Yangxin Huang

Modeling HIV dynamics and antiviral response with consideration of time-varying drug exposures, adherence and phenotypic sensitivity.

Highly active antiretroviral therapies consisting of reverse transcriptase inhibitor drugs and protease inhibitor drugs, which can rapidly suppress HIV below the limit of detection, are currently the most effective treatment for HIV infected patients. In spite of this, many patients fail to achieve viral suppression, probably due to existing or developing drug resistance, poor adherence, pharmacokinetic problems and other clinical factors. In this paper, we develop a viral dynamic model to evaluate how time-varying drug exposure and drug susceptibility affect antiviral response. Plasma concentrations, in turn, are modeled using a standard pharmacokinetic (PK) one-compartment open model with first order absorption and elimination as a function of fixed individual PK parameters and dose times. Imperfect adherence is considered as missed doses in PK models. We discuss the analytic properties of the viral dynamic model and study how time-varying treatment efficacies affect antiviral responses, specifically viral load and T cell counts. The relationship between actual failure time (the time at which the viral growth rate changes from negative to positive) and detectable failure time (the time at which viral load rebounds to above the limit of detection) is investigated. We find that an approximately linear relationship can be used to estimate the actual rebound failure time from the detectable rebound failure time. In addition, the effect of adherence on antiviral response is studied. In particular, we examine how different patterns of adherence affect antiviral response. Results suggest that longer sequences of missed doses increase the chance of treatment failure and accelerate the failure. Simulation experiments are presented to illustrate the relationship between antiviral response and pharmacokinetics, time-varying adherence and drug resistance. The proposed models and methods may be useful in AIDS clinical trial simulations.

Modeling long-term HIV dynamics and antiretroviral response : Effects of drug potency, pharmacokinetics, adherence, and drug resistance

We propose a long-term HIV-1 dynamic model by considering drug potency, drug exposure, and drug susceptibility. Using a Bayesian approach, HIV-1 dynamic parameters were estimated by fitting the model to viral load data from a phase 1/2 randomized clinical study of 2 indinavir (IDV)/ritonavir (RTV)-containing highly active antiretroviral (ARV) therapy regimens in HIV-infected subjects who had previously failed protease inhibitor-containing ARV therapies. A large between-subject variation in estimated viral dynamic parameters was observed, even after accounting for variations in drug exposure and drug susceptibility, suggesting that characteristics of HIV-1 dynamics are host dependent. Significant correlations of baseline factors such as HIV-1 RNA levels and CD4+ cell counts with viral dynamic parameters were found. These correlations coincide with biologic interaction mechanisms between HIV and the host immune system and also provide an explanation for the correlations between the baseline viral load and phase 1 viral decay rate, for which inconsistent results have been reported in the literature. The relations between viral dynamic parameters and virologic response were established, and these results suggest that viral dynamic parameters may play an important role in determining treatment success or failure. In particular, we estimated a drug efficacy threshold for each patient that can be used to assess whether an ARV regimen is potent enough to suppress HIV viruses in the individual patient. Our findings indicate that it is necessary to individualize the ARV regimen to treat HIV-1-infected patients. The proposed mathematic models and statistical techniques may provide a framework to simulate and predict antiviral response for individual patients.

Modeling and Estimation of Replication Fitness of Human Immunodeficiency Virus Type 1 In Vitro Experiments by Using a Growth Competition Assay

ABSTRACT Growth competition assays have been developed to quantify the relative fitnesses of human immunodeficiency virus (HIV-1) mutants. In this article we develop mathematical models to describe viral/cellular dynamic interactions in the assay experiment, from which new competitive fitness indices or parameters are defined. These indices include the log fitness ratio (LFR), the log relative fitness (LRF), and the production rate ratio (PRR). From the population genetics perspective, we clarify the confusion and correct the inconsistency in the definition of relative fitness in the literature of HIV-1 viral fitness. The LFR and LRF are easier to estimate from the experimental data than the PRR, which was misleadingly defined as the relative fitness in recent HIV-1 research literature. Calculation and estimation methods based on two data points and multiple data points were proposed and were carefully studied. In particular, we suggest using both standard linear regression (method of least squares) and a measurement error model approach for more-accurate estimates of competitive fitness parameters from multiple data points. The developed methodologies are generally applicable to any growth competition assays. A user-friendly computational tool also has been developed and is publicly available on the World Wide Web at http://www.urmc.rochester.edu/bstools/vfitness/virusfitness.htm .

