arXiv subjects

Marco Carone

Publications and source records attributed to Marco Carone.

At least 19 recordsLinked to original sources

arXiv2025

Sequentially Doubly Robust Estimation of Conditional Survival Probability with Time-Varying Covariates

It is often of interest to study the association between covariates and the cumulative incidence of a right-censored time-to-event outcome. When time-varying covariates are measured on a fixed discrete time scale, it is desirable to account for these more up-to-date covariates when addressing censoring. For example, in vaccine trials, it is of interest to study the association between immune response levels after administering the vaccine and the cumulative incidence of the endpoint, while accounting for loss to follow-up explained by immune response levels measured at multiple post-vaccination visits. Existing methods rely on stringent parametric assumptions, do not account for informative censoring due to time-varying covariates when time is continuous, only estimate a marginal survival probability, or do not fully use the discrete-time structure of post-treatment covariates. We propose a nonparametric estimator of the continuous-time survival probability conditional on covariates, accounting for censoring due to time-varying covariates measured on a fixed discrete time scale. We show that the estimator is sequentially doubly robust: it is consistent if, within each time window between adjacent visits, the censoring distribution is consistently estimated, or both the time-to-event distribution and a conditional mean probability are consistently estimated. We also show that, in the special case of estimating the marginal survival probability, our estimator is asymptotically efficient. We demonstrate the superior performance of our estimator in a simulation experiment, and apply the method to a COVID-19 vaccine efficacy trial.

stat.ME↗

arXiv2024

Debiased machine learning for counterfactual survival functionals based on left-truncated right-censored data

Learning causal effects of a binary exposure on time-to-event endpoints can be challenging because survival times may be partially observed due to censoring and systematically biased due to truncation. In this work, we present debiased machine learning-based nonparametric estimators of the joint distribution of a counterfactual survival time and baseline covariates for use when the observed data are subject to covariate-dependent left truncation and right censoring and when baseline covariates suffice to deconfound the relationship between exposure and survival time. Our inferential procedures explicitly allow the integration of flexible machine learning tools for nuisance estimation, and enjoy certain robustness properties. The approach we propose can be directly used to make pointwise or uniform inference on smooth summaries of the joint counterfactual survival time and covariate distribution, and can be valuable even in the absence of interventions, when summaries of a marginal survival distribution are of interest. We showcase how our procedures can be used to learn a variety of inferential targets and illustrate their performance in simulation studies.

stat.ME↗

arXiv2024

Stabilized Inverse Probability Weighting via Isotonic Calibration

Inverse weighting with an estimated propensity score is widely used by estimation methods in causal inference to adjust for confounding bias. However, directly inverting propensity score estimates can lead to instability, bias, and excessive variability due to large inverse weights, especially when treatment overlap is limited. In this work, we propose a post-hoc calibration algorithm for inverse propensity weights that generates well-calibrated, stabilized weights from user-supplied, cross-fitted propensity score estimates. Our approach employs a variant of isotonic regression with a loss function specifically tailored to the inverse propensity weights. Through theoretical analysis and empirical studies, we demonstrate that isotonic calibration improves the performance of doubly robust estimators of the average treatment effect.

stat.ME↗

arXiv2024

Doubly robust inference via calibration

Doubly robust estimators are widely used for estimating average treatment effects and other linear summaries of regression functions. While consistency requires only one of two nuisance functions to be estimated consistently, asymptotic normality for linear functionals typically requires sufficiently fast convergence of both. We address this mismatch by showing that calibrating the nuisance estimators within a doubly robust procedure can yield doubly robust asymptotic normality. We introduce the idea of calibrated debiased machine learning (DML) and propose a specific implementation in which standard DML is augmented with a simple isotonic regression adjustment. We show that, under a partial orthogonality condition, a calibrated DML estimator remains asymptotically normal if either the regression function or Riesz representer of the functional is estimated sufficiently well, allowing the other to converge arbitrarily slowly or even inconsistently. We also propose a bootstrap-assisted method for constructing confidence intervals, enabling doubly robust inference without additional nuisance estimation. In a range of semi-synthetic benchmark datasets, calibrated DML reduces bias and improves coverage relative to standard DML. Our method can be integrated into existing DML pipelines by adding just a few lines of code to calibrate cross-fitted estimates via isotonic regression.

