arXiv subjects

Ashkan Ertefaie

Publications and source records attributed to Ashkan Ertefaie.

At least 19 recordsLinked to original sources

arXiv2026

The V-fold jackknife for semiparametric inference: variance estimation, confidence intervals, and simultaneous confidence bands

For decades, the bootstrap has been a default tool for statistical inference because of its broad applicability and minimal analytic requirements. Although its validity is well understood for smooth parametric estimators, its theoretical properties for many modern semiparametric and machine-learning estimators remain largely unstudied. Nevertheless, bootstrap procedures are often used routinely in such settings, even when their validity is unknown and their computational cost is substantial. We develop the $V$-fold jackknife as a computationally efficient and theoretically justified alternative for semiparametric inference. It requires only $V$ leave-fold-out refits and uses the empirical dispersion of jackknife pseudo-values to quantify uncertainty, without deriving or evaluating an influence function. For regular asymptotically linear estimators of pathwise differentiable parameters, we show that, for fixed $V$, the Studentized $V$-fold jackknife statistic converges to a $t$-distribution with $V-1$ degrees of freedom, giving valid confidence intervals even though the jackknife variance estimator does not converge in probability. When $V\to\infty$, we establish consistency of the variance estimator at rate $V^{-1/2}$, allowing $V$ to diverge slowly, for example at rate $\log n$. We also develop simultaneous confidence bands based on the correct componentwise-Studentized limiting distribution. Finally, we extend the theory to generalized asymptotically linear estimators with diverging influence-function variance and slower-than-$\sqrt n$ convergence; scale invariance of Studentization eliminates the need to know the effective convergence rate. Simulations on the average treatment effect, Kaplan--Meier survival curve, and highly adaptive lasso dose-response curves confirm reliable inference, including where influence-function-based standard errors are anti-conservative or unstable.

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arXiv2026

Nonparametric Estimation of Optimal Stochastic Just-In-Time Adaptive Interventions for Distal Outcomes

Mobile and wearable technologies enable the delivery of just-in-time adaptive interventions (JITAIs) -- interventions that adapt treatment delivery to an individual's rapidly changing internal state and context in real-time, real-world settings. Estimating optimal JITAIs, however, remains challenging because these studies often involve dozens of decision points per individual, and existing methods can produce unstable and irregular estimators with substantial bias and slow convergence rates. Advanced reinforcement learning approaches may be difficult to interpret and often target proximal, discounted outcomes rather than the distal end-of-study outcomes that define long-term success in many behavioral and clinical studies. To address these challenges, we develop a nonparametrically efficient estimator of the regimen-response curve for distal outcomes under a class of stochastic policies and introduce a data-adaptive tilting procedure to stabilize estimation in settings with many decision points. We show that the estimated regimen-response curve converges weakly to a Gaussian process, enabling simultaneous confidence bands, and we derive asymptotic theory for the optimizer of the curve, thereby enabling inference for the learned optimal stochastic policy. These developments provide a unified framework for estimation, inference, and optimization of stochastic JITAIs for distal outcomes.

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arXiv2026

Optimal Treatment Policy Estimation for Recurrent Events with a Competing Terminal Event: An Instrumented Difference-in-Differences Approach

Learning reproducible and generalizable optimal treatment policies for chronic diseases requires large, representative populations with long-term follow-up. Administrative health data provide a natural starting point, but their use is often limited by unmeasured confounding. We address this by proposing a novel framework based on Instrumented Difference-in-Differences (iDID) to estimate optimal policies for recurrent event outcomes subject to a terminating event. The iDID design is particularly useful in this setting because it leverages policy-induced treatment variation while allowing for persistent unmeasured differences across populations, relying on assumptions that are more plausible for administrative health data than those required by conventional IV or DID approaches. A key feature of our approach is that it explicitly addresses the fundamental challenge of avoiding policies that trivially reduce recurrent adverse events by increasing mortality. We derive two distinct Inverse Probability Weighted identifications and develop a multiply robust estimator that achieves consistency if any one of several subsets of nuisance models is correctly specified. We establish the estimator's consistency and asymptotic normality through large-sample theory and demonstrate its superior finite-sample performance over existing methods via simulation. Finally, we apply this framework to a national Medicare dataset to optimize first-line Type 2 Diabetes strategies, specifically targeting the minimization of disease-related hospitalizations while accounting for survival.

