Inferences on relative failure rates in stratified mark-specific proportional hazards models with missing marks, with application to HIV vaccine efficacy trials

Fitting Multilevel Vector Autoregressive Models in Stan, JAGS, and Mplus

The influx of intensive longitudinal data creates a pressing need for complex modeling tools that help enrich our understanding of how individuals change over time. Multilevel vector autoregressive (mlVAR) models allow for simultaneous evaluations of reciprocal linkages between dynamic processes and individual differences, and have gained increased recognition in recent years. High-dimensional and other complex variations of mlVAR models, though often computationally intractable in the frequentist framework, can be readily handled using Markov chain Monte Carlo techniques in a Bayesian framework. However, researchers in social science fields may be unfamiliar with ways to capitalize on recent developments in Bayesian software programs. In this paper, we provide step-by-step illustrations and comparisons of options to fit Bayesian mlVAR models using Stan, JAGS and Mplus, supplemented with a Monte Carlo simulation study. An empirical example is used to demonstrate the utility of mlVAR models in studying intra- and inter-individual variations in affective dynamics.

Variable selection for a mark-specific additive hazards model using the adaptive LASSO

In HIV vaccine efficacy trials, mark-specific hazards models have important applications and can be used to evaluate the strain-specific vaccine efficacy. Additive hazards models have been widely used in practice, especially when continuous covariates are present. In this article, we conduct variable selection for a mark-specific additive hazards model. The proposed method is based on an estimating equation with the first derivative of the adaptive LASSO penalty function. The asymptotic properties of the resulting estimators are established. The finite sample behavior of the proposed estimators is evaluated through simulation studies, and an application to a dataset from the first HIV vaccine efficacy trial is provided.

Two Randomized Trials of Neutralizing Antibodies to Prevent HIV-1 Acquisition

BACKGROUND

Whether a broadly neutralizing antibody (bnAb) can be used to prevent human immunodeficiency virus type 1 (HIV-1) acquisition is unclear.

METHODS

We enrolled at-risk cisgender men and transgender persons in the Americas and Europe in the HVTN 704/HPTN 085 trial and at-risk women in sub-Saharan Africa in the HVTN 703/HPTN 081 trial. Participants were randomly assigned to receive, every 8 weeks, infusions of a bnAb (VRC01) at a dose of either 10 or 30 mg per kilogram (low-dose group and high-dose group, respectively) or placebo, for 10 infusions in total. HIV-1 testing was performed every 4 weeks. The VRC01 80% inhibitory concentration (IC80) of acquired isolates was measured with the TZM-bl assay.

RESULTS

Adverse events were similar in number and severity among the treatment groups within each trial. Among the 2699 participants in HVTN 704/HPTN 085, HIV-1 infection occurred in 32 in the low-dose group, 28 in the high-dose group, and 38 in the placebo group. Among the 1924 participants in HVTN 703/HPTN 081, infection occurred in 28 in the low-dose group, 19 in the high-dose group, and 29 in the placebo group. The incidence of HIV-1 infection per 100 person-years in HVTN 704/HPTN 085 was 2.35 in the pooled VRC01 groups and 2.98 in the placebo group (estimated prevention efficacy, 26.6%; 95% confidence interval [CI], -11.7 to 51.8; P = 0.15), and the incidence per 100 person-years in HVTN 703/HPTN 081 was 2.49 in the pooled VRC01 groups and 3.10 in the placebo group (estimated prevention efficacy, 8.8%; 95% CI, -45.1 to 42.6; P = 0.70). In prespecified analyses pooling data across the trials, the incidence of infection with VRC01-sensitive isolates (IC80 <1 μg per milliliter) per 100 person-years was 0.20 among VRC01 recipients and 0.86 among placebo recipients (estimated prevention efficacy, 75.4%; 95% CI, 45.5 to 88.9). The prevention efficacy against sensitive isolates was similar for each VRC01 dose and trial; VRC01 did not prevent acquisition of other HIV-1 isolates.

CONCLUSIONS

VRC01 did not prevent overall HIV-1 acquisition more effectively than placebo, but analyses of VRC01-sensitive HIV-1 isolates provided proof-of-concept that bnAb prophylaxis can be effective. (Supported by the National Institute of Allergy and Infectious Diseases; HVTN 704/HPTN 085 and HVTN 703/HPTN 081 ClinicalTrials.gov numbers, NCT02716675 and NCT02568215.).

