The relationship between virologic and immunologic responses in AIDS clinical research using mixed-effects varying-coefficient models with measurement error

In this article we study the relationship between virologic and immunologic responses in AIDS clinical trials. Since plasma HIV RNA copies (viral load) and CD4+ cell counts are crucial virologic and immunologic markers for HIV infection, it is important to study their relationship during HIV/AIDS treatment. We propose a mixed-effects varying-coefficient model based on an exploratory analysis of data from a clinical trial. Since both viral load and CD4+ cell counts are subject to measurement error, we also consider the measurement error problem in covariates in our model. The regression spline method is proposed for inference for parameters in the proposed model. The regression spline method transforms the unknown nonparametric components into parametric functions. It is relatively simple to implement using readily available software, and parameter inference can be developed from standard parametric models. We apply the proposed models and methods to an AIDS clinical study. From this study, we find an interesting relationship between viral load and CD4+ cell counts during antiviral treatments. Biological interpretations and clinical implications are discussed.     

Estimation of the Timing of Perinatal Transmission of HIV

Knowledge of the timing of perinatal transmission of HIV would be valuable for the determination and evaluation of preventive treatments and would shed light on the mechanism of transmission. Estimation of the distribution of the time of perinatal transmission is difficult, however, because tests of infection status can only be undertaken after birth. DNA and RNA polymerase chain reaction (PCR) assays and HIV culture have been the most commonly used diagnostic tests for perinatal HIV infection. Such tests have high sensitivity and specificity, except when they are given shortly after infection. In this paper we use the time-dependent sensitivity of these diagnostic tests to make nonparametric and semiparametric inferences about the distribution of the time of perinatal HIV transmission as well as the cumulative probability of perinatal transmission. The methods are illustrated with data from a clinical trial conducted by the AIDS Clinical Trials group.     

Hierarchical Bayesian methods for estimation of parameters in a longitudinal HIV dynamic system

HIV dynamics studies have significantly contributed to the understanding of HIV infection and antiviral treatment strategies. But most studies are limited to short-term viral dynamics due to the difficulty of establishing a relationship of antiviral response with multiple treatment factors such as drug exposure and drug susceptibility during long-term treatment. In this article, a mechanism-based dynamic model is proposed for characterizing long-term viral dynamics with antiretroviral therapy, described by a set of nonlinear differential equations without closed-form solutions. In this model we directly incorporate drug concentration, adherence, and drug susceptibility into a function of treatment efficacy, defined as an inhibition rate of virus replication. We investigate a Bayesian approach under the framework of hierarchical Bayesian (mixed-effects) models for estimating unknown dynamic parameters. In particular, interest focuses on estimating individual dynamic parameters. The proposed methods not only help to alleviate the difficulty in parameter identifiability, but also flexibly deal with sparse and unbalanced longitudinal data from individual subjects. For illustration purposes, we present one simulation example to implement the proposed approach and apply the methodology to a data set from an AIDS clinical trial. The basic concept of the longitudinal HIV dynamic systems and the proposed methodologies are generally applicable to any other biomedical dynamic systems.     

Prospective accuracy for longitudinal markers

In this article we focus on appropriate statistical methods for characterizing the prognostic value of a longitudinal clinical marker. Frequently it is possible to obtain repeated measurements. If the measurement has the ability to signify a pending change in the clinical status of a patient then the marker has the potential to guide key medical decisions. Heagerty, Lumley, and Pepe (2000, Biometrics 56, 337-344) proposed characterizing the diagnostic accuracy of a marker measured at baseline by calculating receiver operating characteristic curves for cumulative disease or death incidence by time t. They considered disease status as a function of time, D(t) = 1(Tor= 0, after the baseline time) can discriminate between people who become diseased and those who do not in a subsequent time interval [s, t]. We assume the disease status is derived from an observed event time T and thus interest is in individuals who transition from disease free to diseased. We seek methods that also allow the inclusion of prognostic covariates that permit patient-specific decision guidelines when forecasting a future change in health status. Our proposal is to use flexible semiparametric models to characterize the bivariate distribution of the event time and marker values at an arbitrary time s. We illustrate the new methods by analyzing a well-known data set from HIV research, the Multicenter AIDS Cohort Study data.     