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arXiv2025

On Causal Inference for the Survivor Function

In this expository paper, we consider the problem of causal inference and efficient estimation for the counterfactual survivor function. This problem has previously been considered in the literature in several papers, each relying on the imposition of conditions meant to identify the desired estimand from the observed data. These conditions, generally referred to as either implying or satisfying coarsening at random, are inconsistently imposed across this literature and, in all cases, fail to imply coarsening at random. We establish the first general characterization of coarsening at random, and also sequential coarsening at random, for this estimation problem. Other contributions include the first general characterization of the set of all influence functions for the counterfactual survival probability under sequential coarsening at random, and the corresponding nonparametric efficient influence function. These characterizations are general in that neither impose continuity assumptions on either the underlying failure or censoring time distributions. We further show how the latter compares to alternative forms recently derived in the literature, including establishing the pointwise equivalence of the influence functions for our nonparametric efficient estimator and that recently given in Westling et al (2024, Journal of the American Statistical Association).

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arXiv2025

A structural nested rate model for estimating the effects of time-varying exposure on recurrent event outcomes in the presence of death

Assessing the causal effect of time-varying exposures on recurrent event processes is challenging in the presence of a terminating event. Our objective is to estimate both the short-term and delayed marginal causal effects of exposures on recurrent events while addressing the bias of a potentially correlated terminal event. Existing estimators based on marginal structural models and proportional rate models are unsuitable for estimating delayed marginal causal effects for many reasons, and furthermore, they do not account for competing risks associated with a terminating event. To address these limitations, we propose a class of semiparametric structural nested recurrent event models and two estimators of short-term and delayed marginal causal effects of exposures. We establish the asymptotic linearity of these two estimators under regularity conditions through the novel use of modern empirical process and semiparametric efficiency theory. We examine the performance of these estimators via simulation and provide an R package sncure to apply our methods in real data scenarios. Finally, we present the utility of our methods in the context of a large epidemiological study of 299,661 Medicare beneficiaries, where we estimate the effects of fine particulate matter air pollution on recurrent hospitalizations for cardiovascular disease.

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arXiv2025

Valid post-selection inference for penalized G-estimation

Understanding treatment effect heterogeneity is important for decision making in medical and clinical practices, or handling various engineering and marketing challenges. When dealing with high-dimensional covariates or when the effect modifiers are not predefined and need to be discovered, data-adaptive selection approaches become essential. However, with data-driven model selection, the quantification of statistical uncertainty is complicated by post-selection inference due to difficulties in approximating the sampling distribution of the target estimator. Data-driven model selection tends to favor models with strong effect modifiers with an associated cost of inflated type I errors. Although several frameworks and methods for valid statistical inference have been proposed for ordinary least squares regression following data-driven model selection, fewer options exist for valid inference for effect modifier discovery in causal modeling contexts. In this article, we extend two different methods to develop valid inference for penalized G-estimation that investigates effect modification of proximal treatment effects within the structural nested mean model framework. We show the asymptotic validity of the proposed methods. Using extensive simulation studies, we evaluate and compare the finite sample performance of the proposed methods and the naive inference based on a sandwich variance estimator. Our work is motivated by the study of hemodiafiltration for treating patients with end-stage renal disease at the Centre Hospitalier de l'Universit\'e de Montr\'eal. We apply these methods to draw inference about the effect heterogeneity of dialysis facility on the repeated session-specific hemodiafiltration outcomes.

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arXiv2024

Constructing optimal treatment length strategies to maximize quality-adjusted lifetimes

Real-world clinical decision making is a complex process that involves balancing the risks and benefits of treatments. Quality-adjusted lifetime is a composite outcome that combines patient quantity and quality of life, making it an attractive outcome in clinical research. We propose methods for constructing optimal treatment length strategies to maximize this outcome. Existing methods for estimating optimal treatment strategies for survival outcomes cannot be applied to a quality-adjusted lifetime due to induced informative censoring. We propose a weighted estimating equation that adjusts for both confounding and informative censoring. We also propose a nonparametric estimator of the mean counterfactual quality-adjusted lifetime survival curve under a given treatment length strategy, where the weights are estimated using an undersmoothed sieve-based estimator. We show that the estimator is asymptotically linear and provide a data-dependent undersmoothing criterion. We apply our method to obtain the optimal time for percutaneous endoscopic gastrostomy insertion in patients with amyotrophic lateral sclerosis.

