arXiv subjects

Peter B. Gilbert

Publications and source records attributed to Peter B. Gilbert.

At least 19 recordsLinked to original sources

arXiv2026

Estimating the Wasserstein barycenter of one-dimensional distributions under sparse sampling

We study distributional data under sparse sampling where each unit is represented by a probability distribution on the real line observed only through a small i.i.d.~sample. A natural notion of central tendency for one-dimensional distributional data is the Wasserstein barycenter, whose quantile function is the pointwise average of the unit-level quantile functions. We focus on pointwise estimation of the Wasserstein barycenter quantile function: at a given quantile level, the target is the population mean of the corresponding unit-level quantiles. A naive plug-in estimator is the empirical Wasserstein barycenter, which treats observed unit-level empirical distributions as the true latent unit-level distributions. Under sparse sampling, however, this estimator can be severely biased. We propose an approach that avoids directly estimating either the unit-level distributions or the full population law of distributions. We start with the more ambitious goal of characterizing the distribution of latent unit-level quantiles at a given quantile level. We show that this distribution can be written in terms of the marginal distributions of the unit-level CDF values, which can be estimated using binomial mixture methods. This motivates our estimator, the marginal-constructed barycenter (MCB) estimator, obtained by taking the mean of the estimated distribution of latent unit-level quantiles. We establish conditions under which the MCB estimator is pointwise consistent and asymptotically normal, and show through simulations that it can substantially outperform the empirical Wasserstein barycenter under sparse sampling. We illustrate the method in an analysis of HIV-1 sequence data from the HVTN 502/503 vaccine efficacy trials, using the barycenter to summarize and compare within-participant distributions of viral sequence features when only a small number of sequences are available per participant.

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arXiv2026

Targeted maximum likelihood estimation of vaccine effectiveness and immune correlates in test-negative design studies with missing data

The test-negative design (TND) is a resource-efficient observational study design that can assess vaccine effectiveness and exposure-proximal immune correlates of disease. The TND enrolls symptomatic individuals seeking diagnostic testing and compares case status by an exposure variable, such as vaccination status or immune marker level, that is measured at testing. While the TND reduces confounding by healthcare-seeking behavior, other sources of confounding may remain. TND studies may also have missing data in the exposure variable due to incomplete records or two-phase sampling designs. We present a targeted maximum likelihood estimation approach involving a semiparametric logistic regression model that targets a causal conditional risk ratio of symptomatic disease in the healthcare-seeking population. Under causal and missing at random assumptions, our method produces an efficient, asymptotically linear estimator that provides flexible, data-driven confounding control and valid causal inference when analyzing TND studies with missing exposure variable data. We evaluate our method's finite sample properties using plasmode simulations of a two-phase TND immune correlates study. We also apply our method to assess COVID-19 vaccine effectiveness and antibody marker correlates of COVID-19 from TND study cohorts derived from the Moderna Coronavirus Efficacy phase 3 trial.

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arXiv2026

Efficient estimation of cumulative incidence curves via data fusion with surrogates: application to integrated analysis of vaccine trial and immunobridging data

Refined vaccine regimens containing variant-matched inserts are often authorized based on historical phase 3 efficacy trials together with immunobridging studies. Phase 3 trials are essential for establishing immune biomarkers that reliably predict disease risk or vaccine efficacy against clinical endpoints. Once such immune correlates are identified, updated vaccine regimens can be approved through immunobridging designs that compare the immunogenicity of the updated regimen to that of an already-approved vaccine. We develop methods of inference for the counterfactual cumulative incidence curve using participant-level data from both a historical vaccine efficacy trial and an immunobridging study. We further extend these methods to pathogens with multiple serotypes -- such as dengue virus and influenza -- by estimating cause-specific cumulative incidence curves. We describe the identification assumptions, propose efficient and multiply robust estimators, and assess their finite-sample performance through simulation studies. We then apply the proposed methods to (1) estimating the hypothetical cumulative incidence curve for a bivalent mRNA booster and (2) testing a key assumption of no controlled direct effects, using data from the COVID-19 Variant Immunologic Landscape (COVAIL) Trial, a multistage randomized clinical study evaluating the safety and immunogenicity of a second COVID-19 booster dose.

