This paper considers generalized linear quantile regression for competing risks data when the failure type may be missing. Two estimation procedures for the regression co-efficients, including an inverse probability weighted complete-case estimator and an augmented inverse probability weighted estimator, are discussed under the assumption that the failure type is missing at random. The proposed estimation procedures utilize supplemental auxiliary variables for predicting the missing failure type and for informing its distribution. The asymptotic properties of the two estimators are derived and their asymptotic efficiencies are compared. We show that the augmented estimator is more efficient and possesses a double robustness property against misspecification of either the model for missingness or for the failure type. The asymptotic covariances are estimated using the local functional linearity of the estimating functions. The finite sample performance of the proposed estimation procedures are evaluated through a simulation study. The methods are applied to analyze the ‘Mashi’ trial data for investigating the effect of formula-versus breast-feeding plus extended infant zidovudine prophylaxis on HIV-related death of infants born to HIV-infected mothers in Botswana.
Augmented inverse probability weighted; Auxiliary variables; Competing risks; Double robustness; Efficient estimator; Estimating equation; Inverse probability weighted; Local functional linearity; Logistic regression; Mashi trial; Missing at random; Quantile regression
The RV144 vaccine trial in Thailand demonstrated that an HIV vaccine could prevent infection in humans and highlights the importance of understanding protective immunity against HIV. We used a nonhuman primate model to define immune and genetic mechanisms of protection against mucosal infection by the simian immunodeficiency virus (SIV). A plasmid DNA prime/recombinant adenovirus serotype 5 (rAd5) boost vaccine regimen was evaluated for its ability to protect monkeys from infection by SIVmac251 or SIVsmE660 isolates after repeat intrarectal challenges. Although this prime-boost vaccine regimen failed to protect against SIVmac251 infection, 50% of vaccinated monkeys were protected from infection with SIVsmE660. Among SIVsmE660-infected animals, there was an about one-log reduction in peak plasma virus RNA in monkeys expressing the major histocompatibility complex class I allele Mamu-A*01, implicating cytotoxic T lymphocytes in the control of SIV replication once infection is established. Among Mamu-A*01–negative monkeys challenged with SIVsmE660, no CD8+ T cell response or innate immune response was associated with protection against virus acquisition. However, low levels of neutralizing antibodies and an envelope-specific CD4+ T cell response were associated with vaccine protection in these monkeys. Moreover, monkeys that expressed two TRIM5 alleles that restrict SIV replication were more likely to be protected from infection than monkeys that expressed at least one permissive TRIM5 allele. This study begins to elucidate the mechanism of vaccine protection against immunodeficiency viruses and highlights the need to analyze these immune and genetic correlates of protection in future trials of HIV vaccine strategies.
In vaccine research, immune biomarkers that can reliably predict a vaccine’s effect on the clinical endpoint (i.e., surrogate markers) are important tools for guiding vaccine development. This paper addresses issues on optimizing two-phase sampling study design for evaluating surrogate markers in a principal surrogate framework, motivated by the design of a future HIV vaccine trial. To address the problem of missing potential outcomes in a standard trial design, novel trial designs have been proposed that utilize baseline predictors of the immune response biomarker(s) and/or augment the trial by vaccinating uninfected placebo recipients at the end of the trial and measuring their immune biomarkers. However, inefficient use of the augmented information can lead to counterintuitive results on the precision of estimation. To remedy this problem, we propose a pseudo-score type estimator suitable for the augmented design and characterize its asymptotic properties. This estimator has superior performance compared with existing estimators and allows calculation of analytical variances useful for guiding study design. Based on the new estimator we investigate in detail the problem of optimizing the sampling scheme of a biomarker in a vaccine efficacy trial for efficiently estimating its surrogate effect, as characterized by the vaccine efficacy curve (a causal effect predictiveness curve) and by the predicted overall vaccine efficacy using the biomarker.
Closeout placebo vaccination; Estimated likelihood; Immune correlate; Principal surrogate; Pseudo-score; Two-phase sampling design
A marker of immune function that statistically correlates with protection after vaccination may be either a mechanistic correlate of protection or a nonmechanistic correlate of protection, which does not cause protection, but predicts protection.
Identification of immune correlates of protection after vaccination is an important part of vaccinology for both theoretical and practical reasons. The terminology and definition of correlates have been confusing, because different authors have used variable terms and concepts. Here, we attempt to give precision to the field by defining 3 terms: correlate of protection (CoP), mechanistic correlate of protection (mCoP), and nonmechanistic correlate of protection (nCoP). A CoP is a marker of immune function that statistically correlates with protection after vaccination that may be either an mCoP, which is a mechanistic cause of protection, or an nCoP, which does not cause protection but nevertheless predicts protection through its (partial) correlation with another immune response(s) that mechanistically protects.
It is frequently of interest to estimate the intervention effect that adjusts for post-randomization variables in clinical trials. In the recently completed HPTN 035 trial, there is differential condom use between the three microbicide gel arms and the No Gel control arm, so that intention to treat (ITT) analyses only assess the net treatment effect that includes the indirect treatment effect mediated through differential condom use. Various statistical methods in causal inference have been developed to adjust for post-randomization variables. We extend the principal stratification framework to time-varying behavioral variables in HIV prevention trials with a time-to-event endpoint, using a partially hidden Markov model (pHMM). We formulate the causal estimand of interest, establish assumptions that enable identifiability of the causal parameters, and develop maximum likelihood methods for estimation. Application of our model on the HPTN 035 trial reveals an interesting pattern of prevention effectiveness among different condom-use principal strata.
microbicide; causal inference; posttreatment variables; direct effect
The ALVAC-HIV/AIDSVAX-B/E RV144 vaccine trial showed an estimated efficacy of 31%. RV144 secondary immune correlate analysis demonstrated that the combination of low plasma anti-HIV-1 Env IgA antibodies and high levels of antibody-dependent cellular cytotoxicity (ADCC) inversely correlate with infection risk. One hypothesis is that the observed protection in RV144 is partially due to ADCC-mediating antibodies. We found that the majority (73 to 90%) of a representative group of vaccinees displayed plasma ADCC activity, usually (96.2%) blocked by competition with the C1 region-specific A32 Fab fragment. Using memory B-cell cultures and antigen-specific B-cell sorting, we isolated 23 ADCC-mediating nonclonally related antibodies from 6 vaccine recipients. These antibodies targeted A32-blockable conformational epitopes (n = 19), a non-A32-blockable conformational epitope (n = 1), and the gp120 Env variable loops (n = 3). Fourteen antibodies mediated cross-clade target cell killing. ADCC-mediating antibodies displayed modest levels of V-heavy (VH) chain somatic mutation (0.5 to 1.5%) and also displayed a disproportionate usage of VH1 family genes (74%), a phenomenon recently described for CD4-binding site broadly neutralizing antibodies (bNAbs). Maximal ADCC activity of VH1 antibodies correlated with mutation frequency. The polyclonality and low mutation frequency of these VH1 antibodies reveal fundamental differences in the regulation and maturation of these ADCC-mediating responses compared to VH1 bNAbs.
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
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
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.
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