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arXiv2024

Adaptive sparsening and smoothing of the treatment model for longitudinal causal inference using outcome-adaptive LASSO and marginal fused LASSO

Causal variable selection in time-varying treatment settings is challenging due to evolving confounding effects. Existing methods mainly focus on time-fixed exposures and are not directly applicable to time-varying scenarios. We propose a novel two-step procedure for variable selection when modeling the treatment probability at each time point. We first introduce a novel approach to longitudinal confounder selection using a Longitudinal Outcome Adaptive LASSO (LOAL) that will data-adaptively select covariates with theoretical justification of variance reduction of the estimator of the causal effect. We then propose an Adaptive Fused LASSO that can collapse treatment model parameters over time points with the goal of simplifying the models in order to improve the efficiency of the estimator while minimizing model misspecification bias compared with naive pooled logistic regression models. Our simulation studies highlight the need for and usefulness of the proposed approach in practice. We implemented our method on data from the Nicotine Dependence in Teens study to estimate the effect of the timing of alcohol initiation during adolescence on depressive symptoms in early adulthood.

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arXiv2024

Nonparametric assessment of regimen response curve estimators

Marginal structural models have been widely used in causal inference to estimate mean outcomes under either a static or a prespecified set of treatment decision rules. This approach requires imposing a working model for the mean outcome given a sequence of treatments and possibly baseline covariates. In this paper, we introduce a dynamic marginal structural model that can be used to estimate an optimal decision rule within a class of parametric rules. Specifically, we will estimate the mean outcome as a function of the parameters in the class of decision rules, referred to as a regimen-response curve. In general, misspecification of the working model may lead to a biased estimate with questionable causal interpretability. To mitigate this issue, we will leverage risk to assess "goodness-of-fit" of the imposed working model. We consider the counterfactual risk as our target parameter and derive inverse probability weighting and canonical gradients to map it to the observed data. We provide asymptotic properties of the resulting risk estimators, considering both fixed and data-dependent target parameters. We will show that the inverse probability weighting estimator can be efficient and asymptotic linear when the weight functions are estimated using a sieve-based estimator. The proposed method is implemented on the LS1 study to estimate a regimen-response curve for patients with Parkinson's disease.

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arXiv2024

Sensitivity analysis for constructing optimal regimes in the presence of treatment non-compliance

The current body of research on developing optimal treatment strategies often places emphasis on intention-to-treat analyses, which fail to take into account the compliance behavior of individuals. Methods based on instrumental variables have been developed to determine optimal treatment strategies in the presence of endogeneity. However, these existing methods are not applicable when there are two active treatment options and the average causal effects of the treatments cannot be identified using a binary instrument. In order to address this limitation, we present a procedure that can identify an optimal treatment strategy and the corresponding value function as a function of a vector of sensitivity parameters. Additionally, we derive the canonical gradient of the target parameter and propose a multiply robust classification-based estimator for the optimal treatment strategy. Through simulations, we demonstrate the practical need for and usefulness of our proposed method. We apply our method to a randomized trial on Adaptive Treatment for Alcohol and Cocaine Dependence.