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arXiv2026

Identifying and Estimating Causal Direct Effects Under Unmeasured Confounding

Causal mediation analysis provides techniques for defining and estimating effects that may be endowed with mechanistic interpretations. With many scientific investigations seeking to address mechanistic questions, causal direct and indirect effects have garnered much attention. The natural direct and indirect effects, the most widely used among such causal mediation estimands, are limited in their practical utility due to stringent identification requirements. Accordingly, considerable effort has been invested in developing alternative direct and indirect effect decompositions with relaxed identification requirements. Such efforts often yield effect definitions with nuanced and challenging interpretations. By contrast, relatively limited attention has been paid to relaxing the identification assumptions of the natural direct and indirect effects. Motivated by a secondary aim of a recent non-randomized vaccine prospective cohort study (NCT05168813), we present a set of relaxed conditions under which the natural direct effect is identifiable in spite of unobserved baseline confounding of the exposure-mediator pathway; we use this result to investigate the effect mediated by putative immune correlates of protection. Relaxing the commonly used but restrictive cross-world counterfactual independence assumption, we discuss strategies for evaluating the natural direct effect in non-randomized settings that arise in the analysis of vaccine studies. We revisit prior studies of semi-parametric efficiency theory to demonstrate the construction of flexible, multiply robust estimators of the natural direct effect and discuss efficient estimation strategies that do not place restrictive modeling assumptions on nuisance functions.

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arXiv2025

Proximal Causal Inference for Modified Treatment Policies

The proximal causal inference framework enables the identification and estimation of causal effects in the presence of unmeasured confounding by leveraging two disjoint sets of observed strong proxies: negative control treatments and negative control outcomes. In the point exposure setting, this framework has primarily been applied to estimands comparing counterfactual outcomes under a static fixed intervention or, possibly randomized, regime that depends on baseline covariates. For continuous exposures, alternative hypothetical scenarios can enrich our understanding of causal effects, such as those where each individual receives their observed treatment dose modified in a pre-specified manner - commonly referred to as modified treatment regimes. In this work, we extend the proximal causal inference framework to identify and estimate the mean outcome under a modified treatment regime, addressing this gap in the literature. We propose a flexible strategy that does not rely on the assumption that all confounders have been measured - unlike existing estimators - and leverages modern debiased machine learning techniques using non-parametric estimators of nuisance functions to avoid restrictive parametric assumptions. Our methodology was motivated by immunobridging studies of COVID-19 vaccines aimed at identifying correlates of protection, where the individual's underlying immune capacity is an important unmeasured confounder. We demonstrate its applicability using data from such a study and evaluate its finite-sample performance through simulation studies.

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arXiv2025

Vaccine sieve analysis on deep sequencing data using competing risks Cox regression with failure type subject to misclassification

Understanding how vaccines perform against different pathogen genotypes is crucial for developing effective prevention strategies, particularly for highly genetically diverse pathogens like HIV. Sieve analysis is a statistical framework used to determine whether a vaccine selectively prevents acquisition of certain genotypes while allowing breakthrough of other genotypes that evade immune responses. Traditionally, these analyses are conducted with a single sequence available per individual acquiring the pathogen. However, modern sequencing technology can provide detailed characterization of intra-individual viral diversity by capturing up to hundreds of pathogen sequences per person. In this work, we introduce methodology that extends sieve analysis to account for intra-individual viral diversity. Our approach estimates vaccine efficacy against viral populations with varying true (unobservable) frequencies of vaccine-mismatched mutations. To account for differential resolution of information from differing sequence counts per person, we use competing risks Cox regression with modeled causes of failure and propose an empirical Bayes approach for the classification model. Simulation studies demonstrate that our approach reduces bias, provides nominal confidence interval coverage, and improves statistical power compared to conventional methods. We apply our method to the HVTN 705 Imbokodo trial, which assessed the efficacy of a heterologous vaccine regimen in preventing HIV-1 acquisition.

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arXiv2025

Debiasing hazard-based, time-varying vaccine effects using vaccine-irrelevant infections: An observational extension of a pivotal Phase 3 COVID-19 vaccine efficacy trial

Understanding how vaccine effectiveness (VE) changes over time can provide evidence-based guidance for public health decision making. While commonly reported by practitioners, time-varying VE estimates obtained using Cox regression are vul- nerable to hidden biases. To address these limitations, we describe how to leverage vaccine-irrelevant infections to identify hazard-based, time-varying VE in the pres- ence of unmeasured confounding and selection bias. We articulate assumptions under which our approach identifies a causal effect of an intervention deferring vaccination and interaction with the community in which infections circulate. We develop sieve and efficient influence curve-based estimators and discuss imposing monotone shape constraints and estimating VE against multiple variants. As a case study, we examine the observational booster phase of the Coronavirus Vaccine Efficacy (COVE) trial of the Moderna mRNA-1273 COVID-19 vaccine which used symptom-triggered multi- plex PCR testing to identify acute respiratory illnesses (ARIs) caused by SARS-CoV-2 and 20 off-target pathogens previously identified as compelling negative controls for COVID-19. Accounting for vaccine-irrelevant ARIs supported that the mRNA-1273 booster was more effective and durable against Omicron COVID-19 than suggested by Cox regression. Our work offers an approach to mitigate bias in hazard-based, time- varying treatment effects in randomized and non-randomized studies using negative controls.