stat.ME↗

arXiv2024

Propensity Score Augmentation in Matching-based Estimation of Causal Effects

When assessing the causal effect of a binary exposure using observational data, confounder imbalance across exposure arms must be addressed. Matching methods, including propensity score-based matching, can be used to deconfound the causal relationship of interest. They have been particularly popular in practice, at least in part due to their simplicity and interpretability. However, these methods can suffer from low statistical efficiency compared to many competing methods. In this work, we propose a novel matching-based estimator of the average treatment effect based on a suitably-augmented propensity score model. Our procedure can be shown to have greater statistical efficiency than traditional matching estimators whenever prognostic variables are available, and in some cases, can nearly reach the nonparametric efficiency bound. In addition to a theoretical study, we provide numerical results to illustrate our findings. Finally, we use our novel procedure to estimate the effect of circumcision on risk of HIV-1 infection using vaccine efficacy trial data.

stat.ME↗

arXiv2024

Towards a Unified Theory for Semiparametric Data Fusion with Individual-Level Data

We address the goal of conducting inference about a smooth finite-dimensional parameter by utilizing individual-level data from various independent sources. Recent advancements have led to the development of a comprehensive theory capable of handling scenarios where different data sources align with, possibly distinct subsets of, conditional distributions of a single factorization of the joint target distribution. While this theory proves effective in many significant contexts, it falls short in certain common data fusion problems, such as two-sample instrumental variable analysis, settings that integrate data from epidemiological studies with diverse designs (e.g., prospective cohorts and retrospective case-control studies), and studies with variables prone to measurement error that are supplemented by validation studies. In this paper, we extend the aforementioned comprehensive theory to allow for the fusion of individual-level data from sources aligned with conditional distributions that do not correspond to a single factorization of the target distribution. Assuming conditional and marginal distribution alignments, we provide universal results that characterize the class of all influence functions of regular asymptotically linear estimators and the efficient influence function of any pathwise differentiable parameter, irrespective of the number of data sources, the specific parameter of interest, or the statistical model for the target distribution. This theory paves the way for machine-learning debiased, semiparametric efficient estimation.

math.ST↗

arXiv2024

Investigating symptom duration using current status data: a case study of post-acute COVID-19 syndrome

For infectious diseases, characterizing symptom duration is of clinical and public health importance. Symptom duration may be assessed by surveying infected individuals and querying symptom status at the time of survey response. For example, in a SARS-CoV-2 testing program at the University of Washington, participants were surveyed at least $28$ days after testing positive and asked to report current symptom status. This study design yielded current status data: outcome measurements for each respondent consisted only of the time of survey response and a binary indicator of whether symptoms had resolved by that time. Such study design benefits from limited risk of recall bias, but analyzing the resulting data necessitates tailored statistical tools. Here, we review methods for current status data and describe a novel application of modern nonparametric techniques to this setting. The proposed approach is valid under weaker assumptions compared to existing methods, allows use of flexible machine learning tools, and handles potential survey nonresponse. From the university study, under an assumption that the survey response time is conditionally independent of symptom resolution time within strata of measured covariates, we estimate that 19% of participants experienced ongoing symptoms 30 days after testing positive, decreasing to 7% at 90 days. We assess the sensitivity of these results to deviations from conditional independence, finding the estimates to be more sensitive to assumption violations at 30 days compared to 90 days. Female sex, fatigue during acute infection, and higher viral load were associated with slower symptom resolution.

stat.AP↗

arXiv2024

Combining T-learning and DR-learning: a framework for oracle-efficient estimation of causal contrasts

