An objective of randomized placebo-controlled preventive HIV vaccine efficacy trials is to assess the relationship between the vaccine effect to prevent infection and the genetic distance of the exposing HIV to the HIV strain represented in the vaccine construct. Motivated by this objective, recently a mark-specific proportional hazards model with a continuum of competing risks has been studied, where the genetic distance of the transmitting strain is the continuous `mark' defined and observable only in failures. A high percentage of genetic marks of interest may be missing for a variety of reasons, predominantly due to rapid evolution of HIV sequences after transmission before a blood sample is drawn from which HIV sequences are measured. This research investigates the stratified mark-specific proportional hazards model with missing marks where the baseline functions may vary with strata. We develop two consistent estimation approaches, the first based on the inverse probability weighted complete-case (IPW) technique, and the second based on augmenting the IPW estimator by incorporating auxiliary information predictive of the mark. We investigate the asymptotic properties and finite-sample performance of the two estimators, and show that the augmented IPW estimator, which satisfies a double robustness property, is more efficient.
Augmented inverse probability weighted complete-case estimator; auxiliary marks; competing risks; double robustness; failure time data; genetic data; HIV vaccine trial; mark-specific vaccine efficacy; missing at random; semiparametric model
The HIV Vaccine Trials Network (HVTN) is an international collaboration of scientists and educators facilitating the development of HIV/AIDS preventive vaccines. The HVTN conducts all phases of clinical trials, from evaluating experimental vaccines for safety and immunogenicity, to testing vaccine efficacy. Over the past decade, the HVTN has aimed to improve the process of designing, implementing and analyzing vaccine trials. Several major achievements include streamlining protocol development while maintaining input from diverse stakeholders, establishing a laboratory program with standardized assays and systems allowing for reliable immunogenicity assessments across trials, setting statistical standards for the field and actively engaging with site communities. These achievements have allowed the HVTN to conduct over 50 clinical trials and make numerous scientific contributions to the field.
clinical trial network; HIV; HIV Vaccine Trials Network; vaccine
Five preventative HIV vaccine efficacy trials have been conducted over the last 12 years, all of which evaluated vaccine efficacy (VE) to prevent HIV infection for a single vaccine regimen versus placebo. Now that one of these trials has supported partial VE of a prime-boost vaccine regimen, there is interest in conducting efficacy trials that simultaneously evaluate multiple prime-boost vaccine regimens against a shared placebo group in the same geographic region, for accelerating the pace of vaccine development. This article proposes such a design, which has main objectives (1) to evaluate VE of each regimen versus placebo against HIV exposures occurring near the time of the immunizations; (2) to evaluate durability of VE for each vaccine regimen showing reliable evidence for positive VE; (3) to expeditiously evaluate the immune correlates of protection if any vaccine regimen shows reliable evidence for positive VE; and (4) to compare VE among the vaccine regimens. The design uses sequential monitoring for the events of vaccine harm, non-efficacy, and high efficacy, selected to weed out poor vaccines as rapidly as possible while guarding against prematurely weeding out a vaccine that does not confer efficacy until most of the immunizations are received. The evaluation of the design shows that testing multiple vaccine regimens is important for providing a well-powered assessment of the correlation of vaccine-induced immune responses with HIV infection, and is critically important for providing a reasonably powered assessment of the value of identified correlates as surrogate endpoints for HIV infection.
HIV vaccine efficacy clinical trial; immune correlate of protection; one-way crossover design; surrogate endpoint for HIV infection; two-phase sampling
In the RV144 trial, the estimated efficacy of a vaccine regimen against human immunodeficiency virus type 1 (HIV-1) was 31.2%. We performed a case–control analysis to identify antibody and cellular immune correlates of infection risk.
In pilot studies conducted with RV144 blood samples, 17 antibody or cellular assays met prespecified criteria, of which 6 were chosen for primary analysis to determine the roles of T-cell, IgG antibody, and IgA antibody responses in the modulation of infection risk. Assays were performed on samples from 41 vaccinees who became infected and 205 uninfected vaccinees, obtained 2 weeks after final immunization, to evaluate whether immune-response variables predicted HIV-1 infection through 42 months of follow-up.