Weighted Likelihood Method for Grouped Survival Data in Case–Cohort Studies with Application to HIV Vaccine Trials

Summary Grouped failure time data arise often in HIV studies. In a recent preventive HIV vaccine efficacy trial, immune responses generated by the vaccine were measured from a case–cohort sample of vaccine recipients, who were subsequently evaluated for the study endpoint of HIV infection at prespecified follow‐up visits. Gilbert et al. (2005, Journal of Infectious Diseases 191 , 666–677) and Forthal et al. (2007, Journal of Immunology 178, 6596–6603) analyzed the association between the immune responses and HIV incidence with a Cox proportional hazards model, treating the HIV infection diagnosis time as a right‐censored random variable. The data, however, are of the form of grouped failure time data with case–cohort covariate sampling, and we propose an inverse selection probability‐weighted likelihood method for fitting the Cox model to these data. The method allows covariates to be time dependent, and uses multiple imputation to accommodate covariate data that are missing at random. We establish asymptotic properties of the proposed estimators, and present simulation results showing their good finite sample performance. We apply the method to the HIV vaccine trial data, showing that higher antibody levels are associated with a lower hazard of HIV infection.     

Parameter Identifiability and Estimation of HIV/AIDS Dynamic Models

We use a technique from engineering (Xia and Moog, in IEEE Trans. Autom. Contr. 48(2):330–336, 2003; Jeffrey and Xia, in Tan, W.Y., Wu, H. (Eds.), Deterministic and Stochastic Models of AIDS Epidemics and HIV Infections with Intervention, 2005) to investigate the algebraic identifiability of a popular three-dimensional HIV/AIDS dynamic model containing six unknown parameters. We find that not all six parameters in the model can be identified if only the viral load is measured, instead only four parameters and the product of two parameters (N and λ) are identifiable. We introduce the concepts of an identification function and an identification equation and propose the multiple time point (MTP) method to form the identification function which is an alternative to the previously developed higher-order derivative (HOD) method (Xia and Moog, in IEEE Trans. Autom. Contr. 48(2):330–336, 2003; Jeffrey and Xia, in Tan, W.Y., Wu, H. (Eds.), Deterministic and Stochastic Models of AIDS Epidemics and HIV Infections with Intervention, 2005). We show that the newly proposed MTP method has advantages over the HOD method in the practical implementation. We also discuss the effect of the initial values of state variables on the identifiability of unknown parameters. We conclude that the initial values of output (observable) variables are part of the data that can be used to estimate the unknown parameters, but the identifiability of unknown parameters is not affected by these initial values if the exact initial values are measured with error. These noisy initial values only increase the estimation error of the unknown parameters. However, having the initial values of the latent (unobservable) state variables exactly known may help to identify more parameters. In order to validate the identifiability results, simulation studies are performed to estimate the unknown parameters and initial values from simulated noisy data. We also apply the proposed methods to a clinical data set to estimate HIV dynamic parameters. Although we have developed the identifiability methods based on an HIV dynamic model, the proposed methodologies are generally applicable to any ordinary differential equation systems.     

Covariate analysis of viral eradication studies

An important issue arising in therapeutic studies of hepatitis C and HIV is the identification of and adjustment for covariates associated with viral eradication and resistance. Analyses of such data are complicated by the fact that eradication is an occult event that is not directly observable, resulting in unique types of censored observations that do not arise in other competing risks settings. This paper proposes a semiparametric regression model to assess the association between multiple covariates and the eradication/resistance processes. The proposed methods are based on a piecewise proportional hazards model that allows parameters to vary between observation times. We illustrate the methods with data from recent hepatitis C clinical trials.     

