-care survival.

We develop a transport formula for predicting overall cumulative vaccine efficacy through time t (VE(t)$$VE(t)$$) to prevent clinically significant infection with a genetically diverse pathogen (e. g., HIV infection) in a new setting for which a Phase III preventive vaccine efficacy trial that would directly estimate VE(t)$$VE(t)$$ has not yet been conducted. The formula integrates data from (1) a previous Phase III trial, (2) a Phase I/II immune response biomarker endpoint trial in the new setting where a follow-up Phase III trial is planned, (3) epidemiological data on background HIV infection incidence in the new setting; and (4) genomic epidemiological data on HIV sequence distributions in the previous and new settings. For (1), the randomized vaccine versus placebo Phase III trial yields estimates of vaccine efficacy to prevent particular genotypes of HIV in participant subgroups defined by baseline covariates X and immune responses to vaccination S(1)$$S(1)$$ measured at a fixed time point τ$$\tau $$ (potential outcomes if assigned vaccine); often one or more immune responses to vaccination are available that modify genotype-specific vaccine efficacy. The formula focuses on subgroups defined by X and S(1)$$S(1)$$ and being at-risk for HIV infection at τ$$\tau $$ under both the vaccine and placebo treatment assignments. For (2), the Phase I/II trial tests the same vaccine in a new setting, or a refined new vaccine in the same or new setting, and measures the same baseline covariates and immune responses as the original Phase III trial. For (3), epidemiological data in the new setting are used to project overall background HIV infection rates in the baseline covariate subgroups in the planned Phase III trial, hence re-calibrating for HIV incidence differences in the two settings; whereas for (4), data bases of HIV sequences measured from HIV infected individuals are used to re-calibrate for differences in the distributions of the circulating HIV genotypes in the two settings. The transport formula incorporates a user-specified bridging assumption function that measures differences in HIV genotype-specific conditional biological-susceptibility vaccine efficacies in the two settings, facilitating a sensitivity analysis. We illustrate the transport formula with application to HIV Vaccine Trials Network (HVTN) research. One application of the transport formula is to use predicted VE(t)$$VE(t)$$ as a rational criterion for ranking a set of candidate vaccines being studied in Phase I/II trials for their priority for down-selection into the follow-up Phase III trial.

A fundamental probabilistic equivalence between randomized experiments and observational studies is presented. Given a detailed scenario, the reader is asked to consider which of two possible study designs provides more information regarding the expected difference in an outcome due to a time-fixed treatment. A general solution is described, and a particular worked example is also provided. A mathematical proof is given in the appendix. The demonstrated equivalence helps to clarify common ground between randomized experiments and observational studies, and to provide a foundation for considering both the design and interpretation of studies.

To obtain statistical inference about interaction hypotheses without making strong distributional assumptions, permutation tests based on permuting the outcomes are often being used. It was shown that in continuous and binary data these tests might not be even approximately valid and parametric bootstrap was suggested as a viable alternative, outperforming such permutation tests. We describe an alternative permutation test, permuting the null hypothesis residuals rather than the outcome. Using simulations, we compare accuracy across the permutation tests and parametric bootstrap, studying continuous, binary, and additionally count data. Finally, we address power.