Abstract Objectives Doubly-robust (DR) estimators are widely used for evaluating causal effects in observational studies and are often perceived as more desirable than propensity score weighting, such as inverse probability weighting (IPW), or outcome modeling alone, because they provide extra protection against model misspecification. However, double robustness is an asymptotic property that may not hold in finite samples. We investigate how the finite sample performance of DR estimators depends on the degree of covariate overlap between comparison groups. Methods Using analytical illustrations and extensive numerical studies with synthetic and real-world data, we examine the bias and variance of two representative doubly-robust estimators, the canonical DR (augmented IPW) estimator and the targeted maximum likelihood estimator (TMLE), relative to IPW and outcome regression estimators under different degrees of covariate overlap and model specifications. Results We find that: (i) specification of the outcome model has a stronger influence on DR estimates than specification of the propensity score model, and this dominance increases as overlap decreases; (ii) with poor overlap, DR estimators generally amplify the hazards of extreme weights (large bias and/or variance) regardless of model specifications, and can be inferior to IPW and outcome regression estimators. Conclusions As a practical guide, we recommend always first checking the degree of overlap in applications. In the case of poor overlap, analysts should consider shifting the target estimand from the full study population to a subpopulation with adequate overlap via, e.g., propensity score trimming or overlap weighting, or conducting subgroup analysis.
Abstract Background Epidemiologic exposures arise through different processes, and these processes may shape confounding, selection, measurement, and the feasibility of alternative study designs. A simple framework focused on the exposure-generating process may therefore be useful during early study planning. Methods This was not a systematic review; instead, it was a focused conceptual synthesis of epidemiologic literature on intended and unintended effects, confounding by indication, well-defined interventions, bias, and causal study design. We applied the proposed dimensions to classic and contemporary exposure questions. Results We propose classifying a specified acquired exposure pathway or causal contrast along two dimensions: whether exposure initiation or control is participant/proxy-directed or externally determined, and whether the outcome under study is an intended or unintended effect. Their intersection yields four classes. The classification is conditional on the population, decision-maker, exposure contrast, outcome, and time period; it is not an intrinsic label attached to an exposure. Information bias is treated as a cross-cutting threat, and genetic characteristics are outside the framework’s scope. Conclusions The framework may help investigators anticipate threats to validity and identify feasible study designs. It is a pedagogical heuristic that complements, but does not replace, formal causal tools.
Abstract Objective This paper proposes a unified mathematical framework for binary outcome measures through the introduction of the General Risk Index (GRI). Methods While classical metrics such as the risk ratio (RR), odds ratio (OR), and risk difference (RD) are often treated as distinct entities, we demonstrate that they belong to a single family of indices defined by the relative weighting of concordant and discordant pairs. By parameterizing these weights, we show that the GRI consistently preserves the direction of the treatment effect while providing a continuous spectrum of risk assessment. Results We apply this framework to data from a randomized trial of closed-loop insulin delivery systems, illustrating how the choice of index—and the subsequent weighting of concordant outcomes—can significantly influence the perceived magnitude of clinical impact. Conclusions The GRI provides researchers with a versatile tool for comparing classical indices and selecting the optimal measure based on specific clinical and statistical requirements.
Statistical theory forms a foundation for how epidemiologists learn about populations in public health and medical studies and is fundamental for the understanding of more advanced epidemiological methods (e.g., in causal inference and machine learning). Textbooks provide in-depth coverage of probability and statistical theory, but with such comprehensive coverage that it can be easy to miss the forest for the trees. Here, we provide a summary of fundamental concepts from large-sample statistical theory to allow for more focused understanding tailored to epidemiologists and health science researchers. This primer aims to promote appropriate understanding and application of statistical methods in epidemiologic research. We clarify several often-confused statistical topics and provide a motivation for the application of large-sample inferential methods to data from population health and medical studies. Assumptions underlying commonly used statistical methods that must be considered for valid inference are also discussed. These ideas are contextualized with an example from the Women's Interagency HIV Study.
In observational studies, performing a sensitivity analysis for unmeasured confounding is recommended alongside estimating the causal effect of an exposure on an outcome. This study extended sensitivity analysis frameworks to evaluate the joint effects of two binary exposures, accounting for potential unmeasured confounders. We applied this approach to assess the joint impact of household wealth and maternal education on child nutritional status using data from the 2019 Bangladesh Multiple Indicator Cluster Survey (MICS). A log-binomial regression model was employed to estimate the causal effect in the relative risk scale after adjusting for observed confounders by inverse probability weighting (IPW). Sensitivity analysis explored the robustness of the estimated causal effect under different scenarios of unmeasured confounding. The findings indicate that higher levels of wealth and maternal education significantly reduce the risk of child malnutrition independently and jointly, and the joint effects are robust against unmeasured confounders. Such conclusions underscore the need to account for both exposures in causal inference and provide a framework to assess robustness when unmeasured confounders are a concern in public health studies.
