Comparison of two indinavir/ritonavir regimens in the treatment of HIV-infected individuals

Flexible modeling of multiple nonlinear longitudinal trajectories with censored and non-ignorable missing outcomes

Multivariate nonlinear mixed-effects models (MNLMMs) have become a promising tool for analyzing multi-outcome longitudinal data following nonlinear trajectory patterns. However, such a classical analysis can be challenging due to censorship induced by detection limits of the quantification assay or non-response occurring when participants missed scheduled visits intermittently or discontinued participation. This article proposes an extension of the MNLMM approach, called the MNLMM-CM, by taking the censored and non-ignorable missing responses into account simultaneously. The non-ignorable missingness is described by the selection-modeling factorization to tackle the missing not at random mechanism. A Monte Carlo expectation conditional maximization algorithm coupled with the first-order Taylor approximation is developed for parameter estimation. The techniques for the calculation of standard errors of fixed effects, estimation of unobservable random effects, imputation of censored and missing responses and prediction of future values are also provided. The proposed methodology is motivated and illustrated by the analysis of a clinical HIV/AIDS dataset with censored RNA viral loads and the presence of missing CD4 and CD8 cell counts. The superiority of our method on the provision of more adequate estimation is validated by a simulation study.

Extending multivariate Student's- t $$ t $$ semiparametric mixed models for longitudinal data with censored responses and heavy tails

This article extends the semiparametric mixed model for longitudinal censored data with Gaussian errors by considering the Student's t $$ t $$ -distribution. This model allows us to consider a flexible, functional dependence of an outcome variable over the covariates using nonparametric regression. Moreover, the proposed model takes into account the correlation between observations by using random effects. Penalized likelihood equations are applied to derive the maximum likelihood estimates that appear to be robust against outlying observations with respect to the Mahalanobis distance. We estimate nonparametric functions using smoothing splines under an EM-type algorithm framework. Finally, the proposed approach's performance is evaluated through extensive simulation studies and an application to two datasets from acquired immunodeficiency syndrome clinical trials.

Bayesian censored piecewise regression mixture models with skewness

This paper presents censored mixture regression models with piecewise growth curves for assessing longitudinal data that exhibit multiphasic features. Such features may include censoring, skewness, measurement errors in covariates, and mixtures of unobserved subpopulations. In the process of describing those features, identification of differential effects of predictors on a response variable for a heterogeneous population (subpopulations) has recently been highly sought. Regression mixture models are key methods for assessing differential effects of predictors. In this article, we extend regression mixture models with normal distribution to incorporate (i) skew-normal distribution, (ii) left-censoring, (iii) measurement errors, and (iv) piecewise growth mixture modeling for describing multiphasic trajectories over time where the observed observations come from a mixture of unobserved subgroups. The proposed methods are illustrated using real data from an AIDS clinical study and a Bayesian approach.

A semiparametric mixed-effects model for censored longitudinal data

In longitudinal studies involving laboratory-based outcomes, repeated measurements can be censored due to assay detection limits. Linear mixed-effects (LMEs) models are a powerful tool to model the relationship between a response variable and covariates in longitudinal studies. However, the linear parametric form of linear mixed-effect models is often too restrictive to characterize the complex relationship between a response variable and covariates. More general and robust modeling tools, such as nonparametric and semiparametric regression models, have become increasingly popular in the last decade. In this article, we use semiparametric mixed models to analyze censored longitudinal data with irregularly observed repeated measures. The proposed model extends the censored linear mixed-effect model and provides more flexible modeling schemes by allowing the time effect to vary nonparametrically over time. We develop an Expectation-Maximization (EM) algorithm for maximum penalized likelihood estimation of model parameters and the nonparametric component. Further, as a byproduct of the EM algorithm, the smoothing parameter is estimated using a modified linear mixed-effects model, which is faster than alternative methods such as the restricted maximum likelihood approach. Finally, the performance of the proposed approaches is evaluated through extensive simulation studies as well as applications to data sets from acquired immune deficiency syndrome studies.

Multivariate-t linear mixed models with censored responses, intermittent missing values and heavy tails

Multivariate longitudinal data arisen in medical studies often exhibit complex features such as censored responses, intermittent missing values, and atypical or outlying observations. The multivariate-t linear mixed model (MtLMM) has been recognized as a powerful tool for robust modeling of multivariate longitudinal data in the presence of potential outliers or fat-tailed noises. This paper presents a generalization of MtLMM, called the MtLMM-CM, to properly adjust for censorship due to detection limits of the assay and missingness embodied within multiple outcome variables recorded at irregular occasions. An expectation conditional maximization either (ECME) algorithm is developed to compute parameter estimates using the maximum likelihood (ML) approach. The asymptotic standard errors of the ML estimators of fixed effects are obtained by inverting the empirical information matrix according to Louis' method. The techniques for the estimation of random effects and imputation of missing responses are also investigated. The proposed methodology is illustrated on two real-world examples from HIV-AIDS studies and a simulation study under a variety of scenarios.

Bayesian semiparametric growth models for measurement error and missing data in CD4/CD8 ratio: Application to AIDS Study

In clinical research and practice, there is often an interest in assessing the effect of time varying predictors, such as CD4/CD8 ratio, on immune recovery following antiretroviral therapy. Such predictors are measured with errors, and ignoring those measurement errors during data analysis may lead to biased results. Though parametric methods have been used for reducing biases, they usually depend on untestable assumptions. To relax those assumptions, this paper presents semiparametric mixed-effect models which deal with predictors having measurement errors and missing values. We develop a fully Bayesian approach for fitting these models and discriminating between patients who are potentially progressors or nonprogressors to severe disease condition (AIDS). The proposed methods are demonstrated using real data from an AIDS clinical study.