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 the time-varying Cox model for the cause-specific hazard functions with missing causes

This paper studies the Cox model with time-varying coefficients for cause-specific hazard functions when the causes of failure are subject to missingness. Inverse probability weighted and augmented inverse probability weighted estimators are investigated. The latter is considered as a two-stage estimator by directly utilizing the inverse probability weighted estimator and through modeling available auxiliary variables to improve efficiency. The asymptotic properties of the two estimators are investigated. Hypothesis testing procedures are developed to test the null hypotheses that the covariate effects are zero and that the covariate effects are constant. We conduct simulation studies to examine the finite sample properties of the proposed estimation and hypothesis testing procedures under various settings of the auxiliary variables and the percentages of the failure causes that are missing. These simulation results demonstrate that the augmented inverse probability weighted estimators are more efficient than the inverse probability weighted estimators and that the proposed testing procedures have the expected satisfactory results in sizes and powers. The proposed methods are illustrated using the Mashi clinical trial data for investigating the effect of randomization to formula-feeding versus breastfeeding plus extended infant zidovudine prophylaxis on death due to mother-to-child HIV transmission in Botswana.

Combining Viral Genetics and Statistical Modeling to Improve HIV-1 Time-of-infection Estimation towards Enhanced Vaccine Efficacy Assessment

Knowledge of the time of HIV-1 infection and the multiplicity of viruses that establish HIV-1 infection is crucial for the in-depth analysis of clinical prevention efficacy trial outcomes. Better estimation methods would improve the ability to characterize immunological and genetic sequence correlates of efficacy within preventive efficacy trials of HIV-1 vaccines and monoclonal antibodies. We developed new methods for infection timing and multiplicity estimation using maximum likelihood estimators that shift and scale (calibrate) estimates by fitting true infection times and founder virus multiplicities to a linear regression model with independent variables defined by data on HIV-1 sequences, viral load, diagnostics, and sequence alignment statistics. Using Poisson models of measured mutation counts and phylogenetic trees, we analyzed longitudinal HIV-1 sequence data together with diagnostic and viral load data from the RV217 and CAPRISA 002 acute HIV-1 infection cohort studies. We used leave-one-out cross validation to evaluate the prediction error of these calibrated estimators versus that of existing estimators and found that both infection time and founder multiplicity can be estimated with improved accuracy and precision by calibration. Calibration considerably improved all estimators of time since HIV-1 infection, in terms of reducing bias to near zero and reducing root mean squared error (RMSE) to 5-10 days for sequences collected 1-2 months after infection. The calibration of multiplicity assessments yielded strong improvements with accurate predictions (ROC-AUC above 0.85) in all cases. These results have not yet been validated on external data, and the best-fitting models are likely to be less robust than simpler models to variation in sequencing conditions. For all evaluated models, these results demonstrate the value of calibration for improved estimation of founder multiplicity and of time since HIV-1 infection.

Prediction of VRC01 neutralization sensitivity by HIV-1 gp160 sequence features

The broadly neutralizing antibody (bnAb) VRC01 is being evaluated for its efficacy to prevent HIV-1 infection in the Antibody Mediated Prevention (AMP) trials. A secondary objective of AMP utilizes sieve analysis to investigate how VRC01 prevention efficacy (PE) varies with HIV-1 envelope (Env) amino acid (AA) sequence features. An exhaustive analysis that tests how PE depends on every AA feature with sufficient variation would have low statistical power. To design an adequately powered primary sieve analysis for AMP, we modeled VRC01 neutralization as a function of Env AA sequence features of 611 HIV-1 gp160 pseudoviruses from the CATNAP database, with objectives: (1) to develop models that best predict the neutralization readouts; and (2) to rank AA features by their predictive importance with classification and regression methods. The dataset was split in half, and machine learning algorithms were applied to each half, each analyzed separately using cross-validation and hold-out validation. We selected Super Learner, a nonparametric ensemble-based cross-validated learning method, for advancement to the primary sieve analysis. This method predicted the dichotomous resistance outcome of whether the IC50 neutralization titer of VRC01 for a given Env pseudovirus is right-censored (indicating resistance) with an average validated AUC of 0.868 across the two hold-out datasets. Quantitative log IC50 was predicted with an average validated R2 of 0.355. Features predicting neutralization sensitivity or resistance included 26 surface-accessible residues in the VRC01 and CD4 binding footprints, the length of gp120, the length of Env, the number of cysteines in gp120, the number of cysteines in Env, and 4 potential N-linked glycosylation sites; the top features will be advanced to the primary sieve analysis. This modeling framework may also inform the study of VRC01 in the treatment of HIV-infected persons.