Hierarchical Bayesian inference for HIV dynamic differential equation models incorporating multiple treatment factors

Studies on HIV dynamics in AIDS research are very important in understanding the pathogenesis of HIV‐1 infection and also in assessing the effectiveness of antiretroviral (ARV) treatment. Viral dynamic models can be formulated through a system of nonlinear ordinary differential equations (ODE), but there has been only limited development of statistical methodologies for inference. This article, motivated by an AIDS clinical study, discusses a hierarchical Bayesian nonlinear mixed‐effects modeling approach to dynamic ODE models without a closed‐form solution. In this model, we fully integrate viral load, medication adherence, drug resistance, pharmacokinetics, baseline covariates and time‐dependent drug efficacy into the data analysis for characterizing long‐term virologic responses. Our method is implemented by a data set from an AIDS clinical study. The results suggest that modeling HIV dynamics and virologic responses with consideration of time‐varying clinical factors as well as baseline characteristics may be important for HIV/AIDS studies in providing quantitative guidance to better understand the virologic responses to ARV treatment and to help the evaluation of clinical trial design in response to existing therapies.     

Estimating HIV Incidence Based on Combined Prevalence Testing

Summary .  Knowledge of incidence rates of HIV and other infectious diseases is important in evaluating the state of an epidemic as well as for designing interventional studies. Estimation of disease incidence from longitudinal studies can be expensive and time consuming. Alternatively, Janssen et al. (1998,  Journal of the American Medical Association   280, 42–48) proposed the estimation of HIV incidence at a single point in time based on the combined use of a standard and "detuned" antibody assay. This article frames the problem from a longitudinal perspective, from which the maximum likelihood estimator of incidence is determined and compared with the Janssen estimator. The formulation also allows estimation for general situations, including different batteries of tests among subjects, inclusion of covariates, and a comparative evaluation of different test batteries to help guide study design. The methods are illustrated with data from an HIV interventional trial and a seroprevalence survey recently conducted in Botswana.     

Hidden Markov models for settings with interval-censored transition times and uncertain time origin: application to HIV genetic analyses

The simplicity and flexibility of Markov models make them appealing for investigations of the acquisition of HIV drug-resistance mutations, whose presence can define specific Markov states. Because the exact time of acquiring a mutation is not observed during clinical research studies on HIV infection, it is important that methods for fitting such models accommodate interval-censored transition times. Furthermore, many such studies include patients with extensive treatment experience prior to the onset of the studies. Therefore, the virus in these patients may have already acquired resistance mutations by study entry. Retrospective data regarding the time on treatment, which is often known or known with error, provide information about the acquisition rates before the start of a study. Finally, variability in the genetic sequences of circulating HIV creates uncertainty in the Markov states. This paper considers approaches to fitting Markov models to data with interval-censored transition times when the time origin and the Markov states are known with error. The methods were applied to AIDS Clinical Trial Group protocol 398, a randomized comparison of mono- versus dual-protease inhibitor use in heavily pretreated patients. We found that the estimated rates of acquiring certain classes of mutations depended on the presence of others, and that the precision of these estimates can be considerably improved by inclusion of retrospective data.     

Cross‐sectional human immunodeficiency virus incidence estimation accounting for heterogeneity across communities

Accurate estimation of human immunodeficiency virus (HIV) incidence rates is crucial for the monitoring of HIV epidemics, the evaluation of prevention programs, and the design of prevention studies. Traditional cohort approaches to measure HIV incidence require repeatedly testing large cohorts of HIV‐uninfected individuals with an HIV diagnostic test (eg, enzyme‐linked immunosorbent assay) for long periods of time to identify new infections, which can be prohibitively costly, time‐consuming, and subject to loss to follow‐up. Cross‐sectional approaches based on the usual HIV diagnostic test and biomarkers of recent infection offer important advantages over standard cohort approaches, in terms of time, cost, and attrition. Cross‐sectional samples usually consist of individuals from different communities. However, small sample sizes limit the ability to estimate community‐specific incidence and existing methods typically ignore heterogeneity in incidence across communities. We propose a permutation test for the null hypothesis of no heterogeneity in incidence rates across communities, develop a random‐effects model to account for this heterogeneity and to estimate community‐specific incidence, and provide one way to estimate the coefficient of variation. We evaluate the performance of the proposed methods through simulation studies and apply them to the data from the National Institute of Mental Health Project ACCEPT, a phase 3 randomized controlled HIV prevention trial in Sub‐Saharan Africa, to estimate the overall and community‐specific HIV incidence rates.     