A Bayesian Approach to Joint Mixed-Effects Models with a Skew-Normal Distribution and Measurement Errors in Covariates

In recent years, nonlinear mixed-effects (NLME) models have been proposed for modeling complex longitudinal data. Covariates are usually introduced in the models to partially explain intersubject variations. However, one often assumes that both model random error and random effects are normally distributed, which may not always give reliable results if the data exhibit skewness. Moreover, some covariates such as CD4 cell count may be often measured with substantial errors. In this article, we address these issues simultaneously by jointly modeling the response and covariate processes using a Bayesian approach to NLME models with covariate measurement errors and a skew-normal distribution. A real data example is offered to illustrate the methodologies by comparing various potential models with different distribution specifications. It is showed that the models with skew-normality assumption may provide more reasonable results if the data exhibit skewness and the results may be important for HIV/AIDS studies in providing quantitative guidance to better understand the virologic responses to antiretroviral treatment.

Analysis of Longitudinal and Survival Data: Joint Modeling, Inference Methods, and Issues

In the past two decades, joint models of longitudinal and survival data have received much attention in the literature. These models are often desirable in the following situations: (i) survival models with measurement errors or missing data in time-dependent covariates, (ii) longitudinal models with informative dropouts, and (iii) a survival process and a longitudinal process are associated via latent variables. In these cases, separate inferences based on the longitudinal model and the survival model may lead to biased or inefficient results. In this paper, we provide a brief overview of joint models for longitudinal and survival data and commonly used methods, including the likelihood method and two-stage methods.

A Bayesian approach for estimating antiviral efficacy in HIV dynamic models

Abstract The study of HIV dynamics is one of the most important developments in recent AIDS research. It has led to a new understanding of the pathogenesis of HIV infection. Although important findings in HIV dynamics have been published in prestigious scientific journals, the statistical methods for parameter estimation and model-fitting used in those papers appear surprisingly crude and have not been studied in more detail. For example, the unidentifiable parameters were simply imputed by mean estimates from previous studies, and important pharmacological/clinical factors were not considered in the modelling. In this paper, a viral dynamic model is developed to evaluate the effect of pharmacokinetic variation, drug resistance and adherence on antiviral responses. In the context of this model, we investigate a Bayesian modelling approach under a non-linear mixed-effects (NLME) model framework. In particular, our modelling strategy allows us to estimate time-varying antiviral efficacy of a regimen during the whole course of a treatment period by incorporating the information of drug exposure and drug susceptibility. Both simulated and real clinical data examples are given to illustrate the proposed approach. The Bayesian approach has great potential to be used in many aspects of viral dynamics modelling since it allow us to fit complex dynamic models and identify all the model parameters. Our results suggest that Bayesian approach for estimating parameters in HIV dynamic models is flexible and powerful.

Pharmacodynamics of Antiretroviral Agents in HIV-1 Infected Patients: Using Viral Dynamic Models That Incorporate Drug Susceptibility and Adherence ∗