Of six primary variables, two correlated significantly with infection risk: the binding of IgG antibodies to variable regions 1 and 2 (V1V2) of HIV-1 envelope proteins (Env) correlated inversely with the rate of HIV-1 infection (estimated odds ratio, 0.57 per 1-SD increase; P = 0.02; q = 0.08), and the binding of plasma IgA antibodies to Env correlated directly with the rate of infection (estimated odds ratio, 1.54 per 1-SD increase; P = 0.03; q = 0.08). Neither low levels of V1V2 antibodies nor high levels of Env-specific IgA antibodies were associated with higher rates of infection than were found in the placebo group. Secondary analyses suggested that Env-specific IgA antibodies may mitigate the effects of potentially protective antibodies.
This immune-correlates study generated the hypotheses that V1V2 antibodies may have contributed to protection against HIV-1 infection, whereas high levels of Env-specific IgA antibodies may have mitigated the effects of protective antibodies. Vaccines that are designed to induce higher levels of V1V2 antibodies and lower levels of Env-specific IgA antibodies than are induced by the RV144 vaccine may have improved efficacy against HIV-1 infection.
Treatment-selection markers are biological molecules or patient characteristics associated with one’s response to treatment. They can be used to predict treatment effects for individual subjects and subsequently help deliver treatment to those most likely to benefit from it. Statistical tools are needed to evaluate a marker’s capacity to help with treatment selection. The commonly adopted criterion for a good treatment-selection marker has been the interaction between marker and treatment. While a strong interaction is important, it is, however, not suffcient for good marker performance. In this paper, we develop novel measures for assessing a continuous treatment-selection marker, based on a potential outcomes framework. Under a set of assumptions, we derive the optimal decision rule based on the marker to classify individuals according to treatment benefit, and characterize the marker’s performance using the corresponding classification accuracy as well as the overall distribution of the classifier. We develop a constrained maximum-likelihood method for estimation and testing in a randomized trial setting. Simulation studies are conducted to demonstrate the performance of our methods. Finally, we illustrate the methods using an HIV vaccine trial where we explore the value of the level of pre-existing immunity to Adenovirus serotype 5 for predicting a vaccine-induced increase in the risk of HIV acquisition.
Classification accuracy; Constrained maximum likelihood; Monotone treatment effect; Potential outcomes; Sensitivity analysis; Treatment-selection marker
This commentary takes up Pearl's welcome challenge to clearly articulate the scientific value of principal stratification estimands that we and colleagues have investigated, in the area of randomized placebo-controlled preventive vaccine efficacy trials, especially trials of HIV vaccines. After briefly arguing that certain principal stratification estimands for studying vaccine effects on post-infection outcomes are of genuine scientific interest, the bulk of our commentary argues that the “causal effect predictiveness” (CEP) principal stratification estimand for evaluating immune biomarkers as surrogate endpoints is not of ultimate scientific interest, because it evaluates surrogacy restricted to the setting of a particular vaccine efficacy trial, but is nevertheless useful for guiding the selection of primary immune biomarker endpoints in Phase I/II vaccine trials and for facilitating assessment of transportability/bridging surrogacy.
principal stratification; causal inference; vaccine trial
In randomized studies researchers may be interested in the effect of treatment assignment on a time-to-event outcome that only exists in a subset selected after randomization. For example, in preventative HIV vaccine trials, it is of interest to determine whether randomization to vaccine affects the time from infection diagnosis until initiation of antiretroviral therapy. Earlier work assessed the effect of treatment on outcome among the principal stratum of individuals who would have been selected regardless of treatment assignment. These studies assumed monotonicity, that one of the principal strata was empty (eg, every person infected in the vaccine arm would have been infected if randomized to placebo). Here we present a sensitivity analysis approach for relaxing monotonicity with a time-to-event outcome. We also consider scenarios where selection is unknown for some subjects because of non-informative censoring (e.g., infection status k years after randomization is unknown for some because of staggered study entry). We illustrate our method using data from an HIV vaccine trial.