The 2-sample problem for failure rates depending on a continuous mark: an application to vaccine efficacy

The efficacy of an HIV vaccine to prevent infection is likely to depend on the genetic variation of the exposing virus. This paper addresses the problem of using data on the HIV sequences that infect vaccine efficacy trial participants to (1) test for vaccine efficacy more powerfully than procedures that ignore the sequence data and (2) evaluate the dependence of vaccine efficacy on the divergence of infecting HIV strains from the HIV strain that is contained in the vaccine. Because hundreds of amino acid sites in each HIV genome are sequenced, it is natural to treat the genetic divergence as a continuous mark variable that accompanies each failure (infection) time. Problems (1) and (2) can then be approached by testing whether the ratio of the mark-specific hazard functions for the vaccine and placebo groups is unity or independent of the mark. We develop nonparametric and semiparametric tests for these null hypotheses and nonparametric techniques for estimating the mark-specific relative risks. The asymptotic properties of the procedures are established. In addition, the methods are studied in simulations and are applied to HIV genetic sequence data collected in the first HIV vaccine efficacy trial.     

HIV-1 Transmission during Early Infection in Men Who Have Sex with Men: A Phylodynamic Analysis

Background

Conventional epidemiological surveillance of infectious diseases is focused on characterization of incident infections and estimation of the number of prevalent infections. Advances in methods for the analysis of the population-level genetic variation of viruses can potentially provide information about donors, not just recipients, of infection. Genetic sequences from many viruses are increasingly abundant, especially HIV, which is routinely sequenced for surveillance of drug resistance mutations. We conducted a phylodynamic analysis of HIV genetic sequence data and surveillance data from a US population of men who have sex with men (MSM) and estimated incidence and transmission rates by stage of infection.

Methods and Findings

We analyzed 662 HIV-1 subtype B sequences collected between October 14, 2004, and February 24, 2012, from MSM in the Detroit metropolitan area, Michigan. These sequences were cross-referenced with a database of 30,200 patients diagnosed with HIV infection in the state of Michigan, which includes clinical information that is informative about the recency of infection at the time of diagnosis. These data were analyzed using recently developed population genetic methods that have enabled the estimation of transmission rates from the population-level genetic diversity of the virus. We found that genetic data are highly informative about HIV donors in ways that standard surveillance data are not. Genetic data are especially informative about the stage of infection of donors at the point of transmission. We estimate that 44.7% (95% CI, 42.2%–46.4%) of transmissions occur during the first year of infection.

Conclusions

In this study, almost half of transmissions occurred within the first year of HIV infection in MSM. Our conclusions may be sensitive to un-modeled intra-host evolutionary dynamics, un-modeled sexual risk behavior, and uncertainty in the stage of infected hosts at the time of sampling. The intensity of transmission during early infection may have significance for public health interventions based on early treatment of newly diagnosed individuals. Please see later in the article for the Editors'' Summary     

Design of Viral Dynamic Studies for Efficiently Assessing Potency of Anti‐HIV Therapies in AIDS Clinical Trials

The study of HIV dynamics is one of the most important developments in recent AIDS research. It greatly improves our understanding of the pathogenesis of HIV infection. Recently it has been proposed to use HIV dynamics to evaluate the efficacy of antiviral treatments. Currently a large number of AIDS clinical trials on HIV dynamics are in development worldwide. However, many design issues that arise from HIV dynamic studies have not been addressed. In this paper, we study these problems using intensive Monte Carlo simulations and analytic methods. We evaluate a finite number of feasible candidate designs, which are currently used and proposed in AIDS clinical trials from different perspectives. We compare the viral dynamic marker and classical viral load change markers in terms of power for identifying treatment difference, asymptotic relative efficiency, and sensitivity. Finally we propose some useful suggestions for practitioners based on our results.     

