Stephen R. Cole

Epidemiology stands to benefit greatly from combining data sources with complementary strengths. We propose a study design and estimators to combine information from multiple observational studies to simultaneously address confounding and outcome measurement error. Using inverse probability weighted, g-computation, and augmented inverse probability weighted estimators, we show how to combine information from two studies wherein the first study is subject to outcome misclassification (but has adequate confounder control) and the second study has gold-standard outcomes (but inadequate confounder control). Monte Carlo experiments demonstrate that the proposed estimators remove both confounding and measurement biases and provide appropriate 95% confidence interval coverage, while standard analyses fall short. Fusion designs offer a principled approach to combine data from multiple sources to address multiple biases in epidemiologic research.

Positivity and causal consistency are sometimes presented as general validity requirements. Positivity, however, is not a general requirement for causal inference and does not address the more demanding practical needs for adequate numbers of observations. Common statistical methods in health and medical research depend on large-sample approximations; yet, approximation accuracy is rarely discussed in research reports, even in cases where it has clearly failed. Prioritization by generality and practical importance shifts the emphasis to approximation accuracy over positivity, with the latter better cast as a technical requirement for specific types of methods. Meanwhile, consistency mixes requirements for operationally clear definitions of treatments with more general needs for accurate measurement. All statistical methods depend on conceptual precision and measurement accuracy; hence, those conditions belong among fundamental requirements for valid inferences, alongside control of selection bias and confounding. When measurement problems are addressed in the basic assumptions of formalizations, consistency can be seen as a definition of the targeted outcome variable in a causal model, rather than a central assumption that mixes separate concerns about construct ambiguity and coarsening.

Misclassification between causes of death can produce bias in estimated cumulative incidence functions. When estimating causal quantities, such as comparing the cumulative incidence of death due to specific causes under interventions, such bias can lead to suboptimal decision making. Here, a consistent semiparametric estimator of the cumulative incidence function under interventions in settings with misclassification between two event types is presented. The measurement parameters for this estimator can be informed by validation data or expert knowledge. Moreover, a modified bootstrap approach to variance estimation is proposed for confidence interval construction. The proposed estimator was applied to estimate the cumulative incidence of AIDS‐related mortality in the Multicenter AIDS Cohort Study under single‐ versus combination‐drug antiretroviral therapy regimens that may be subject to confounding. The proposed estimator is shown to be consistent and performed well in finite samples via a series of simulation experiments.

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Causal inference methods can be applied to estimate the effect of a point exposure or treatment on an outcome of interest using data from observational studies. For example, in the Women’s Interagency HIV Study, it is of interest to understand the effects of incarceration on the number of sexual partners and the number of cigarettes smoked after incarceration. In settings like this where the outcome is a count, the estimand is often the causal mean ratio, that is, the ratio of the counterfactual mean count under exposure to the counterfactual mean count under no exposure. This paper considers estimators of the causal mean ratio based on inverse probability of treatment weights, the parametric g-formula, and doubly robust estimation, each of which can account for overdispersion, zero-inflation, and heaping in the measured outcome. Methods are compared in simulations and are applied to data from the Women’s Interagency HIV Study.

Higher-order evidence (ie, evidence about evidence) allows epidemiologists and other health data scientists to account for measurement error in validation data. Here, to illustrate the use of higher-order evidence, we provide a minimal nontrivial example of estimating the proportion and show how higher-order evidence can be used to construct sensitivity analyses. The proposed method provides a flexible approach to account for multiple levels of distortion in the results of epidemiologic studies.