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arXiv2025

Inference on Variable Importance for Treatment Effect Heterogeneity: Shapley Values and Beyond

We provide an inferential framework to assess variable importance for heterogeneous treatment effects. This assessment is especially useful in high-risk domains such as medicine, where decision makers hesitate to rely on black-box treatment recommendation algorithms. The variable importance measures we consider are local in that they may differ across individuals, while the inference is global in that it tests whether a given variable is important for any individual. Our approach builds on recent developments in semiparametric theory for function-valued parameters, and is valid even when statistical machine learning algorithms are employed to quantify treatment effect heterogeneity. We demonstrate the applicability of our method to infectious disease prevention strategies.

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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.

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arXiv2025

Evaluation of Surrogate Endpoints Based on Meta-Analysis with Surrogate Indices

The meta-analytic (MA) framework is the gold standard for evaluating putative surrogate endpoints but it is not well-suited for complex surrogates. We address this limitation by considering real-valued summaries of complex surrogates as alternative, univariate putative surrogates. We focus on the surrogate index as a specific summary measure with desirable properties. We first formalize the data-generating mechanism underlying the MA framework, making explicit the assumptions required for valid inferences in any evaluation of trial-level surrogacy. These assumptions are often left implicit in the MA framework. Building on this formalization, we show that, under certain conditions, the surrogate index maximizes the trial-level surrogacy among all real-valued summaries. When the surrogate index is estimated, we show that valid inference about the trial-level surrogacy of this estimated surrogate index is possible. The proposed approach can be implemented using standard software and is illustrated using COVID-19 vaccine efficacy trials, where antibody markers are evaluated as candidate surrogate endpoints.

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arXiv2025

Targeted Data Fusion for Region-Specific Survival Effects in the AMP HIV Prevention Trials

The Antibody Mediated Prevention (AMP) trials opened a new scientific frontier by showing that passively administered monoclonal broadly neutralizing antibodies (bnAbs) could prevent HIV-1 acquisition. Conducted across multiple geographic regions, including the United States, Brazil, Peru, Switzerland, and sub-Saharan Africa, the AMP trials revealed substantial regional heterogeneity in treatment efficacy. These differences, together with privacy and regulatory limits on central data pooling, call for methods that borrow strength across regions without sharing individual-level data. To estimate region- and treatment-specific survival curves under distributional heterogeneity, we develop a federated learning approach that combines site-specific estimators via an L1-regularized criterion that downweights data sources not aligned with the target. We further extend the framework to a general class of causal contrasts, including the risk difference (RD), survival ratio (SR), and restricted mean survival time (RMST) difference. Through extensive simulations and an analysis of the AMP trials under different target populations, we show that the proposed approach provides privacy-preserving, region-adaptive inference with improved precision.

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arXiv2024

On the Role of Surrogates in Conformal Inference of Individual Causal Effects

Learning the Individual Treatment Effect (ITE) is essential for personalized decision-making, yet causal inference has traditionally focused on aggregated treatment effects. While integrating conformal prediction with causal inference can provide valid uncertainty quantification for ITEs, the resulting prediction intervals are often excessively wide, limiting their practical utility. To address this limitation, we introduce \underline{S}urrogate-assisted \underline{C}onformal \underline{I}nference for \underline{E}fficient I\underline{N}dividual \underline{C}ausal \underline{E}ffects (SCIENCE), a framework designed to construct more efficient prediction intervals for ITEs. SCIENCE accommodates the covariate shifts between source data and target data and applies to various data configurations, including semi-supervised and surrogate-assisted semi-supervised learning. Leveraging semi-parametric efficiency theory, SCIENCE produces rate double-robust prediction intervals under mild rate convergence conditions, permitting the use of flexible non-parametric models to estimate nuisance functions. We quantify efficiency gains by comparing semi-parametric efficiency bounds with and without the surrogates. Simulation studies demonstrate that our surrogate-assisted intervals offer substantial efficiency improvements over existing methods while maintaining valid group-conditional coverage. Applied to the phase 3 Moderna COVE COVID-19 vaccine trial, SCIENCE illustrates how multiple surrogate markers can be leveraged to generate more efficient prediction intervals.

