arXiv subjects

Peter B. Gilbert

Publications and source records attributed to Peter B. Gilbert.

33 records · Page 2Linked to original sources

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.

stat.ME↗

arXiv2023

Efficient nonparametric estimation of the covariate-adjusted threshold-response function, a support-restricted stochastic intervention

Identifying a biomarker or treatment-dose threshold that marks a specified level of risk is an important problem, especially in clinical trials. This risk, viewed as a function of thresholds and possibly adjusted for covariates, we call the threshold-response function. Extending the work of Donovan, Hudgens and Gilbert (2019), we propose a nonparametric efficient estimator for the covariate-adjusted threshold-response function, which utilizes machine learning and Targeted Minimum-Loss Estimation (TMLE). We additionally propose a more general estimator, based on sequential regression, that also applies when there is outcome missingness. We show that the threshold-response for a given threshold may be viewed as the expected outcome under a stochastic intervention where all participants are given a treatment dose above the threshold. We prove the estimator is efficient and characterize its asymptotic distribution. A method to construct simultaneous 95% confidence bands for the threshold-response function and its inverse is given. Furthermore, we discuss how to adjust our estimator when the treatment or biomarker is missing-at-random, as is the case in clinical trials with biased sampling designs, using inverse-probability-weighting. The methods are assessed in a diverse set of simulation settings with rare outcomes and cumulative case-control sampling. The methods are employed to estimate neutralizing antibody thresholds for virologically confirmed dengue risk in the CYD14 and CYD15 dengue vaccine trials.

stat.ME↗

arXiv2022

Estimation and Hypothesis Testing of Strain-Specific Vaccine Efficacy with Missing Strain Types, with Applications to a COVID-19 Vaccine Trial

Statistical methods are developed for analysis of clinical and virus genetics data from phase 3 randomized, placebo-controlled trials of vaccines against novel coronavirus COVID-19. Vaccine efficacy (VE) of a vaccine to prevent COVID-19 caused by one of finitely many genetic strains of SARS-CoV-2 may vary by strain. The problem of assessing differential VE by viral genetics can be formulated under a competing risks model where the endpoint is virologically confirmed COVID-19 and the cause-of-failure is the infecting SARS-CoV-2 genotype. Strain-specific VE is defined as one minus the cause-specific hazard ratio (vaccine/placebo). For the COVID-19 VE trials, the time to COVID-19 is right-censored, and a substantial percentage of failure cases are missing the infecting virus genotype. We develop estimation and hypothesis testing procedures for strain-specific VE when the failure time is subject to right censoring and the cause-of-failure is subject to missingness, focusing on $J \ge 2$ discrete categorical unordered or ordered virus genotypes. The stratified Cox proportional hazards model is used to relate the cause-specific outcomes to explanatory variables. The inverse probability weighted complete-case (IPW) estimator and the augmented inverse probability weighted complete-case (AIPW) estimator are investigated. Hypothesis tests are developed to assess whether the vaccine provides at least a specified level of efficacy against some viral genotypes and whether VE varies across genotypes, adjusting for covariates. The finite-sample properties of the proposed tests are studied through simulations and are shown to have good performances. In preparation for the real data analyses, the developed methods are applied to a pseudo dataset mimicking the Moderna COVE trial.

stat.ME↗

arXiv2021

A general framework for inference on algorithm-agnostic variable importance

In many applications, it is of interest to assess the relative contribution of features (or subsets of features) toward the goal of predicting a response -- in other words, to gauge the variable importance of features. Most recent work on variable importance assessment has focused on describing the importance of features within the confines of a given prediction algorithm. However, such assessment does not necessarily characterize the prediction potential of features, and may provide a misleading reflection of the intrinsic value of these features. To address this limitation, we propose a general framework for nonparametric inference on interpretable algorithm-agnostic variable importance. We define variable importance as a population-level contrast between the oracle predictiveness of all available features versus all features except those under consideration. We propose a nonparametric efficient estimation procedure that allows the construction of valid confidence intervals, even when machine learning techniques are used. We also outline a valid strategy for testing the null importance hypothesis. Through simulations, we show that our proposal has good operating characteristics, and we illustrate its use with data from a study of an antibody against HIV-1 infection.