Importance: Accurate assessment of gestational age (GA) is essential to good pregnancy care but often requires ultrasonography, which may not be available in low-resource settings. This study developed a deep learning artificial intelligence (AI) model to estimate GA from blind ultrasonography sweeps and incorporated it into the software of a low-cost, battery-powered device.Objective: To evaluate GA estimation accuracy of an AI-enabled ultrasonography tool when used by novice users with no prior training in sonography.Design, Setting, and Participants: This prospective diagnostic accuracy study enrolled 400 individuals with viable, single, nonanomalous, first-trimester pregnancies in Lusaka, Zambia, and Chapel Hill, North Carolina. Credentialed sonographers established the “ground truth” GA via transvaginal crown-rump length measurement. At random follow-up visits throughout gestation, including a primary evaluation window from 14 0/7 weeks’ to 27 6/7 weeks’ gestation, novice users obtained blind sweeps of the maternal abdomen using the AI-enabled device (index test) and credentialed sonographers performed fetal biometry with a high-specification machine (study standard).Main Outcomes and Measures: The primary outcome was the mean absolute error (MAE) of the index test and study standard, which was calculated by comparing each method’s estimate to the previously established GA and considered equivalent if the difference fell within a prespecified margin of ±2 days.Results: In the primary evaluation window, the AI-enabled device met criteria for equivalence to the study standard, with an MAE (SE) of 3.2 (0.1) days vs 3.0 (0.1) days (difference, 0.2 days [95% CI, −0.1 to 0.5]). Additionally, the percentage of assessments within 7 days of the ground truth GA was comparable (90.7% for the index test vs 92.5% for the study standard). Performance was consistent in prespecified subgroups, including the Zambia and North Carolina cohorts and those with high body mass index.Conclusions and Relevance: Between 14 and 27 weeks’ gestation, novice users with no prior training in ultrasonography estimated GA as accurately with the low-cost, point-of-care AI tool as credentialed sonographers performing standard biometry on high-specification machines. These findings have immediate implications for obstetrical care in low-resource settings, advancing the World Health Organization goal of ultrasonography estimation of GA for all pregnant people.Trial Registration: ClinicalTrials.gov Identifier: NCT05433519

Higher-order evidence is evidence about evidence. Epidemiologic examples of higher-order evidence include the settings where the study data constitute first-order evidence and estimates of misclassification comprise the second-order evidence (e.g., sensitivity, specificity) of a binary exposure or outcome collected in the main study. While sampling variability in higher-order evidence is typically acknowledged, higher-order evidence is often assumed to be free of measurement error (e.g., gold standard measures). Here we provide two examples, each with multiple scenarios where second-order evidence is imperfectly measured, and this measurement error can either amplify or attenuate standard corrections to first-order evidence. We propose a way to account for such imperfections that requires third-order evidence. Further illustrations and exploration of how higher-order evidence impacts results of epidemiologic studies is warranted.

We thank Dijkzeul and Labrecque for their letter ( 1) on our recent missing outcome data paper ( 2). Regarding their first point on homogeneity constraints, it might be helpful to consider our scenario B (i.e., missing at random with positivity). Here, both g-computation (stratified by treatment) and multiple imputation (including treatment-covariate product term) models were saturated, and therefore asymptotically equivalent. Neither estimator makes a homogeneity assumption with respect to completing the missing data. And both estimators make marginal comparisons of the mean outcomes between completed treated and untreated data (which is reasonable because this is a randomized trial). Here, g-computation is a nonparametric maximum likelihood estimator, and multiple imputation approaches maximum likelihood as the number of imputations tends towards infinity. Some discussion of how g-computation and multiple imputation relate is provided in Westreich et al. ( 3). Now, in our scenario C (i.e., missing at random without positivity), all the same above points hold, except, as noted by Dijkzeul and Labrecque, all women with 17α-hydroxyprogesterone caproate (17p) treatment and short cervix are missing outcomes. The imputed outcomes, whether by g-computation or multiple imputation, can depend on 17p or short cervix but cannot depend on their product (because no such outcome data is observed). Both g-computation and multiple imputation make this same homogeneity assumption, with the differences in performance most likely attributable to random error. In scenario C, the standard errors for g-computation (500 bootstrap samples) and multiple imputation (50 imputations) were 0.340 and 0.274 (see Cole et al. ( 2), Table 2 and Web Table 1). However, with 10,000 bootstrap samples and 5,000 imputations, the standard errors were instead 0.328 and 0.355.