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arXiv2024

Penalized G-estimation for effect modifier selection in a structural nested mean model for repeated outcomes

Effect modification occurs when the impact of the treatment on an outcome varies based on the levels of other covariates known as effect modifiers. Modeling these effect differences is important for etiological goals and for purposes of optimizing treatment. Structural nested mean models (SNMMs) are useful causal models for estimating the potentially heterogeneous effect of a time-varying exposure on the mean of an outcome in the presence of time-varying confounding. A data-adaptive selection approach is necessary if the effect modifiers are unknown a priori and need to be identified. Although variable selection techniques are available for estimating the conditional average treatment effects using marginal structural models or for developing optimal dynamic treatment regimens, all of these methods consider a single end-of-follow-up outcome. In the context of an SNMM for repeated outcomes, we propose a doubly robust penalized G-estimator for the causal effect of a time-varying exposure with a simultaneous selection of effect modifiers and prove the oracle property of our estimator. We conduct a simulation study for the evaluation of its performance in finite samples and verification of its double-robustness property. Our work is motivated by the study of hemodiafiltration for treating patients with end-stage renal disease at the Centre Hospitalier de l'Universit\'e de Montr\'eal. We apply the proposed method to investigate the effect heterogeneity of dialysis facility on the repeated session-specific hemodiafiltration outcomes.

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arXiv2023

Nonparametric estimation of a covariate-adjusted counterfactual treatment regimen response curve

Flexible estimation of the mean outcome under a treatment regimen (i.e., value function) is the key step toward personalized medicine. We define our target parameter as a conditional value function given a set of baseline covariates which we refer to as a stratum based value function. We focus on semiparametric class of decision rules and propose a sieve based nonparametric covariate adjusted regimen-response curve estimator within that class. Our work contributes in several ways. First, we propose an inverse probability weighted nonparametrically efficient estimator of the smoothed regimen-response curve function. We show that asymptotic linearity is achieved when the nuisance functions are undersmoothed sufficiently. Asymptotic and finite sample criteria for undersmoothing are proposed. Second, using Gaussian process theory, we propose simultaneous confidence intervals for the smoothed regimen-response curve function. Third, we provide consistency and convergence rate for the optimizer of the regimen-response curve estimator; this enables us to estimate an optimal semiparametric rule. The latter is important as the optimizer corresponds with the optimal dynamic treatment regimen. Some finite-sample properties are explored with simulations.

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arXiv2023

Causal inference for the expected number of recurrent events in the presence of a terminal event

While recurrent event analyses have been extensively studied, limited attention has been given to causal inference within the framework of recurrent event analysis. We develop a multiply robust estimation framework for causal inference in recurrent event data with a terminal failure event. We define our estimand as the vector comprising both the expected number of recurrent events and the failure survival function evaluated along a sequence of landmark times. We show that the estimand can be identified under a weaker condition than conditionally independent censoring and derive the associated class of influence functions under general censoring and failure distributions (i.e., without assuming absolute continuity). We propose a particular estimator within this class for further study, conduct comprehensive simulation studies to evaluate the small-sample performance of our estimator, and illustrate the proposed estimator using a large Medicare dataset to assess the causal effect of PM$_{2.5}$ on recurrent cardiovascular hospitalization.

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arXiv2023

Inference for relative sparsity

In healthcare, there is much interest in estimating policies, or mappings from covariates to treatment decisions. Recently, there is also interest in constraining these estimated policies to the standard of care, which generated the observed data. A relative sparsity penalty was proposed to derive policies that have sparse, explainable differences from the standard of care, facilitating justification of the new policy. However, the developers of this penalty only considered estimation, not inference. Here, we develop inference for the relative sparsity objective function, because characterizing uncertainty is crucial to applications in medicine. Further, in the relative sparsity work, the authors only considered the single-stage decision case; here, we consider the more general, multi-stage case. Inference is difficult, because the relative sparsity objective depends on the unpenalized value function, which is unstable and has infinite estimands in the binary action case. Further, one must deal with a non-differentiable penalty. To tackle these issues, we nest a weighted Trust Region Policy Optimization function within a relative sparsity objective, implement an adaptive relative sparsity penalty, and propose a sample-splitting framework for post-selection inference. We study the asymptotic behavior of our proposed approaches, perform extensive simulations, and analyze a real, electronic health record dataset.