Causal inference; HIV; Kaplan-Meier; Monotonicity; Principal stratification
Recently, the RV144 randomized, double-blind, efficacy trial in Thailand reported that a prime-boost human immunodeficiency virus (HIV) vaccine regimen conferred ∼30% protection against HIV acquisition. However, different analyses seemed to give conflicting results, and a heated debate ensued as scientists and the broader public struggled with their interpretation. The lack of accounting for statistical principles helped flame the debate, and we leverage these principles to provide a more scientific interpretation. We first address interpretation of frequentist results, including interpretation of P values, synthesis of results from multiple analyses (ie, intention-to-treat versus per-protocol/fully immunized), and accounting for external efficacy trials. Second, we address how Bayesian statistics, which provide clearly interpretable statements about probabilities that the vaccine efficacy takes certain values, provide more information for weighing the evidence about efficacy than do frequentist statistics alone. Third, we evaluate RV144 for completeness of end point ascertainment and integrity of blinding, necessary tasks for establishing robustly interpretable results.
Identification of an immune response to vaccination that reliably predicts protection from clinically significant infection, i.e. an immunological surrogate endpoint, is a primary goal of vaccine research. Using this problem of evaluating an immunological surrogate as an illustration, we describe a hierarchy of three criteria for a valid surrogate endpoint and statistical analysis frameworks for evaluating them. Based on a placebo-controlled vaccine efficacy trial, the first level entails assessing the correlation of an immune response with a study endpoint in the study groups, and the second level entails evaluating an immune response as a surrogate for the study endpoint that can be used for predicting vaccine efficacy for a setting similar to that of the vaccine trial. We show that baseline covariates, innovative study design, and a potential outcomes formulation can be helpful for this assessment. The third level entails validation of a surrogate endpoint via meta-analysis, where the goal is to evaluate how well the immune response can be used to predict vaccine efficacy for new settings (building bridges). A simulated vaccine trial and two example vaccine trials are presented, one supporting that certain anti-influenza antibody levels are an excellent surrogate for influenza illness and another supporting that certain anti-HIV antibody levels are not useful as a surrogate for HIV infection.
clinical trial; counterfactual; immune correlate; meta-analysis; potential outcomes; principal surrogate; statistical surrogate
We analyzed HIV-1 genome sequences from 68 newly-infected volunteers in the Step HIV-1 vaccine trial. To determine whether the vaccine exerted selective T-cell pressure on breakthrough viruses, we identified potential T-cell epitopes in the founder sequences and compared them to epitopes in the vaccine. We found greater distances for sequences from vaccine recipients than from placebo recipients (p-values ranging from < 0.0001 to 0.09). The most significant signature site distinguishing vaccine from placebo recipients was Gag-84, a site encompassed by several epitopes contained in the vaccine and restricted by HLA alleles common in the cohort. Moreover, the extended divergence was confined to the vaccine components of the virus (Gag, Pol, Nef) and not found in other HIV-1 proteins. These results represent the first evidence of selective pressure from vaccine-induced T-cell responses on HIV-1 infection.
After one or more Phase 2 trials show that a candidate preventive vaccine induces immune responses that putatively protect against an infectious disease for which there is no licensed vaccine, the next step is to evaluate the efficacy of the candidate. The trial-designer faces the question of what is the optimal size of the initial efficacy trial? Part of the answer will entail deciding between a large Phase 3 licensure trial or an intermediate-sized Phase 2b screening trial, the latter of which may be designed to directly contribute to the evidence-base for licensing the candidate, or, to test a scientific concept for moving the vaccine field forward, acknowledging that the particular candidate will never be licensable. Using the HIV vaccine field as a case study, we describe distinguishing marks of Phase 2b and Phase 3 prevention efficacy trials, and compare the expected utility of these trial types using Pascal’s decision-theoretic framework. By integrating values/utilities on (1) Correct or incorrect conclusions resulting from the trial; (2) Timeliness of obtaining the trial results; (3) Precision for estimating the intervention effect; and (4) Resources expended; this decision framework provides a more complete approach to selecting the optimal efficacy trial size than a traditional approach that is based primarily on power calculations. Our objective is to help inform the decision-process for planning an initial efficacy trial design.
