arXiv subjects

Michael P. Fay

Publications and source records attributed to Michael P. Fay.

5 recordsLinked to original sources

arXiv2026

Comparing Two Survival Functions at a Fixed Timepoint

For comparing two survival curves at a fixed timepoint with right censoring, a standard method uses asymptotic methods on two Kaplan-Meier estimators with Greenwood variance estimators and transformations using the delta method. Confidence intervals on associated estimands can either breakdown or undercover due to Kaplan-Meier estimates of zero or one, small sample sizes, or heavy censoring. Although others have proposed adjustments to the Greenwood variance for a single sample, these adjustments have not been incorporated into the two-sample application of the delta method and we do that here as well as provide modifications when Kaplan-Meier estimates are zero or one. An alternative non-asymptotic existing method called melding on the beta product confidence procedure (BPCP) appears to have at least nominal coverage regardless of the sample size. Without censoring the problem reduces to comparing two independent binomials and melding on the BPCP gives p-values equivalent to Fisher's exact test p-values and further gives compatible confidence intervals for treatment comparison estimands; however, the melding can be very conservative. In this paper, we expand the melding on the BPCP intervals to include mid-p versions, which are designed to achieve coverage closer to nominal without guaranteeing coverage for all cases. We study these existing methods and our minor modifications of them primarily by numerical methods or simulation. Results suggest only the melding on the BPCP can guarantee coverage in all studied scenarios, and the mid-p version most often has closest to nominal coverage. We provide R functions in the bpcp R package.

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arXiv2026

Vaccine Efficacy Estimands Implied by Common Estimators Used in Individual Randomized Field Trials

We review vaccine efficacy (VE) estimands for susceptibility in individual randomized trials with natural (unmeasured) exposure, where individual responses are measured as time from vaccination until an event (e.g., disease from the infectious agent). Common VE estimands are written as $1-\theta$, where $\theta$ is some ratio effect measure (e.g., ratio of incidence rates, cumulative incidences, hazards, or odds) comparing outcomes under vaccination versus control. Although the ratio effects are approximately equal with low control event rates, we explore the quality of that approximation using a nonparametric formulation. Traditionally, the primary endpoint VE estimands are full immunization (or biological) estimands that represent a subset of the intent-to-treat population, excluding those that have the event before the vaccine has been able to ramp-up to its full effect, requiring care for proper causal interpretation. Besides these primary VE estimands that summarize an effect of the vaccine over the full course of the study, we also consider local VE estimands that measure the effect at particular time points. We discuss interpretational difficulties of local VE estimands (e.g., depletion of susceptibles bias), and using frailty models as sensitivity analyses for the individual-level causal effects over time.

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arXiv2023

Mediation Analyses for the Effect of Antibodies in Vaccination

We review standard mediation assumptions as they apply to identifying antibody effects in a randomized vaccine trial and propose new study designs to allow identification of an estimand that was previously unidentifiable. For these mediation analyses, we partition the total ratio effect (one minus the vaccine effect) from a randomized vaccine trial into indirect (effects through antibodies) and direct effects (other effects). Identifying $λ$, the proportion of the total effect due to an indirect effect, depends on a cross-world quantity, the potential outcome among vaccinated individuals with antibody levels as if given placebo, or vice versa. We review assumptions for identifying $λ$ and show that there are two versions of $λ$, unless the effect of adding antibodies to the placebo arm is equal in magnitude to the effect of subtracting antibodies from the vaccine arm. We focus on the case when individuals in the placebo arm are unlikely to have the needed antibodies. In that case, if a standard assumption (given confounders, potential mediators and potential outcomes are independent) is true, only one version of $λ$ is identifiable, and if not neither is identifiable. We propose alternatives for identifying the other version of $λ$, using experimental design to identify a formerly cross-world quantity. Two alternative experimental designs use a three arm trial with the extra arm being passive immunization (administering monoclonal antibodies), with or without closeout vaccination. Another alternative is to combine information from a placebo-controlled vaccine trial with a placebo-controlled passive immunization trial.

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arXiv2021

Practical Valid Inferences for the Two-Sample Binomial Problem

Our interest is whether two binomial parameters differ, which parameter is larger, and by how much. This apparently simple problem was addressed by Fisher in the 1930's, and has been the subject of many review papers since then. Yet there continues to be new work on this issue and no consensus solution. Previous reviews have focused primarily on testing and the properties of validity and power, or primarily on confidence intervals, their coverage, and expected length. Here we evaluate both. For example, we consider whether a p-value and its matching confidence interval are compatible, meaning that the p-value rejects at level $α$ if and only if the $1-α$ confidence interval excludes all null parameter values. For focus, we only examine non-asymptotic inferences, so that most of the p-values and confidence intervals are valid (i.e., exact) by construction. Within this focus, we review different methods emphasizing many of the properties and interpretational aspects we desire from applied frequentist inference: validity, accuracy, good power, equivariance, compatibility, coherence, and parameterization and direction of effect. We show that no one method can meet all the desirable properties and give recommendations based on which properties are given more importance.

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arXiv2018

Valid and Approximately Valid Confidence Intervals for Current Status Data

We introduce a new framework for creating point-wise confidence intervals for the distribution of event times for current status data. Existing methods are based on asymptotics. Our framework is based on binomial properties and motivates confidence intervals that are very simple to apply and are valid, i.e., guarantee nominal coverage. Although these confidence intervals are necessarily conservative for small sample sizes, asymptotically their coverage rate approaches the nominal one. This binomial framework also motivates approximately valid confidence intervals, and simulations show that these approximate intervals generally have coverage rates closer to the nominal level with shorter length than existing intervals, including the likelihood ratio-based confidence interval. Unlike previous asymptotic methods that require different asymptotic distributions for continuous or grid-based assessment, the binomial framework can be applied to either type of assessment distribution.

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