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↗

arXiv2020

Efficient nonparametric inference on the effects of stochastic interventions under two-phase sampling, with applications to vaccine efficacy trials

The advent and subsequent widespread availability of preventive vaccines has altered the course of public health over the past century. Despite this success, effective vaccines to prevent many high-burden diseases, including HIV, have been slow to develop. Vaccine development can be aided by the identification of immune response markers that serve as effective surrogates for clinically significant infection or disease endpoints. However, measuring immune response marker activity is often costly, which has motivated the usage of two-phase sampling for immune response evaluation in clinical trials of preventive vaccines. In such trials, the measurement of immunological markers is performed on a subset of trial participants, where enrollment in this second phase is potentially contingent on the observed study outcome and other participant-level information. We propose nonparametric methodology for efficiently estimating a counterfactual parameter that quantifies the impact of a given immune response marker on the subsequent probability of infection. Along the way, we fill in theoretical gaps pertaining to the asymptotic behavior of nonparametric efficient estimators in the context of two-phase sampling, including a multiple robustness property enjoyed by our estimators. Techniques for constructing confidence intervals and hypothesis tests are presented, and an open source software implementation of the methodology, the txshift R package, is introduced. We illustrate the proposed techniques using data from a recent preventive HIV vaccine efficacy trial.

stat.ME↗

arXiv2019

Ongoing Vaccine and Monoclonal Antibody HIV Prevention Efficacy Trials and Considerations for Sequel Efficacy Trial Designs

Four randomized placebo-controlled efficacy trials of a candidate vaccine or passively infused monoclonal antibody for prevention of HIV-1 infection are underway (HVTN 702 in South African men and women; HVTN 705 in sub-Saharan African women; HVTN 703/HPTN 081 in sub-Saharan African women; HVTN 704/HPTN 085 in U.S., Peruvian, Brazilian, and Swiss men or transgender persons who have sex with men). Several challenges are posed to the optimal design of the sequel efficacy trials, including: (1) how to account for the evolving mosaic of effective prevention interventions that may be part of the trial design or standard of prevention; (2) how to define viable and optimal sequel trial designs depending on the primary efficacy results and secondary 'correlates of protection' results of each of the ongoing trials; and (3) how to define the primary objective of sequel efficacy trials if HIV-1 incidence is expected to be very low in all study arms such that a standard trial design has a steep opportunity cost. After summarizing the ongoing trials, I discuss statistical science considerations for sequel efficacy trial designs, both generally and specifically to each trial listed above. One conclusion is that the results of 'correlates of protection' analyses, which ascertain how different host immunological markers and HIV-1 viral features impact HIV-1 risk and prevention efficacy, have an important influence on sequel trial design. This influence is especially relevant for the monoclonal antibody trials because of the focused pre-trial hypothesis that potency and coverage of serum neutralization constitutes a surrogate endpoint for HIV-1 infection... (see manuscript for the full abstract)

stat.AP↗

arXiv2018

Post-randomization Biomarker Effect Modification in an HIV Vaccine Clinical Trial

While the HVTN 505 trial showed no overall efficacy of the tested vaccine to prevent HIV infection over placebo, previous studies, biological theories, and the finding that immune response markers strongly correlated with infection in vaccine recipients generated the hypothesis that a qualitative interaction occurred. This hypothesis can be assessed with statistical methods for studying treatment effect modification by an intermediate response variable (i.e., principal stratification effect modification (PSEM) methods). However, available PSEM methods make untestable structural risk assumptions, such that assumption-lean versions of PSEM methods are needed in order to surpass the high bar of evidence to demonstrate a qualitative interaction. Fortunately, the survivor average causal effect (SACE) literature is replete with assumption-lean methods that can be readily adapted to the PSEM application for the special case of a binary intermediate response variable. We map this adaptation, opening up a host of new PSEM methods for a binary intermediate variable measured via two-phase sampling, for a dichotomous or failure time final outcome and including or excluding the SACE monotonicity assumption. The new methods support that the vaccine partially protected vaccine recipients with a high polyfunctional CD8+ T cell response, an important new insight for the HIV vaccine field.