Clinical trial; Decision analysis; HIV vaccine; Intermediate-sized efficacy trial; Licensure; Microbicide; Phase 2b versus Phase 3
In the past decade, several principal stratification–based statistical methods have been developed for testing and estimation of a treatment effect on an outcome measured after a postrandomization event. Two examples are the evaluation of the effect of a cancer treatment on quality of life in subjects who remain alive and the evaluation of the effect of an HIV vaccine on viral load in subjects who acquire HIV infection. However, in general the developed methods have not addressed the issue of missing outcome data, and hence their validity relies on a missing completely at random (MCAR) assumption. Because in many applications the MCAR assumption is untenable, while a missing at random (MAR) assumption is defensible, we extend the semiparametric likelihood sensitivity analysis approach of Gilbert and others (2003) and Jemiai and Rotnitzky (2005) to allow the outcome to be MAR. We combine these methods with the robust likelihood–based method of Little and An (2004) for handling MAR data to provide semiparametric estimation of the average causal effect of treatment on the outcome. The new method, which does not require a monotonicity assumption, is evaluated in a simulation study and is applied to data from the first HIV vaccine efficacy trial.
Causal inference; HIV vaccine trial; Missing at random; Posttreatment selection bias; Principal stratification; Sensitivity analysis
Most randomized efficacy trials of interventions to prevent HIV or other infectious diseases have assessed intervention efficacy by a method that either does not incorporate baseline covariates, or that incorporates them in a non-robust or inefficient way. Yet, it has long been known that randomized treatment effects can be assessed with greater efficiency by incorporating baseline covariates that predict the response variable. Tsiatis et al. (2007) and Zhang et al. (2008) advocated a semiparametric efficient approach, based on the theory of Robins et al. (1994), for consistently estimating randomized treatment effects that optimally incorporates predictive baseline covariates, without any parametric assumptions. They stressed the objectivity of the approach, which is achieved by separating the modeling of baseline predictors from the estimation of the treatment effect. While their work adequately justifies implementation of the method for large Phase 3 trials (because its optimality is in terms of asymptotic properties), its performance for intermediate-sized screening Phase 2b efficacy trials, which are increasing in frequency, is unknown. Furthermore, the past work did not consider a right-censored time-to-event endpoint, which is the usual primary endpoint for a prevention trial. For Phase 2b HIV vaccine efficacy trials, we study finite-sample performance of Zhang et al.'s (2008) method for a dichotomous endpoint, and develop and study an adaptation of this method to a discrete right-censored time-to-event endpoint. We show that, given the predictive capacity of baseline covariates collected in real HIV prevention trials, the methods achieve 5-15% gains in efficiency compared to methods in current use. We apply the methods to the first HIV vaccine efficacy trial. This work supports implementation of the discrete failure time method for prevention trials.
Auxiliary; Covariate Adjustment; Intermediate-sized Phase 2b Efficacy Trial; Semiparametric Efficiency
Simulation studies were conducted to estimate the statistical power of repeated low-dose challenge experiments in non-human primates to detect a candidate HIV vaccine’s effect. The effect of various design parameters on power was explored. Simulation results indicate repeated low-dose challenge studies with total sample size 50 (25 per arm) typically provide adequate power to detect a 50% reduction in the per-exposure probability of infection due to vaccination. Power generally increases with the maximum number of allowable challenges per animal, the per-exposure risk of infection in controls, and the proportion susceptible to infection.
HIV; Macaque; Vaccine
We investigated effects of vaccination with AIDSVAX B/E HIV-1 candidate vaccine on blood and seminal plasma HIV-1 ribonucleic acid viral load (BVL and SVL, respectively) in vaccine recipients (VR) and placebo recipients (PR) who acquired infection.
Linear mixed models were fitted for repeated measurements of BVL. Generalized estimating equations were used to assess the difference in SVL detectability between VR and PR.
A total of 196 participants became HIV-1 infected during the trial. Thirty-two (16%) became infected with HIV-1 subtype B and 164 (84%) with HIV-1 subtype CRF01_AE. Per protocol-specified analysis, there were no differences in BVL levels between VR and PR. When stratified by HIV-1-infecting subtype, vaccination with AIDSVAX B/E was initially associated with higher BVL among HIV-1 CRF01_AE-infected VR compared to HIV-1 CRF01_AE-infected PR, however, this difference did not persist over time. HIV-1 subtype B-infected VR had slightly higher BVL levels and were more likely to have detectable SVL during the follow-up period than HIV-1 subtype B-infected PR.