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arXiv2024

A class of nonparametric methods for evaluating the effect of continuous treatments on survival outcomes

In randomized trials and observational studies, it is often necessary to evaluate the extent to which an intervention affects a time-to-event outcome, which is only partially observed due to right censoring. For instance, in infectious disease studies, it is frequently of interest to characterize the relationship between risk of acquisition of infection with a pathogen and a biomarker previously measuring for an immune response against that pathogen induced by prior infection and/or vaccination. It is common to conduct inference within a causal framework, wherein we desire to make inferences about the counterfactual probability of survival through a given time point, at any given exposure level. To determine whether a causal effect is present, one can assess if this quantity differs by exposure level. Recent work shows that, under typical causal assumptions, summaries of the counterfactual survival distribution are identifiable. Moreover, when the treatment is multi-level, these summaries are also pathwise differentiable in a nonparametric probability model, making it possible to construct estimators thereof that are unbiased and approximately normal. In cases where the treatment is continuous, the target estimand is no longer pathwise differentiable, rendering it difficult to construct well-behaved estimators without strong parametric assumptions. In this work, we extend beyond the traditional setting with multilevel interventions to develop approaches to nonparametric inference with a continuous exposure. We introduce methods for testing whether the counterfactual probability of survival time by a given time-point remains constant across the range of the continuous exposure levels. The performance of our proposed methods is evaluated via numerical studies, and we apply our method to data from a recent pair of efficacy trials of an HIV monoclonal antibody.

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arXiv2024

Addressing Confounding and Continuous Exposure Measurement Error Using Corrected Score Functions

Confounding and exposure measurement error can introduce bias when drawing inference about the marginal effect of an exposure on an outcome of interest. While there are broad methodologies for addressing each source of bias individually, confounding and exposure measurement error frequently co-occur, and there is a need for methods that address them simultaneously. In this paper, corrected score methods are derived under classical additive measurement error to draw inference about marginal exposure effects using only measured variables. Three estimators are proposed based on g-formula, inverse probability weighting, and doubly-robust estimation techniques. The estimators are shown to be consistent and asymptotically normal, and the doubly-robust estimator is shown to exhibit its namesake property. The methods, which are implemented in the R package mismex, perform well in finite samples under both confounding and measurement error as demonstrated by simulation studies. The proposed doubly-robust estimator is applied to study the effects of two biomarkers on HIV-1 infection using data from the HVTN 505 preventative vaccine trial.

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arXiv2024

A Surrogate Endpoint Based Provisional Approval Causal Roadmap

For many rare diseases with no approved preventive interventions, promising interventions exist, yet it has been difficult to conduct a pivotal phase 3 trial that could provide direct evidence demonstrating a beneficial effect on the target disease outcome. When a promising putative surrogate endpoint(s) for the target outcome is available, surrogate-based provisional approval of an intervention may be pursued. We apply the Causal Roadmap rubric to define a surrogate endpoint based provisional approval causal roadmap, which combines observational study data that estimates the relationship between the putative surrogate and the target outcome, with a phase 3 surrogate endpoint study that collects the same data but is very under-powered to assess the treatment effect (TE) on the target outcome. The objective is conservative estimation/inference for the TE with an estimated lower uncertainty bound that allows (through two bias functions) for an imperfect surrogate and imperfect transport of the conditional target outcome risk in the untreated between the observational and phase 3 studies. Two estimators of TE (plug-in, nonparametric efficient one-step) with corresponding inference procedures are developed. Finite-sample performance of the plug-in estimator is evaluated in two simulation studies, with R code provided. The roadmap is illustrated with contemporary Group B Streptococcus vaccine development.

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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.

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arXiv2023

Data fusion using weakly aligned sources

We introduce a new data fusion method that utilizes multiple data sources to estimate a smooth, finite-dimensional parameter. Most existing methods only make use of fully aligned data sources that share common conditional distributions of one or more variables of interest. However, in many settings, the scarcity of fully aligned sources can make existing methods require unduly large sample sizes to be useful. Our approach enables the incorporation of weakly aligned data sources that are not perfectly aligned, provided their degree of misalignment is known up to finite-dimensional parameters. {We quantify the additional efficiency gains achieved through the integration of these weakly aligned sources. We characterize the semiparametric efficiency bound and provide a general means to construct estimators achieving these efficiency gains.} We illustrate our results by fusing data from two harmonized HIV monoclonal antibody prevention efficacy trials to study how a neutralizing antibody biomarker associates with HIV genotype.

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arXiv2023

Semiparametric logistic regression for inference on relative vaccine efficacy in case-only studies with informative missingness

We develop semiparametric methods for estimating subgroup-specific relative vaccine efficacy against multiple viral strains in a partially vaccinated population. Focusing on observational case-only studies, we address informative missingness in strain type due to vaccination status, pre-vaccination characteristics, and post-infection factors such as viral load. We establish general conditions for the nonparametric identification of relative conditional vaccine efficacy between strains using covariate-adjusted conditional odds ratio parameters. Assuming a log-linear parametric form for strain-specific conditional vaccine efficacy, we propose targeted maximum likelihood estimators based on partially linear logistic regression, leveraging machine learning for flexible confounding adjustment. Finally, we apply our methods to estimate relative strain-specific conditional vaccine efficacy in the ENSEMBLE COVID-19 vaccine trial.

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