We developed a novel HIV-1 dynamic model with consideration of pharmacokinetics, drug adherence and drug susceptibility to link plasma drug concentration to the long-term changes in HIV-1 RNA observation after initiation of therapy. A Bayesian approach is proposed to fit this model to clinical data from ACTG A5055, a study of two dosage regimens of indinavir (IDV) with ritonavir (RTV) in subjects failing their first protease inhibitor treatment. The HIV RNA testing was completed at days 0, 7, 14, 28, 56, 84, 112, 140, and 168. An intensive pharmacokinetic (PK) evaluation was performed on day 14 and multiple trough concentrations were subsequently collected. Pill counts were used to monitor adherence. IC50 for IDV and RTV were determined at baseline and at virologic failure. Viral dynamic model fitting residuals were used to assess the significance of covariate effects on long-term virologic response. As univariate predictors, none of the four PK parameters Ctrough, C12 hour, Cmax, and AUC was significantly related to virologic response (p>0.05). By including drug susceptibility (IC50), or IC50 and adherence measured by pill counts together, Ctrough, C12 hour, Cmax and AUC were each significantly correlated to long-term virologic response (p=0.0055,0.0002,0.0136,0.0002 with IC50 and adherence measured by pill counts considered). The IC50 and adherence measured by pill counts alone were not related to the virologic response. In predicting virologic response adherence measured by pill counts did not provide any additional information to PK parameters (p=0.064), to drug susceptibility IC50 (p=0.086), and to their combination (p=0.22). Simple regression approaches did not detect any significant pharmacodynamic (PD) relationships. Any single factor of PK, adherence measured by pill counts and drug susceptibility did not contribute to long-term virologic response. But their combinations in viral dynamic modeling significantly predicted virologic response. The HIV dynamic modeling can appropriately capture complicated nonlinear relationships and interactions among multiple covariates.

Bayesian inference on joint models of HIV dynamics for time‐to‐event and longitudinal data with skewness and covariate measurement errors

Normality (symmetry) of the model random errors is a routine assumption for mixed-effects models in many longitudinal studies, but it may be unrealistically obscuring important features of subject variations. Covariates are usually introduced in the models to partially explain inter-subject variations, but some covariates such as CD4 cell count may be often measured with substantial errors. This paper formulates a class of models in general forms that considers model errors to have skew-normal distributions for a joint behavior of longitudinal dynamic processes and time-to-event process of interest. For estimating model parameters, we propose a Bayesian approach to jointly model three components (response, covariate, and time-to-event processes) linked through the random effects that characterize the underlying individual-specific longitudinal processes. We discuss in detail special cases of the model class, which are offered to jointly model HIV dynamic response in the presence of CD4 covariate process with measurement errors and time to decrease in CD4/CD8 ratio, to provide a tool to assess antiretroviral treatment and to monitor disease progression. We illustrate the proposed methods using the data from a clinical trial study of HIV treatment. The findings from this research suggest that the joint models with a skew-normal distribution may provide more reliable and robust results if the data exhibit skewness, and particularly the results may be important for HIV/AIDS studies in providing quantitative guidance to better understand the virologic responses to antiretroviral treatment.

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.

Evaluation of a Multiple-Cycle, Recombinant Virus, Growth Competition Assay That Uses Flow Cytometry To Measure Replication Efficiency of Human Immunodeficiency Virus Type 1 in Cell Culture

ABSTRACT Human immunodeficiency virus type 1 (HIV-1) replication efficiency or fitness, as measured in cell culture, has been postulated to correlate with clinical outcome of HIV infection, although this is still controversial. One limitation is the lack of high-throughput assays that can measure replication efficiency over multiple rounds of replication. We have developed a multiple-cycle growth competition assay to measure HIV-1 replication efficiency that uses flow cytometry to determine the relative proportions of test and reference viruses, each of which expresses a different reporter gene in place of nef. The reporter genes are expressed on the surface of infected cells and are detected by commercially available fluorescence-labeled antibodies. This method is less labor-intensive than those that require isolation and amplification of nucleic acids. The two reporter gene products are detected with similar specificity and sensitivity, and the proportion of infected cells in culture correlates with the amount of viral p24 antigen produced in the culture supernatant. HIV replication efficiencies of six different drug-resistant site-directed mutants were reproducibly quantified and were similar to those obtained with a growth competition assay in which the relative proportion of each variant was measured by sequence analysis, indicating that recombination between the pol and reporter genes was negligible. This assay also reproducibly quantified the relative fitness conferred by protease and reverse transcriptase sequences containing multiple drug resistance mutations, amplified from patient plasma. This flow cytometry-based growth competition assay offers advantages over current assays for HIV replication efficiency and should prove useful for the evaluation of patient samples in clinical trials.