Subtle differences in BVL and SVL were detected between VR and PR. These results may help to further understand the dynamics between HIV-1 vaccination, HIV-1-infecting subtypes, and subsequent viral expression in different body compartments.
HIV-1 vaccine; HIV-1 RNA viral load; Injecting drug users
The restricted neutralization breadth of vaccine-elicited antibodies is a major limitation of current human immunodeficiency virus-1 (HIV-1) candidate vaccines. In order to permit the efficient identification of vaccines with enhanced capacity for eliciting cross-reactive neutralizing antibodies (NAbs) and to assess the overall breadth and potency of vaccine-elicited NAb reactivity, we assembled a panel of 109 molecularly cloned HIV-1 Env pseudoviruses representing a broad range of genetic and geographic diversity. Viral isolates from all major circulating genetic subtypes were included, as were viruses derived shortly after transmission and during the early and chronic stages of infection. We assembled a panel of genetically diverse HIV-1-positive (HIV-1+) plasma pools to assess the neutralization sensitivities of the entire virus panel. When the viruses were rank ordered according to the average sensitivity to neutralization by the HIV-1+ plasmas, a continuum of average sensitivity was observed. Clustering analysis of the patterns of sensitivity defined four subgroups of viruses: those having very high (tier 1A), above-average (tier 1B), moderate (tier 2), or low (tier 3) sensitivity to antibody-mediated neutralization. We also investigated potential associations between characteristics of the viral isolates (clade, stage of infection, and source of virus) and sensitivity to NAb. In particular, higher levels of NAb activity were observed when the virus and plasma pool were matched in clade. These data provide the first systematic assessment of the overall neutralization sensitivities of a genetically and geographically diverse panel of circulating HIV-1 strains. These reference viruses can facilitate the systematic characterization of NAb responses elicited by candidate vaccine immunogens.
We consider estimation, from a double-blind randomized trial, of treatment effect within levels of base-line covariates on an outcome that is measured after a post-treatment event E has occurred in the subpopulation 𝒫E,E that would experience event E regardless of treatment. Specifically, we consider estimation of the parameters γ indexing models for the outcome mean conditional on treatment and base-line covariates in the subpopulation 𝒫E,E. Such parameters are not identified from randomized trial data but become identified if additionally it is assumed that the subpopulation 𝒫Ē,E of subjects that would experience event E under the second treatment but not under the first is empty and a parametric model for the conditional probability that a subject experiences event E if assigned to the first treatment given that the subject would experience the event if assigned to the second treatment, his or her outcome under the second treatment and his or her pretreatment covariates. We develop a class of estimating equations whose solutions comprise, up to asymptotic equivalence, all consistent and asymptotically normal estimators of γ under these two assumptions. In addition, we derive a locally semiparametric efficient estimator of γ. We apply our methods to estimate the effect on mean viral load of vaccine versus placebo after infection with human immunodeficiency virus (the event E) in a placebo-controlled randomized acquired immune deficiency syndrome vaccine trial.
Counterfactuals; Missing data; Potential outcomes; Principal stratification; Structural model; Vaccine trials
Defining the specificities of the anti-human immunodeficiency virus type 1 (HIV-1) envelope antibodies able to mediate broad heterologous neutralization will assist in identifying targets for an HIV-1 vaccine. We screened 70 plasmas from chronically HIV-1-infected individuals for neutralization breadth. Of these, 16 (23%) were found to neutralize 80% or more of the viruses tested. Anti-CD4 binding site (CD4bs) antibodies were found in almost all plasmas independent of their neutralization breadth, but they mainly mediated neutralization of the laboratory strain HxB2 with little effect on the primary virus, Du151. Adsorption with Du151 monomeric gp120 reduced neutralizing activity to some extent in most plasma samples when tested against the matched virus, although these antibodies did not always confer cross-neutralization. For one plasma, this activity was mapped to a site overlapping the CD4-induced (CD4i) epitope and CD4bs. Anti-membrane-proximal external region (MPER) (r = 0.69; P < 0.001) and anti-CD4i (r = 0.49; P < 0.001) antibody titers were found to be correlated with the neutralization breadth. These anti-MPER antibodies were not 4E10- or 2F5-like but spanned the 4E10 epitope. Furthermore, we found that anti-cardiolipin antibodies were correlated with the neutralization breadth (r = 0.67; P < 0.001) and anti-MPER antibodies (r = 0.6; P < 0.001). Our study suggests that more than one epitope on the envelope glycoprotein is involved in the cross-reactive neutralization elicited during natural HIV-1 infection, many of which are yet to be determined, and that polyreactive antibodies are possibly involved in this phenomenon.
