arXiv subjects

Erin E. Gabriel

Publications and source records attributed to Erin E. Gabriel.

8 recordsLinked to original sources

arXiv2026

On the limitations of causal inference with current-treatment Cox models

Cox models with time-varying treatments often include only the current treatment level. Translating such a model into causally meaningful intervention-specific survival probabilities relies on the Markov property: that the hazard is independent of treatment history conditional on current treatment. For the Markov property to not be population-specific, it needs to hold also conditional on any unmeasured prognostic heterogeneity (frailty). Using a discrete-time argument, earlier work concluded that the Markov property can hold both conditionally and marginally only in the absence of a treatment effect or an effect of the unmeasured heterogeneity. We broaden this argument by developing a continuous-time framework that encompasses both proposed extensions of the Kaplan-Meier curve and current-treatment marginal structural Cox models, and sharpen it by characterizing precisely the conditions under which the Markov property can hold both conditionally and marginally. Specifically, we show that it requires the absence of treatment-frailty interaction on the additive hazard scale. As frailty is inherently unmeasured, such a no-interaction assumption cannot be verified. Consequently, causal interpretation of a current-treatment marginal structural Cox model rests on a strong and unverifiable structural assumption. Illustrating this point, we construct a setting in which a Cox model is correctly specified conditionally on current treatment only, although the marginal Markov property fails. Transforming the fitted model to the survival scale does not recover the true intervention-specific survival probabilities. Thus, moving from the hazard scale to the survival scale is not in itself sufficient to obtain a causal interpretation in the time-varying treatment setting.

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arXiv2026

Deriving Complete Constraints in Hidden Variable Models

Hidden variable graphical models can sometimes imply constraints on the observable distribution that are more complex than simple conditional independence relations. These observable constraints can falsify assumptions of the model that would otherwise be untestable due to the unobserved variables and can be used to constrain estimation procedures to improve statistical efficiency. Knowing the complete set of observable constraints is thus ideal, but this can be difficult to determine in many settings. In models with categorical observed variables and a joint distribution that is completely characterized by linear relations to the unobservable response function variables, we develop a systematic method for deriving the complete set of observable constraints. We illustrate the method in several new settings, including ones that imply both inequality and equality constraints.

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arXiv2026

Nonparametric efficient estimation of the longitudinal front-door functional

The front-door criterion is an identification strategy for the intervention-specific mean outcome in settings where the standard back-door criterion fails due to unmeasured exposure-outcome confounders, but an intermediate variable exists that completely mediates the effect of exposure on the outcome and is not affected by unmeasured confounding. The front-door criterion has been extended to the longitudinal setting, where exposure and mediator vary over time. However, with the exception of a simple plug-in estimator, no suitable estimation techniques have been proposed. In this work, we derive nonparametric efficient estimators of the longitudinal front-door functional. The estimators accommodate high-dimensional mediators, are multiply robust, and allow for the use of data-adaptive methods for estimating nuisance functions while still providing valid inference. The theoretical properties of the estimators are illustrated in a simulation study, and we apply the estimators to a trial of peanut allergy in infants.

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arXiv2025

Bounds for causal mediation effects

Several frameworks have been proposed for studying causal mediation analysis. What these frameworks have in common is that they all make assumptions for point identifications that can be violated even when treatment is randomized. When a causal effect is not point-identified, one can sometimes derive bounds, i.e. a range of possible values that are consistent with the observed data. In this work, we study causal bounds for mediation effects under both the natural effects framework and the separable effects framework. In particular, we show that when there are unmeasured confounders for the intermediate variables(s) the sharp symbolic bounds on separable (in)direct effect coincide with existing bounds for natural (in)direct effects in the analogous setting. We compare these bounds to valid bounds for the natural direct effects when only the cross-world independence assumption does not hold. Furthermore, we demonstrate the use and compare the results of the bounds on data from a trial investigating the effect of peanut consumption on the development of peanut allergy in infants through specific pathways of measured immunological biomarkers.

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arXiv2024

The impact of coarsening an exposure on partial identifiability in instrumental variable settings

In instrumental variable (IV) settings, such as in imperfect randomized trials and observational studies with Mendelian randomization, one may encounter a continuous exposure, the causal effect of which is not of true interest. Instead, scientific interest may lie in a coarsened version of this exposure. Although there is a lengthy literature on the impact of coarsening of an exposure with several works focusing specifically on IV settings, all methods proposed in this literature require parametric assumptions. Instead, just as in the standard IV setting, one can consider partial identification via bounds making no parametric assumptions. This was first pointed out in Alexander Balke's PhD dissertation. We extend and clarify his work and derive novel bounds in several settings, including for a three-level IV, which will most likely be the case in Mendelian randomization. We demonstrate our findings in two real data examples, a randomized trial for peanut allergy in infants and a Mendelian randomization setting investigating the effect of homocysteine on cardiovascular disease.

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arXiv2020

Nonparametric bounds for causal effects in imperfect randomized experiments

Nonignorable missingness and noncompliance can occur even in well-designed randomized experiments making the intervention effect that the experiment was designed to estimate nonidentifiable. Nonparametric causal bounds provide a way to narrow the range of possible values for a nonidentifiable causal effect with minimal assumptions. We derive novel bounds for the causal risk difference for a binary outcome and intervention in randomized experiments with nonignorable missingness caused by a variety of mechanisms and with or without noncompliance. We illustrate the use of the proposed bounds in our motivating data example of peanut consumption on the development of peanut allergies in infants.

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arXiv2020

Causal bounds for outcome-dependent sampling in observational studies

Outcome-dependent sampling designs are common in many different scientific fields including epidemiology, ecology, and economics. As with all observational studies, such designs often suffer from unmeasured confounding, which generally precludes the nonparametric identification of causal effects. Nonparametric bounds can provide a way to narrow the range of possible values for a nonidentifiable causal effect without making additional untestable assumptions. The nonparametric bounds literature has almost exclusively focused on settings with random sampling, and the bounds have often been derived with a particular linear programming method. We derive novel bounds for the causal risk difference, often referred to as the average treatment effect, in six settings with outcome-dependent sampling and unmeasured confounding for a binary outcome and exposure. Our derivations of the bounds illustrate two approaches that may be applicable in other settings where the bounding problem cannot be directly stated as a system of linear constraints. We illustrate our derived bounds in a real data example involving the effect of vitamin D concentration on mortality.

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arXiv2015

Comparing Biomarkers as Trial Level General Surrogates

An intermediate response measure that accurately predicts efficacy in a new setting can reduce trial cost and time to product licensure. In this paper, we define a trial level general surrogate as a trial level intermediate response that accurately predicts trial level clinical responses. Methods for evaluating trial level general surrogates have been developed previously. Many methods in the literature use trial level intermediate responses for prediction. However, all existing methods focus on surrogate evaluation and prediction in new settings, rather than comparison of candidate trial level surrogates, and few formalize the use of cross validation to quantify the expected prediction error. Our proposed method uses Bayesian non-parametric modeling and cross-validation to estimate the absolute prediction error for use in evaluating and comparing candidate trial level general surrogates. Simulations show that our method performs well across a variety of scenarios. We use our method to evaluate and to compare candidate trial level general surrogates in several multi-national trials of a pentavalent rotavirus vaccine. We identify two immune measures that have potential value as trial level general surrogates and use the measures to predict efficacy in a trial with no clinical outcomes measured.

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