We introduce efficient plug-in (EP) learning, a novel framework for the estimation of heterogeneous causal contrasts, such as the conditional average treatment effect and conditional relative risk. The EP-learning framework enjoys the same oracle efficiency as Neyman-orthogonal learning strategies, such as DR-learning and R-learning, while addressing some of their primary drawbacks: (i) their practical applicability can be hindered by non-convex loss functions; and (ii) they may suffer from poor performance and instability due to inverse probability weighting and pseudo-outcomes that violate bounds. To overcome these issues, the EP-learner leverages an efficient plug-in estimator of the population risk function for the causal contrast. In doing so, it inherits the stability of plug-in strategies such as T-learning, while improving on their efficiency. Under reasonable conditions, EP-learners based on empirical risk minimization are oracle-efficient, exhibiting asymptotic equivalence to the minimizer of an oracle-efficient one-step debiased estimator of the population risk function. In simulation experiments, we show that EP-learners of the conditional average treatment effect and conditional relative risk outperform state-of-the-art competitors, including the T-learner, R-learner, and DR-learner. Open-source implementations of the proposed methods are available in our \texttt{R} package \texttt{hte3}.

stat.ML↗

arXiv2023

Assessing variable importance in survival analysis using machine learning

Given a collection of features available for inclusion in a predictive model, it may be of interest to quantify the relative importance of a subset of features for the prediction task at hand. For example, in HIV vaccine trials, participant baseline characteristics are used to predict the probability of HIV acquisition over the intended follow-up period, and investigators may wish to understand how much certain types of predictors, such as behavioral factors, contribute toward overall predictiveness. Time-to-event outcomes such as time to HIV acquisition are often subject to right censoring, and existing methods for assessing variable importance are typically not intended to be used in this setting. We describe a broad class of algorithm-agnostic variable importance measures for prediction in the context of survival data. We propose a nonparametric efficient estimation procedure that incorporates flexible learning of nuisance parameters, yields asymptotically valid inference, and enjoys double-robustness. We assess the performance of our proposed procedure via numerical simulations and analyze data from the HVTN 702 vaccine trial to inform enrollment strategies for future HIV vaccine trials.

stat.ME↗

arXiv2023

Adaptive debiased machine learning using data-driven model selection techniques

Debiased machine learning estimators for smooth functionals in nonparametric models can exhibit substantial variability and instability, often leading practitioners to instead rely on parametric or semiparametric working models. Such models, however, may be misspecified and can therefore introduce bias. We study how data-driven model selection can be combined with debiased machine learning to construct estimators that adapt to structure in the data-generating distribution. To this end, we propose Adaptive Debiased Machine Learning (ADML), a nonparametric framework for constructing superefficient estimators of pathwise differentiable parameters. The framework unifies a broad class of previously proposed adaptive estimators, including methods based on variable selection, learned feature representations, and collaborative targeted learning. It requires only high-level conditions and approximate validity of the selection procedure, which are implied by lower-level conditions already assumed in important settings, including sieve-based selection, sparsity-based methods such as the Lasso, and data-adaptive feature representations. We show that ADML estimators yield regular and efficient root-$n$ inference for an oracle projection parameter induced by a data-adaptive oracle submodel. This oracle parameter coincides with the target parameter at the true distribution but typically has a smaller efficiency bound, thereby yielding superefficiency for the target parameter. As a practical illustration, we introduce a broad class of automatic ADML estimators for continuous linear functionals of the outcome regression, in which model selection is performed directly on the regression itself. Motivated by overlap challenges in causal inference, we develop new superefficient plug-in estimators for the average treatment effect based on calibration in semiparametric regression models.