In randomized clinical trials designed to compare the magnitude of vaccine-induced immune responses between vaccination regimens, the statistical method used for the analysis typically does not account for baseline participant characteristics. This article shows that incorporating baseline variables predictive of the immunogenicity study endpoint can provide large gains in precision and power for estimation and testing of the group mean difference (requiring fewer subjects for the same scientific output) compared to conventional methods, and recommends the “semiparametric efficient” method described in Tsiatis et al. [Tsiatis AA, Davidian M, Zhang M, Lu X. Covariate adjustment for two-sample treatment comparisons in randomized clinical trials: a principled yet flexible approach. Stat Med 2007. doi:10.1002/sim.3113] for practical use. As such, vaccine clinical trial programs can be improved (1) by investigating baseline predictors (e.g., readouts from laboratory assays) of vaccine-induced immune responses, and (2) by implementing the proposed semiparametric efficient method in trials where baseline predictors are available.
Immune responses; Statistical analysis; Vaccine trial
Both the magnitude and breadth of neutralization against multiple strains of virus are main endpoints for comparing antibody-based HIV-1 vaccine candidates in Phase I and II trials, and are key markers to be evaluated in vaccine efficacy trials as immune correlates of protection against HIV-1 infection. More generally, consideration of both magnitude and breadth is encountered when there is interest in comparing quantitative multivariate response data between groups. In this paper, we discuss two approaches to simultaneously evaluating the magnitude and breadth of a multivariate response. We suggest methods for the summarization and group comparison of multivariate response data that are subject to left and/or right censoring. Applications to data from a phase III clinical trial (Vax004) are discussed. Simulation-based sample size calculations and power analyses of the described methods also are presented.
Censored data; Group comparison; Immunological data; Multivariate data; Sample size
Evaluation of HIV vaccine candidates in non-human primates (NHPs) is a critical step toward developing a successful vaccine to control the HIV pandemic. Historically, HIV vaccine regimens have been tested in NHPs by administering a single high dose of the challenge virus. More recently, evaluation of candidate HIV vaccines has entailed repeated low-dose challenges which more closely mimic typical exposure in natural transmission settings. In this paper, we consider evaluation of the type and magnitude of vaccine efficacy from such experiments. Based on the principal stratification framework, we also address evaluation of potential immunological surrogate endpoints for infection.
Causal inference; Correlates of protection; HIV; Potential outcomes; Surrogate marker; Vaccine trial
Observational data and non-human primate challenge studies suggest that cell-mediated immune (CMI) responses may provide control of HIV replication. The Step Study is the first direct assessment of the efficacy of a CMI vaccine to protect against HIV infection or alter early plasma HIV levels in humans.
HIV-seronegative participants (3000) were randomized (1:1) to receive 3 injections of MRKAd5 HIV-1 gag/pol/nef vaccine or placebo. Randomization was pre-stratified by gender, baseline adenovirus type 5 (Ad5) titer, and study site. Participants were tested ~every 6 months for HIV acquisition; early plasma HIV RNA was measured ~3 months post-HIV diagnosis.