Estimation of a Semiparametric Varying-Coefficient Mixed Regressive Spatial Autoregressive Model

A semiparametric varying-coefficient mixed regressive spatial autoregressive model is used to study covariate effects on spatially dependent responses, where the effects of some covariates are allowed to vary with other variables. A semiparametric series-based least squares estimating procedure is proposed with the introduction of instrumental variables and series approximations of the conditional expectations. The estimators for both the nonparametric and parametric components of the model are shown to be consistent and their asymptotic distributions are derived. The proposed estimators perform well in simulations. The proposed method is applied to analyze a data set on teen pregnancy to investigate effects of neighborhood as well as other social and economic factors on the teen pregnancy rate.

Sieve analysis of breakthrough HIV-1 sequences in HVTN 505 identifies vaccine pressure targeting the CD4 binding site of Env-gp120

Although the HVTN 505 DNA/recombinant adenovirus type 5 vector HIV-1 vaccine trial showed no overall efficacy, analysis of breakthrough HIV-1 sequences in participants can help determine whether vaccine-induced immune responses impacted viruses that caused infection. We analyzed 480 HIV-1 genomes sampled from 27 vaccine and 20 placebo recipients and found that intra-host HIV-1 diversity was significantly lower in vaccine recipients (P ≤ 0.04, Q-values ≤ 0.09) in Gag, Pol, Vif and envelope glycoprotein gp120 (Env-gp120). Furthermore, Env-gp120 sequences from vaccine recipients were significantly more distant from the subtype B vaccine insert than sequences from placebo recipients (P = 0.01, Q-value = 0.12). These vaccine effects were associated with signatures mapping to CD4 binding site and CD4-induced monoclonal antibody footprints. These results suggest either (i) no vaccine efficacy to block acquisition of any viral genotype but vaccine-accelerated Env evolution post-acquisition; or (ii) vaccine efficacy against HIV-1s with Env sequences closest to the vaccine insert combined with increased acquisition due to other factors, potentially including the vaccine vector.

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

An objective of preventive HIV vaccine efficacy trials is to understand how vaccine-induced immune responses to specific protein sequences of HIV-1 associate with subsequent infection with specific sequences of HIV, where the immune response biomarkers are measured in vaccine recipients via a two-phase sampling design. Motivated by this objective, we investigate the stratified mark-specific proportional hazards model under two-phase biomarker sampling, where the mark is the genetic distance of an infecting HIV-1 sequence to an HIV-1 sequence represented inside the vaccine. Estimation and inference procedures based on inverse probability weighting of complete-cases and on augmented inverse probability weighting of complete-cases are developed. Asymptotic properties of the estimators are derived and their finite-sample performances are examined in simulation studies. The methods are shown to have satisfactory performance, and are applied to the RV144 vaccine trial to assess whether immune response correlates of HIV-1 infection are stronger for HIV-1 infecting sequences similar to the vaccine than for sequences distant from the vaccine. Augmented inverse probability weighting; auxiliary variables; case-cohort design; censored failure time; competing risks; HIV vaccine efficacy trial.

Mark-specific additive hazards regression with continuous marks

For survival data, mark variables are only observed at uncensored failure times, and it is of interest to investigate whether there is any relationship between the failure time and the mark variable. The additive hazards model, focusing on hazard differences rather than hazard ratios, has been widely used in practice. In this article, we propose a mark-specific additive hazards model in which both the regression coefficient functions and the baseline hazard function depend nonparametrically on a continuous mark. An estimating equation approach is developed to estimate the regression functions, and the asymptotic properties of the resulting estimators are established. In addition, some formal hypothesis tests are constructed for various hypotheses concerning the mark-specific treatment effects. The finite sample behavior of the proposed estimators is evaluated through simulation studies, and an application to a data set from the first HIV vaccine efficacy trial is provided.