stat.ME↗

arXiv2023

Causal isotonic calibration for heterogeneous treatment effects

We propose causal isotonic calibration, a novel nonparametric method for calibrating predictors of heterogeneous treatment effects. Furthermore, we introduce cross-calibration, a data-efficient variant of calibration that eliminates the need for hold-out calibration sets. Cross-calibration leverages cross-fitted predictors and generates a single calibrated predictor using all available data. Under weak conditions that do not assume monotonicity, we establish that both causal isotonic calibration and cross-calibration achieve fast doubly-robust calibration rates, as long as either the propensity score or outcome regression is estimated accurately in a suitable sense. The proposed causal isotonic calibrator can be wrapped around any black-box learning algorithm, providing robust and distribution-free calibration guarantees while preserving predictive performance.

stat.ML↗

arXiv2022

Individualized treatment rules under stochastic treatment cost constraints

Estimation and evaluation of individualized treatment rules have been studied extensively, but real-world treatment resource constraints have received limited attention in existing methods. We investigate a setting in which treatment is intervened upon based on covariates to optimize the mean counterfactual outcome under treatment cost constraints when the treatment cost is random. In a particularly interesting special case, an instrumental variable corresponding to encouragement to treatment is intervened upon with constraints on the proportion receiving treatment. For such settings, we first develop a method to estimate optimal individualized treatment rules. We further construct an asymptotically efficient plug-in estimator of the corresponding average treatment effect relative to a given reference rule.

stat.ME↗

arXiv2022

A framework for leveraging machine learning tools to estimate personalized survival curves

The conditional survival function of a time-to-event outcome subject to censoring and truncation is a common target of estimation in survival analysis. This parameter may be of scientific interest and also often appears as a nuisance in nonparametric and semiparametric problems. In addition to classical parametric and semiparametric methods (e.g., based on the Cox proportional hazards model), flexible machine learning approaches have been developed to estimate the conditional survival function. However, many of these methods are either implicitly or explicitly targeted toward risk stratification rather than overall survival function estimation. Others apply only to discrete-time settings or require inverse probability of censoring weights, which can be as difficult to estimate as the outcome survival function itself. Here, we employ a decomposition of the conditional survival function in terms of observable regression models in which censoring and truncation play no role. This allows application of an array of flexible regression and classification methods rather than only approaches that explicitly handle the complexities inherent to survival data. We outline estimation procedures based on this decomposition, empirically assess their performance, and demonstrate their use on data from an HIV vaccine trial.

stat.ME↗

arXiv2022

Can the potential benefit of individualizing treatment be assessed using trial summary statistics alone?

Individualizing treatment assignment can improve outcomes for diseases with patient-to-patient variability in comparative treatment effects. When a clinical trial demonstrates that some patients improve on treatment while others do not, it is tempting to assume that treatment effect heterogeneity exists. However, if variability in response is mainly driven by factors other than treatment, investigating the extent to which covariate data can predict differential treatment response is a potential waste of resources. Motivated by recent meta-analyses assessing the potential of individualizing treatment for major depressive disorder using only summary statistics, we provide a method that uses summary statistics widely available in published clinical trial results to bound the benefit of optimally assigning treatment to each patient. We also offer alternate bounds for settings in which trial results are stratified by another covariate. We demonstrate our approach using summary statistics from a depression treatment trial. Our methods are implemented in the rct2otrbounds R package, which is available at https://github.com/ngalanter/rct2otrbounds .

stat.ME↗

arXiv2022

A general adaptive framework for multivariate point null testing

As a common step in refining their scientific inquiry, investigators are often interested in performing some screening of a collection of given statistical hypotheses. For example, they may wish to determine whether any one of several patient characteristics are associated with a health outcome of interest. Existing generic methods for testing a multivariate hypothesis -- such as multiplicity corrections applied to individual hypothesis tests -- can easily be applied across a variety of problems but can suffer from low power in some settings. Tailor-made procedures can attain higher power by building around problem-specific information but typically cannot be easily adapted to novel settings. In this work, we propose a general framework for testing a multivariate point null hypothesis in which the test statistic is adaptively selected to provide increased power. We present theoretical large-sample guarantees for our test under both fixed and local alternatives. In simulation studies, we show that tests created using our framework can perform as well as tailor-made methods when the latter are available, and we illustrate how our procedure can be used to create tests in two settings in which tailor-made methods are not currently available.

