Estimation of Stratified Mark-Specific Proportional Hazards Models under Two-Phase Sampling with Application to HIV Vaccine Efficacy Trials

Estimation and Hypothesis Testing of Strain-Specific Vaccine Efficacy With Missing Strain Types With Application to a COVID-19 Vaccine Trial

Based on data from a randomized, controlled vaccine efficacy trial, this article develops statistical methods for assessing vaccine efficacy (VE) to prevent COVID-19 infections by a discrete set of genetic strains of SARS-CoV-2. Strain-specific VE adjusting for possibly time-varying covariates is estimated using augmented inverse probability weighting to address missing viral genotypes under a competing risks model that allows separate baseline hazards for different risk groups. Hypothesis tests are developed to assess whether the vaccine provides at least a specified level of VE against some viral genotypes and whether VE varies across genotypes. Asymptotic properties providing analytic inferences are derived and finite-sample properties of the estimators and hypothesis tests are studied through simulations. This research is motivated by the fact that previous analyses of COVID-19 vaccine efficacy did not account for missing genotypes, which can cause severe bias and efficiency loss. The theoretical properties and simulations demonstrate superior performance of the new methods. Application to the Moderna COVE trial identifies several SARS-CoV-2 genotype features with differential vaccine efficacy across genotypes, including lineage (Reference, Epsilon, Gamma, Zeta), indicators of residue match vs. mismatch to the vaccine-strain residue at Spike amino acid positions (identifying signatures of differential VE), and a weighted Hamming distance to the vaccine strain. The results show VE decreases against genotypes more distant from the vaccine strain, highlighting the need to update COVID-19 vaccine strains.

Semiparametric additive time-varying coefficients model for longitudinal data with censored time origin

Statistical analysis of longitudinal data often involves modeling treatment effects on clinically relevant longitudinal biomarkers since an initial event (the time origin). In some studies including preventive HIV vaccine efficacy trials, some participants have biomarkers measured starting at the time origin, whereas others have biomarkers measured starting later with the time origin unknown. The semiparametric additive time-varying coefficient model is investigated where the effects of some covariates vary nonparametrically with time while the effects of others remain constant. Weighted profile least squares estimators coupled with kernel smoothing are developed. The method uses the expectation maximization approach to deal with the censored time origin. The Kaplan-Meier estimator and other failure time regression models such as the Cox model can be utilized to estimate the distribution and the conditional distribution of left censored event time related to the censored time origin. Asymptotic properties of the parametric and nonparametric estimators and consistent asymptotic variance estimators are derived. A two-stage estimation procedure for choosing weight is proposed to improve estimation efficiency. Numerical simulations are conducted to examine finite sample properties of the proposed estimators. The simulation results show that the theory and methods work well. The efficiency gain of the two-stage estimation procedure depends on the distribution of the longitudinal error processes. The method is applied to analyze data from the Merck 023/HVTN 502 Step HIV vaccine study.

Estimation of conditional cumulative incidence functions under generalized semiparametric regression models with missing covariates, with application to analysis of biomarker correlates in vaccine trials

This article studies generalized semiparametric regression models for conditional cumulative incidence functions with competing risks data when covariates are missing by sampling design or happenstance. A doubly-robust augmented inverse probability weighted complete-case (AIPW) approach to estimation and inference is investigated. This approach modifies IPW complete-case estimating equations by exploiting the key features in the relationship between the missing covariates and the phase-one data to improve efficiency. An iterative numerical procedure is derived to solve the nonlinear estimating equations. The asymptotic properties of the proposed estimators are established. A simulation study examining the finite-sample performances of the proposed estimators shows that the AIPW estimators are more efficient than the IPW estimators. The developed method is applied to the RV144 HIV-1 vaccine efficacy trial to investigate vaccine-induced IgG binding antibodies to HIV-1 as correlates of acquisition of HIV-1 infection while taking account of whether the HIV-1 sequences are near or far from the HIV-1 sequences represented in the vaccine construct.

Neutralizing antibody correlates of sequence specific dengue disease in a tetravalent dengue vaccine efficacy trial in Asia

In the CYD14 trial of the CYD-TDV dengue vaccine in 2-14 year-olds, neutralizing antibody (nAb) titers to the vaccine-insert dengue strains correlated inversely with symptomatic, virologically-confirmed dengue (VCD). Also, vaccine efficacy against VCD was higher against dengue prM/E amino acid sequences closer to the vaccine inserts. We integrated the nAb and sequence data types by assessing nAb titers as a correlate of sequence-specific VCD separately in the vaccine arm and in the placebo arm. In both vaccine and placebo recipients the correlation of nAb titer with sequence-specific VCD was stronger for dengue nAb contact site sequences closer to the vaccine (p = 0.005 and p = 0.012, respectively). The risk of VCD in vaccine (placebo) recipients was 6.7- (1.80)-fold lower at the 90th vs 10th percentile of nAb for viruses perfectly matched to CYD-TDV, compared to 2.1- (0.78)-fold lower at the 90th vs 10th percentile for viruses with five amino acid mismatches. The evidence for a stronger sequence-distance dependent correlate of risk for the vaccine arm indicates departure from the Prentice criteria for a valid sequence-distance specific surrogate endpoint and suggests that the nAb marker may affect dengue risk differently depending on whether nAbs arise from infection or also by vaccination. However, when restricting to baseline-seropositive 9-14 year-olds, the correlation pattern became more similar between the vaccine and placebo arms, supporting nAb titers as an approximate surrogate endpoint in this population. No sequence-specific nAb titer correlates of VCD were seen in baseline-seronegative participants. Integrated immune response/pathogen sequence data correlates analyses could help increase knowledge of correlates of risk and surrogate endpoints for other vaccines against genetically diverse pathogens. Trial registration: EU Clinical Trials Register 2014-001708-24; registration date 2014-05-26.