Nonparametric confidence intervals for the ratio of marginal hazard rates of paired survival times

Paired survival times with potential censoring are often observed from two treatment groups in clinical trials and other types of clinical studies. The ratio of marginal hazard rates may be used to quantify the treatment effect in these studies. In this paper, a recently proposed nonparametric kernel method is used to estimate the marginal hazard rate, and the method of variance estimates recovery (MOVER) is used for the construction of the confidence intervals of a time‐dependent hazard ratio based on the confidence limits of a single marginal hazard rate. Two methods are proposed: one uses the delta method and another adopts the transformation method to construct confidence limits for the marginal hazard rate. Simulations are performed to evaluate the performance of the proposed methods. Real data from two clinical trials are analyzed using the proposed methods.     

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

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

HIV-1 Vaccine-Induced T-Cell Reponses Cluster in Epitope Hotspots that Differ from Those Induced in Natural Infection with HIV-1

Several recent large clinical trials evaluated HIV vaccine candidates that were based on recombinant adenovirus serotype 5 (rAd-5) vectors expressing HIV-derived antigens. These vaccines primarily elicited T-cell responses, which are known to be critical for controlling HIV infection. In the current study, we present a meta-analysis of epitope mapping data from 177 participants in three clinical trials that tested two different HIV vaccines: MRKAd-5 HIV and VRC-HIVAD014-00VP. We characterized the population-level epitope responses in these trials by generating population-based epitope maps, and also designed such maps using a large cohort of 372 naturally infected individuals. We used these maps to address several questions: (1) Are vaccine-induced responses randomly distributed across vaccine inserts, or do they cluster into immunodominant epitope hotspots? (2) Are the immunodominance patterns observed for these two vaccines in three vaccine trials different from one another? (3) Do vaccine-induced hotspots overlap with epitope hotspots induced by chronic natural infection with HIV-1? (4) Do immunodominant hotspots target evolutionarily conserved regions of the HIV genome? (5) Can epitope prediction methods be used to identify these hotspots? We found that vaccine responses clustered into epitope hotspots in all three vaccine trials and some of these hotspots were not observed in chronic natural infection. We also found significant differences between the immunodominance patterns generated in each trial, even comparing two trials that tested the same vaccine in different populations. Some of the vaccine-induced immunodominant hotspots were located in highly variable regions of the HIV genome, and this was more evident for the MRKAd-5 HIV vaccine. Finally, we found that epitope prediction methods can partially predict the location of vaccine-induced epitope hotspots. Our findings have implications for vaccine design and suggest a framework by which different vaccine candidates can be compared in early phases of evaluation.     

Assessing antiviral potency of anti-HIV therapies in vivo by comparing viral decay rates in viral dynamic models

A virologic marker, the number of HIV RNA copies or viral load, is currently used to evaluate anti-HIV therapies in AIDS clinical trials. This marker can be used to assess the antiviral potency of therapies, but is easily affected by noncompliance, drug resistance, toxicities, and other factors during the long-term treatment evaluation process. Recently it has been suggested to use viral dynamics to assess the potency of antiviral drugs and therapies, since viral decay rates in viral dynamic models have been shown to be related to the antiviral drug potency directly, and they need a shorter evaluation time. In this paper we first review the two statistical approaches for characterizing HIV dynamics and estimating viral decay rates: the individual nonlinear least squares regression (INLS) method and the population nonlinear mixed-effect model (PMEM) approach. To compare the viral decay rates between two treatment arms, parametric and nonparametric tests, based on the estimates of viral decay rates (the derived variables) from both the INLS and PMEM methods, are proposed and studied. We show, using the concept of exchangeability, that the test based on the empirical Bayes' estimates from the PMEM is valid, powerful and robust. This proposed method is very useful in most practical cases where the INLS-based tests and the general likelihood ratio test may not apply. We validate and compare various tests for finite samples using Monte Carlo simulations. Finally, we apply the proposed tests to an AIDS clinical trial to compare the antiviral potency between a 3-drug combination regimen and a 4-drug combination regimen. The proposed tests provide some significant evidence that the 4-drug regimen is more potent than the 3-drug regimen, while the naive methods fail to give a significant result.*To whom correspondence should be addressed.