The vaccine elicited IFN-γ ELISPOT responses in 75% of vaccinees. In a pre-specified interim analysis among participants with baseline Ad5 ≤200, 24 of 741 vaccinees became HIV infected, versus 21 of 762 placebo recipients. All but one infection occurred in men. The early geometric mean plasma HIV RNA was comparable in infected vaccine and placebo recipients. In exploratory multivariate analyses, HIV incidence was higher in vaccinees versus placebo recipients among Ad5 seropositive men (5.1% versus 2.2% per year, respectively) and uncircumcised men (5.2% versus 1.4% per year, respectively). HIV incidence was similar in vaccinees versus placebo recipients among Ad5 seronegative men and circumcised men.
This CMI vaccine did not prevent HIV infection or lower early viral level. Mechanisms for failure of the vaccine to protect and for the increased HIV infection rates in subgroups of vaccinees are being explored. Additional follow-up will determine if elevated HIV incidence in vaccinee subgroups persists.
HIV vaccine; efficacy; adenovirus; HIV acquisition; viral load; male circumcision; test of concept
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.
Competing risks; distribution-free confidence bands and tests; failure time data; genetic data; HIV vaccine trial; pointwise and simultaneous confidence bands; semiparametric model; survival analysis
The RV144 clinical trial of a prime/boost immunizing regimen using recombinant canary pox (ALVAC-HIV) and two gp120 proteins (AIDSVAX B and E) was previously shown to have a 31.2% efficacy rate. Plasma specimens from vaccine and placebo recipients were used in an extensive set of assays to identify correlates of HIV-1 infection risk. Of six primary variables that were studied, only one displayed a significant inverse correlation with risk of infection: the antibody (Ab) response to a fusion protein containing the V1 and V2 regions of gp120 (gp70-V1V2). This finding prompted a thorough examination of the results generated with the complete panel of 13 assays measuring various V2 Abs in the stored plasma used in the initial pilot studies and those used in the subsequent case-control study. The studies revealed that the ALVAC-HIV/AIDSVAX vaccine induced V2-specific Abs that cross-react with multiple HIV-1 subgroups and recognize both conformational and linear epitopes. The conformational epitope was present on gp70-V1V2, while the predominant linear V2 epitope mapped to residues 165–178, immediately N-terminal to the putative α4β7 binding motif in the mid-loop region of V2. Odds ratios (ORs) were calculated to compare the risk of infection with data from 12 V2 assays, and in 11 of these, the ORs were ≤1, reaching statistical significance for two of the variables: Ab responses to gp70-V1V2 and to overlapping V2 linear peptides. It remains to be determined whether anti-V2 Ab responses were directly responsible for the reduced infection rate in RV144 and whether anti-V2 Abs will prove to be important with other candidate HIV vaccines that show efficacy, however, the results support continued dissection of Ab responses to the V2 region which may illuminate mechanisms of protection from HIV-1 infection and may facilitate the development of an effective HIV-1 vaccine.
Human immunodeficiency virus type 1 (HIV-1) Nef is a multifunctional protein that confers an ability to evade killing by cytotoxic T lymphocytes (CTLs) as well as other advantages to the virus in vivo. Here we exploited mathematical modeling and related statistical methods to estimate the impact of Nef activity on viral replication in vivo in relation to CTLs. Our results indicate that downregulation of major histocompatibility complex class I (MHC-I) A and B by wild-type Nef confers an advantage to the virus of about 82% in decreased CTL killing efficiency on average, meaning that abolishing the MHC-I downregulation function of Nef would increase killing by more than fivefold. We incorporated this estimate, as well as prior estimates of replicative enhancement by Nef, into a previously published model of HIV-1 and CTLs in vivo (W. D. Wick, O. O. Yang, L. Corey, and S. G. Self, J. Virol. 79:13579-13586, 2005), generalized to permit CTL recognition of multiple epitopes. A sequence database analysis revealed that 92.9% of HIV-1 epitopes are A or B restricted, and a previous study found an average of about 19 epitopes recognized (M. M. Addo et al., J. Virol. 77:2081-2092, 2003). We combined these estimates in the model in order to predict the impact of inhibiting Nef function in the general (chronically infected) population by a drug. The predicted impact on viral load ranged from negligible to 2.4 orders of magnitude, depending on the effects of the drug and the CTL dynamical scenario assumed. We conclude that inhibiting Nef could make a substantial reduction in disease burden, lengthening the time before the necessity of undertaking combination therapy with other antiretroviral drugs.