stat.AP↗

arXiv2018

Generating survival times using Cox proportional hazards models with cyclic time-varying covariates, with application to a multiple-dose monoclonal antibody clinical trial

In two harmonized efficacy studies to prevent HIV infection through multiple infusions of the monoclonal antibody VRC01, a key objective is to evaluate whether the serum concentration of VRC01, which changes cyclically over time along with the infusion schedule, is associated with the rate of HIV infection. Simulation studies are needed in the development of such survival models. In this paper, we consider simulating event time data with a continuous time-varying covariate whose values vary with time through multiple drug administration cycles, and whose effect on survival changes differently before and after a threshold within each cycle. The latter accommodates settings with a zero-protection biomarker threshold above which the drug provides a varying level of protection depending on the biomarker level, but below which the drug provides no protection. We propose two simulation approaches: one based on simulating survival data under a single-dose regimen first before data are aggregated over multiple doses, and another based on simulating survival data directly under a multiple-dose regimen. We generate time-to-event data following a Cox proportional hazards model based on inverting the cumulative hazard function and a log link function for relating the hazard function to the covariates. The method's validity is assessed in two sets of simulation experiments. The results indicate that the proposed procedures perform well in producing data that conform to their cyclic nature and assumptions of the Cox proportional hazards model.

stat.ME↗

arXiv2018

Pharmacokinetics Simulations for Studying Correlates of Prevention Efficacy of Passive HIV-1 Antibody Prophylaxis in the Antibody Mediated Prevention (AMP) Study

A key objective in two phase 2b AMP clinical trials of VRC01 is to evaluate whether drug concentration over time, as estimated by non-linear mixed effects pharmacokinetics (PK) models, is associated with HIV infection rate. We conducted a simulation study of marker sampling designs, and evaluated the effect of study adherence and sub-cohort sample size on PK model estimates in multiple-dose studies. With m=120, even under low adherence (about half of study visits missing per participant), reasonably unbiased and consistent estimates of most fixed and random effect terms were obtained. Coarsened marker sampling schedules were also studied.

q-bio.QM↗

arXiv2017

Evaluation of Treatment Effect Modification by Biomarkers Measured Pre- and Post-randomization in the Presence of Non-monotone Missingness

In vaccine studies, investigators are often interested in studying effect modifiers of clinical treatment efficacy by biomarker-based principal strata, which is useful for selecting biomarker study endpoints for evaluating treatments in new trials, exploring biological mechanisms of clinical treatment efficacy, and studying mediators of clinical treatment efficacy. However, in trials where participants may enter the study with prior exposure therefore with variable baseline biomarker values, clinical treatment efficacy may depend jointly on a biomarker measured at baseline and measured at a fixed time after vaccination. Therefore, it is of interest to conduct a bivariate effect modification analysis by biomarker-based principal strata and baseline biomarker values. Previous methods allow this assessment if participants who have the biomarker measured at the the fixed time point post randomization would also have the biomarker measured at baseline. However, additional complications in study design could happen in practice. For example, in the Dengue correlates study, baseline biomarker values were only available from a fraction of participants who have biomarkers measured post-randomization. How to conduct the bivariate effect modification analysis in these studies remains an open research question. In this article, we propose an estimated likelihood method to utilize the sub-sampled baseline biomarker in the effect modification analysis and illustrate our method with datasets from two dengue phase 3 vaccine efficacy trials.