A Hybrid Approach for the Stratified Mark-Specific Proportional Hazards Model with Missing Covariates and Missing Marks, with Application to Vaccine Efficacy Trials

Deployment of the recently licensed CYD-TDV dengue vaccine requires understanding of how the risk of dengue disease in vaccine recipients depends jointly on a host biomarker measured after vaccination (neutralization titer - NAb) and on a "mark" feature of the dengue disease failure event (the amino acid sequence distance of the dengue virus to the dengue sequence represented in the vaccine). The CYD14 phase 3 trial of CYD-TDV measured NAb via case-cohort sampling and the mark in dengue disease failure events, with about a third missing marks. We addressed the question of interest by developing inferential procedures for the stratified mark-specific proportional hazards model with missing covariates and missing marks. Two hybrid approaches are investigated that leverage both augmented inverse probability weighting and nearest neighborhood hot deck multiple imputation. The two approaches differ in how the imputed marks are pooled in estimation. Our investigation shows that NNHD imputation can lead to biased estimation without properly selected neighborhood. Simulations show that the developed hybrid methods perform well with unbiased NNHD imputations from proper neighborhood selection. The new methods applied to CYD14 show that NAb is strongly inversely associated with risk of dengue disease in vaccine recipients, more strongly against dengue viruses with shorter distances.

Analysis of Generalized Semiparametric Regression Models for Cumulative Incidence Functions with Missing Covariates

The cumulative incidence function quantifies the probability of failure over time due to a specific cause for competing risks data. The generalized semiparametric regression models for the cumulative incidence functions with missing covariates are investigated. The effects of some covariates are modeled as non-parametric functions of time while others are modeled as parametric functions of time. Different link functions can be selected to add flexibility in modeling the cumulative incidence functions. The estimation procedures based on the direct binomial regression and the inverse probability weighting of complete cases are developed. This approach modifies the full data weighted least squares equations by weighting the contributions of observed members through the inverses of estimated sampling probabilities which depend on the censoring status and the event types among other subject characteristics. The asymptotic properties of the proposed estimators are established. The finite-sample performances of the proposed estimators and their relative efficiencies under different two-phase sampling designs are examined in simulations. The methods are applied to analyze data from the RV144 vaccine efficacy trial to investigate the associations of immune response biomarkers with the cumulative incidence of HIV-1 infection.

Hypothesis tests for stratified mark-specific proportional hazards models with missing covariates, with application to HIV vaccine efficacy trials

This article develops hypothesis testing procedures for the stratified mark-specific proportional hazards model with missing covariates where the baseline functions may vary with strata. The mark-specific proportional hazards model has been studied to evaluate mark-specific relative risks where the mark is the genetic distance of an infecting HIV sequence to an HIV sequence represented inside the vaccine. This research is motivated by analyzing the RV144 phase 3 HIV vaccine efficacy trial, to understand associations of immune response biomarkers on the mark-specific hazard of HIV infection, where the biomarkers are sampled via a two-phase sampling nested case-control design. We test whether the mark-specific relative risks are unity and how they change with the mark. The developed procedures enable assessment of whether risk of HIV infection with HIV variants close or far from the vaccine sequence are modified by immune responses induced by the HIV vaccine; this question is interesting because vaccine protection occurs through immune responses directed at specific HIV sequences. The test statistics are constructed based on augmented inverse probability weighted complete-case estimators. The asymptotic properties and finite-sample performances of the testing procedures are investigated, demonstrating double-robustness and effectiveness of the predictive auxiliaries to recover efficiency. The finite-sample performance of the proposed tests are examined through a comprehensive simulation study. The methods are applied to the RV144 trial.

Complex immune correlates of protection in HIV-1 vaccine efficacy trials

Development of an efficacious HIV-1 vaccine is a major priority for improving human health worldwide. Vaccine-mediated protection against human pathogens can be achieved through elicitation of protective innate, humoral, and cellular responses. Identification of specific immune responses responsible for pathogen protection enables vaccine development and provides insights into host defenses against pathogens and the immunological mechanisms that most effectively fight infection. Defining immunological correlates of transmission risk in preclinical and clinical HIV-1 vaccine trials has moved the HIV-1 vaccine development field forward and directed new candidate vaccine development. Immune correlate studies are providing novel hypotheses about immunological mechanisms that may be responsible for preventing HIV-1 acquisition. Recent results from HIV-1 immune correlates work has demonstrated that there are multiple types of immune responses that together, comprise an immune correlate-thus implicating polyfunctional immune control of HIV-1 transmission. An in depth understanding of these complex immunological mechanisms of protection against HIV-1 will accelerate the development of an efficacious HIV-1 vaccine.