Predicting Overall Vaccine Efficacy in a New Setting by Re-Calibrating Baseline Covariate and Intermediate Response Endpoint Effect Modifiers of Type-Specific Vaccine Efficacy

We develop a transport formula for predicting overall cumulative vaccine efficacy through time t (VE(t)) to prevent clinically significant infection with a genetically diverse pathogen (e.g., HIV infection) in a new setting for which a Phase III preventive vaccine efficacy trial that would directly estimate VE(t) has not yet been conducted. The formula integrates data from (1) a previous Phase III trial, (2) a Phase I/II immune response biomarker endpoint trial in the new setting where a follow-up Phase III trial is planned, (3) epidemiological data on background HIV infection incidence in the new setting; and (4) genomic epidemiological data on HIV sequence distributions in the previous and new settings. For (1), the randomized vaccine versus placebo Phase III trial yields estimates of vaccine efficacy to prevent particular genotypes of HIV in participant subgroups defined by baseline covariates X and immune responses to vaccination S(1) measured at a fixed time point τ (potential outcomes if assigned vaccine); often one or more immune responses to vaccination are available that modify genotype-specific vaccine efficacy. The formula focuses on subgroups defined by X and S(1) and being at-risk for HIV infection at τ under both the vaccine and placebo treatment assignments. For (2), the Phase I/II trial tests the same vaccine in a new setting, or a refined new vaccine in the same or new setting, and measures the same baseline covariates and immune responses as the original Phase III trial. For (3), epidemiological data in the new setting are used to project overall background HIV infection rates in the baseline covariate subgroups in the planned Phase III trial, hence re-calibrating for HIV incidence differences in the two settings; whereas for (4), data bases of HIV sequences measured from HIV infected individuals are used to re-calibrate for differences in the distributions of the circulating HIV genotypes in the two settings. The transport formula incorporates a user-specified bridging assumption function that measures differences in HIV genotype-specific conditional biological-susceptibility vaccine efficacies in the two settings, facilitating a sensitivity analysis. We illustrate the transport formula with application to HIV Vaccine Trials Network (HVTN) research. One application of the transport formula is to use predicted VE(t) as a rational criterion for ranking a set of candidate vaccines being studied in Phase I/II trials for their priority for down-selection into the follow-up Phase III trial.

Goodness-of-fit test of the stratified mark-specific proportional hazards model with continuous mark

Motivated by the need to assess HIV vaccine efficacy, previous studies proposed an extension of the discrete competing risks proportional hazards model, in which the cause of failure is replaced by a continuous mark only observed at the failure time. However the model assumptions may fail in several ways, and no diagnostic testing procedure for this situation has been proposed. A goodness-of-fit test procedure for the stratified mark-specific proportional hazards model in which the regression parameters depend nonparametrically on the mark and the baseline hazards depends nonparametrically on both time and the mark is proposed. The test statistics are constructed based on the weighted cumulative mark-specific martingale residuals. The critical values of the proposed test statistics are approximated using the Gaussian multiplier method. The performance of the proposed tests are examined extensively in simulations for a variety of the models under the null hypothesis and under different types of alternative models. An analysis of the 'Step' HIV vaccine efficacy trial using the proposed method is presented. The analysis suggests that the HIV vaccine candidate may increase susceptibility to HIV acquisition.

Comprehensive sieve analysis of breakthrough HIV-1 sequences in the RV144 vaccine efficacy trial

The RV144 clinical trial showed the partial efficacy of a vaccine regimen with an estimated vaccine efficacy (VE) of 31% for protecting low-risk Thai volunteers against acquisition of HIV-1. The impact of vaccine-induced immune responses can be investigated through sieve analysis of HIV-1 breakthrough infections (infected vaccine and placebo recipients). A V1/V2-targeted comparison of the genomes of HIV-1 breakthrough viruses identified two V2 amino acid sites that differed between the vaccine and placebo groups. Here we extended the V1/V2 analysis to the entire HIV-1 genome using an array of methods based on individual sites, k-mers and genes/proteins. We identified 56 amino acid sites or "signatures" and 119 k-mers that differed between the vaccine and placebo groups. Of those, 19 sites and 38 k-mers were located in the regions comprising the RV144 vaccine (Env-gp120, Gag, and Pro). The nine signature sites in Env-gp120 were significantly enriched for known antibody-associated sites (p = 0.0021). In particular, site 317 in the third variable loop (V3) overlapped with a hotspot of antibody recognition, and sites 369 and 424 were linked to CD4 binding site neutralization. The identified signature sites significantly covaried with other sites across the genome (mean = 32.1) more than did non-signature sites (mean = 0.9) (p < 0.0001), suggesting functional and/or structural relevance of the signature sites. Since signature sites were not preferentially restricted to the vaccine immunogens and because most of the associations were insignificant following correction for multiple testing, we predict that few of the genetic differences are strongly linked to the RV144 vaccine-induced immune pressure. In addition to presenting results of the first complete-genome analysis of the breakthrough infections in the RV144 trial, this work describes a set of statistical methods and tools applicable to analysis of breakthrough infection genomes in general vaccine efficacy trials for diverse pathogens.