stat.ME↗

arXiv2017

Partial Bridging of Vaccine Efficacy to New Populations

Suppose one has data from one or more completed vaccine efficacy trials and wishes to estimate the efficacy in a new setting. Often logistical or ethical considerations make running another efficacy trial impossible. Fortunately, if there is a biomarker that is the primary modifier of efficacy, then the biomarker-conditional efficacy may be identical in the completed trials and the new setting, or at least informative enough to meaningfully bound this quantity. Given a sample of this biomarker from the new population, we might hope we can bridge the results of the completed trials to estimate the vaccine efficacy in this new population. Unfortunately, even knowing the true conditional efficacy in the new population fails to identify the marginal efficacy due to the unknown conditional unvaccinated risk. We define a curve that partially identifies (lower bounds) the marginal efficacy in the new population as a function of the population's marginal unvaccinated risk, under the assumption that one can identify bounds on the conditional unvaccinated risk in the new population. Interpreting the curve only requires identifying plausible regions of the marginal unvaccinated risk in the new population. We present a nonparametric estimator of this curve and develop valid lower confidence bounds that concentrate at a parametric rate. We use vaccine terminology throughout, but the results apply to general binary interventions and bounded outcomes.

stat.ME↗

arXiv2015

Nonparametric Bounds and Sensitivity Analysis of Treatment Effects

This paper considers conducting inference about the effect of a treatment (or exposure) on an outcome of interest. In the ideal setting where treatment is assigned randomly, under certain assumptions the treatment effect is identifiable from the observable data and inference is straightforward. However, in other settings such as observational studies or randomized trials with noncompliance, the treatment effect is no longer identifiable without relying on untestable assumptions. Nonetheless, the observable data often do provide some information about the effect of treatment, that is, the parameter of interest is partially identifiable. Two approaches are often employed in this setting: (i) bounds are derived for the treatment effect under minimal assumptions, or (ii) additional untestable assumptions are invoked that render the treatment effect identifiable and then sensitivity analysis is conducted to assess how inference about the treatment effect changes as the untestable assumptions are varied. Approaches (i) and (ii) are considered in various settings, including assessing principal strata effects, direct and indirect effects and effects of time-varying exposures. Methods for drawing formal inference about partially identified parameters are also discussed.

stat.ME↗

arXiv2009

Proportional hazards models with continuous marks

For time-to-event data with finitely many competing risks, the proportional hazards model has been a popular tool for relating the cause-specific outcomes to covariates [Prentice et al. Biometrics 34 (1978) 541--554]. This article studies an extension of this approach to allow a continuum of competing risks, in which the cause of failure is replaced by a continuous mark only observed at the failure time. We develop inference for the proportional hazards model in which the regression parameters depend nonparametrically on the mark and the baseline hazard depends nonparametrically on both time and mark. This work is motivated by the need to assess HIV vaccine efficacy, while taking into account the genetic divergence of infecting HIV viruses in trial participants from the HIV strain that is contained in the vaccine, and adjusting for covariate effects. Mark-specific vaccine efficacy is expressed in terms of one of the regression functions in the mark-specific proportional hazards model. The new approach is evaluated in simulations and applied to the first HIV vaccine efficacy trial.

math.ST↗

arXiv2008

Assessing surrogate endpoints in vaccine trials with case-cohort sampling and the Cox model

Assessing immune responses to study vaccines as surrogates of protection plays a central role in vaccine clinical trials. Motivated by three ongoing or pending HIV vaccine efficacy trials, we consider such surrogate endpoint assessment in a randomized placebo-controlled trial with case-cohort sampling of immune responses and a time to event endpoint. Based on the principal surrogate definition under the principal stratification framework proposed by Frangakis and Rubin [Biometrics 58 (2002) 21--29] and adapted by Gilbert and Hudgens (2006), we introduce estimands that measure the value of an immune response as a surrogate of protection in the context of the Cox proportional hazards model. The estimands are not identified because the immune response to vaccine is not measured in placebo recipients. We formulate the problem as a Cox model with missing covariates, and employ novel trial designs for predicting the missing immune responses and thereby identifying the estimands. The first design utilizes information from baseline predictors of the immune response, and bridges their relationship in the vaccine recipients to the placebo recipients. The second design provides a validation set for the unmeasured immune responses of uninfected placebo recipients by immunizing them with the study vaccine after trial closeout. A maximum estimated likelihood approach is proposed for estimation of the parameters. Simulated data examples are given to evaluate the proposed designs and study their properties.

stat.AP↗