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arXiv2023

Relative Sparsity for Medical Decision Problems

Existing statistical methods can estimate a policy, or a mapping from covariates to decisions, which can then instruct decision makers (e.g., whether to administer hypotension treatment based on covariates blood pressure and heart rate). There is great interest in using such data-driven policies in healthcare. However, it is often important to explain to the healthcare provider, and to the patient, how a new policy differs from the current standard of care. This end is facilitated if one can pinpoint the aspects of the policy (i.e., the parameters for blood pressure and heart rate) that change when moving from the standard of care to the new, suggested policy. To this end, we adapt ideas from Trust Region Policy Optimization (TRPO). In our work, however, unlike in TRPO, the difference between the suggested policy and standard of care is required to be sparse, aiding with interpretability. This yields ``relative sparsity," where, as a function of a tuning parameter, $λ$, we can approximately control the number of parameters in our suggested policy that differ from their counterparts in the standard of care (e.g., heart rate only). We propose a criterion for selecting $λ$, perform simulations, and illustrate our method with a real, observational healthcare dataset, deriving a policy that is easy to explain in the context of the current standard of care. Our work promotes the adoption of data-driven decision aids, which have great potential to improve health outcomes.

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arXiv2022

Structural mean models for instrumented difference-in-differences

In the standard difference-in-differences research design, the parallel trends assumption may be violated when the relationship between the exposure trend and the outcome trend is confounded by unmeasured confounders. Progress can be made if there is an exogenous variable that (i) does not directly influence the change in outcome means (i.e. the outcome trend) except through influencing the change in exposure means (i.e. the exposure trend), and (ii) is not related to the unmeasured exposure - outcome confounders on the trend scale. Such exogenous variable is called an instrument for difference-in-differences. For continuous outcomes that lend themselves to linear modelling, so-called instrumented difference-in-differences methods have been proposed. In this paper, we will suggest novel multiplicative structural mean models for instrumented difference-in-differences, which allow one to identify and estimate the average treatment effect on count and rare binary outcomes, in the whole population or among the treated, when a valid instrument for difference-in-differences is available. We discuss the identifiability of these models, then develop efficient semi-parametric estimation approaches that allow the use of flexible, data-adaptive or machine learning methods to estimate the nuisance parameters. We apply our proposal on health care data to investigate the risk of moderate to severe weight gain under sulfonylurea treatment compared to metformin treatment, among new users of antihyperglycemic drugs.

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arXiv2022

Valid post-selection inference in Robust Q-learning

Q-learning facilitates the development of an optimal adaptive treatment strategy through stagewise regression on a pre-specified set of tailoring variables and confounders. Semiparametric robust Q-learning eliminates the residual confounding that can occur when parametric working models for confounding influences are misspecified. However, in the presence of many potential tailoring variables, constructing an optimal adaptive treatment strategy using either approach may lead to including extraneous variables that contribute little or no benefit while increasing implementation costs, thereby placing an undue burden on patients. Using data-driven selection processes to identify a smaller set of informative prognostic factors is straightforward; however, proper statistical inference must account for this selection process. In this paper, we adapt the Universal Post-Selection Inference (UPoSI) procedure to the semiparametric Robust Q-learning method. UPoSI, introduced for use with linear models, allows for very general variable selection mechanisms. Our approach addresses the unique challenges stemming from the use of UPoSI with semiparametric multistage decision methods. Theoretical and simulation results demonstrate the validity of the proposed confidence regions. We illustrate our proposed methods through an application to adaptive treatment strategy estimation for substance abuse.

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arXiv2021

Causal Mediation Analysis: Selection with Asymptotically Valid Inference

Researchers are often interested in learning not only the effect of treatments on outcomes, but also the pathways through which these effects operate. A mediator is a variable that is affected by treatment and subsequently affects outcome. Existing methods for penalized mediation analyses may lead to ignoring important mediators and either assume that finite-dimensional linear models are sufficient to remove confounding bias, or perform no confounding control at all. In practice, these assumptions may not hold. We propose a method that considers the confounding functions as nuisance parameters to be estimated using data-adaptive methods. We then use a novel regularization method applied to this objective function to identify a set of important mediators. We derive the asymptotic properties of our estimator and establish the oracle property under certain assumptions. Asymptotic results are also presented in a local setting which contrast the proposal with the standard adaptive lasso. We also propose a perturbation bootstrap technique to provide asymptotically valid post-selection inference for the mediated effects of interest. The performance of these methods will be discussed and demonstrated through simulation studies.

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