stat.ME↗

arXiv2021

Assessment of Immune Correlates of Protection via Controlled Vaccine Efficacy and Controlled Risk

Immune correlates of protection (CoPs) are immunologic biomarkers accepted as a surrogate for an infectious disease clinical endpoint and thus can be used for traditional or provisional vaccine approval. To study CoPs in randomized, placebo-controlled trials, correlates of risk (CoRs) are first assessed in vaccine recipients. This analysis does not assess causation, as a CoR may fail to be a CoP. We propose a causal CoP analysis that estimates the controlled vaccine efficacy curve across biomarker levels $s$, $CVE(s)$, equal to one minus the ratio of the controlled-risk curve $r_C(s)$ at $s$ and placebo risk, where $r_C(s)$ is causal risk if all participants are assigned vaccine and the biomarker is set to $s$. The criterion for a useful CoP is wide variability of $CVE(s)$ in $s$. Moreover, estimation of $r_C(s)$ is of interest in itself, especially in studies without a placebo arm. For estimation of $r_C(s)$, measured confounders can be adjusted for by any regression method that accommodates missing biomarkers, to which we add sensitivity analysis to quantify robustness of CoP evidence to unmeasured confounding. Application to two harmonized phase 3 trials supports that 50% neutralizing antibody titer has value as a controlled vaccine efficacy CoP for virologically confirmed dengue (VCD): in CYD14 the point estimate (95% confidence interval) for $CVE(s)$ accounting for measured confounders and building in conservative margin for unmeasured confounding increases from 29.6% (95% CI 3.5 to 45.9) at titer 1:36 to 78.5% (95% CI 67.9 to 86.8) at titer 1:1200; these estimates are 17.4% (95% CI -14.4 to 36.5) and 84.5% (95% CI 79.6 to 89.1) for CYD15.

stat.ME↗

arXiv2021

Inference for treatment-specific survival curves using machine learning

In the absence of data from a randomized trial, researchers often aim to use observational data to draw causal inference about the effect of a treatment on a time-to-event outcome. In this context, interest often focuses on the treatment-specific survival curves; that is, the survival curves were the entire population under study to be assigned to receive the treatment or not. Under certain causal conditions, including that all confounders of the treatment-outcome relationship are observed, the treatment-specific survival can be identified with a covariate-adjusted survival function. Several estimators of this function have been proposed, including estimators based on outcome regression, inverse probability weighting, and doubly robust estimators. In this article, we propose a new cross-fitted doubly-robust estimator that incorporates data-adaptive (e.g. machine learning) estimators of the conditional survival functions. We establish conditions on the nuisance estimators under which our estimator is consistent and asymptotically linear, both pointwise and uniformly in time. We also propose a novel ensemble learner for combining multiple candidate estimators of the conditional survival estimators. Notably, our methods and results accommodate events occurring in discrete or continuous time (or both). We investigate the practical performance of our methods using numerical studies and an application to the effect of a surgical treatment to prevent metastases of parotid carcinoma on mortality.

stat.ME↗

arXiv2021

Inference on function-valued parameters using a restricted score test

It is often of interest to make inference on an unknown function that is a local parameter of the data-generating mechanism, such as a density or regression function. Such estimands can typically only be estimated at a slower-than-parametric rate in nonparametric and semiparametric models, and performing calibrated inference can be challenging. In many cases, these estimands can be expressed as the minimizer of a population risk functional. Here, we propose a general framework that leverages such representation and provides a nonparametric extension of the score test for inference on an infinite-dimensional risk minimizer. We demonstrate that our framework is applicable in a wide variety of problems. As both analytic and computational examples, we describe how to use our general approach for inference on a mean regression function under (i) nonparametric and (ii) partially additive models, and evaluate the operating characteristics of the resulting procedures via simulations.

stat.ME↗