Heterogeneous growth bent-cable models for time-to-event and longitudinal data: application to AIDS studies

The major limitations of growth curve mixture models for HIV/AIDS data are the usual assumptions of normality and monophasic curves within latent classes. This article addresses these limitations by using non-normal skewed distributions and multiphasic patterns for outcomes of prospective studies. For such outcomes, new skew-t (ST) distributions are proposed for modeling heterogeneous growth trajectories, which exhibit not abrupt but gradual multiphasic changes from a declining trend to an increasing trend over time. We assess these clinically important features of longitudinal HIV/AIDS data using the bent-cable framework within a context of a joint modeling of time-to-event process and response process. A real dataset from an AIDS clinical study is used to illustrate the proposed methods.

Multivariate longitudinal data analysis with censored and intermittent missing responses

The multivariate linear mixed model (MLMM) has emerged as an important analytical tool for longitudinal data with multiple outcomes. However, the analysis of multivariate longitudinal data could be complicated by the presence of censored measurements because of a detection limit of the assay in combination with unavoidable missing values arising when subjects miss some of their scheduled visits intermittently. This paper presents a generalization of the MLMM approach, called the MLMM-CM, for a joint analysis of the multivariate longitudinal data with censored and intermittent missing responses. A computationally feasible expectation maximization-based procedure is developed to carry out maximum likelihood estimation within the MLMM-CM framework. Moreover, the asymptotic standard errors of fixed effects are explicitly obtained via the information-based method. We illustrate our methodology by using simulated data and a case study from an AIDS clinical trial. Experimental results reveal that the proposed method is able to provide more satisfactory performance as compared with the traditional MLMM approach.

Bayesian semiparametric modeling for HIV longitudinal data with censoring and skewness

In biomedical studies, the analysis of longitudinal data based on Gaussian assumptions is common practice. Nevertheless, more often than not, the observed responses are naturally skewed, rendering the use of symmetric mixed effects models inadequate. In addition, it is also common in clinical assays that the patient's responses are subject to some upper and/or lower quantification limit, depending on the diagnostic assays used for their detection. Furthermore, responses may also often present a nonlinear relation with some covariates, such as time. To address the aforementioned three issues, we consider a Bayesian semiparametric longitudinal censored model based on a combination of splines, wavelets, and the skew-normal distribution. Specifically, we focus on the use of splines to approximate the general mean, wavelets for modeling the individual subject trajectories, and on the skew-normal distribution for modeling the random effects. The newly developed method is illustrated through simulated data and real data concerning AIDS/HIV viral loads.

A mechanistic nonlinear model for censored and mismeasured covariates in longitudinal models, with application in AIDS studies

When modeling longitudinal data, the true values of time-varying covariates may be unknown because of detection-limit censoring or measurement error. A common approach in the literature is to empirically model the covariate process based on observed data and then predict the censored values or mismeasured values based on this empirical model. Such an empirical model can be misleading, especially for censored values since the (unobserved) censored values may behave very differently than observed values due to the underlying data-generation mechanisms or disease status. In this paper, we propose a mechanistic nonlinear covariate model based on the underlying data-generation mechanisms to address censored values and mismeasured values. Such a mechanistic model is based on solid scientific or biological arguments, so the predicted censored or mismeasured values are more reasonable. We use a Monte Carlo EM algorithm for likelihood inference and apply the methods to an AIDS dataset, where viral load is censored by a lower detection limit. Simulation results confirm that the proposed models and methods offer substantial advantages over existing empirical covariate models for censored and mismeasured covariates.

Joint two-part Tobit models for longitudinal and time-to-event data

In this article, we show how Tobit models can address problems of identifying characteristics of subjects having left-censored outcomes in the context of developing a method for jointly analyzing time-to-event and longitudinal data. There are some methods for handling these types of data separately, but they may not be appropriate when time to event is dependent on the longitudinal outcome, and a substantial portion of values are reported to be below the limits of detection. An alternative approach is to develop a joint model for the time-to-event outcome and a two-part longitudinal outcome, linking them through random effects. This proposed approach is implemented to assess the association between the risk of decline of CD4/CD8 ratio and rates of change in viral load, along with discriminating between patients who are potentially progressors to AIDS from patients who do not. We develop a fully Bayesian approach for fitting joint two-part Tobit models and illustrate the proposed methods on simulated and real data from an AIDS clinical study.

Bayesian two-part bent-cable Tobit models with skew distributions: Application to AIDS studies

This paper presents a new development of a bent-cable two-part Tobit model to identify both phasic patterns and mixture of advancing (to AIDS) and non-advancing patients of HIV. In identification of such phasic patterns, estimation of a transition period for the development of drug resistance to antiretroviral (ARV) drug or therapy is carried out using longitudinal data that have a gradual change from a declining phase to an increasing phase. In addition to phasic changes, there are also problems of skewness and left-censoring in the response variable because of a lower limit of detection. A relatively large percentage of data below limit of detection are recorded more than expected under an assumed skew-distribution. To properly accommodate these features, we present an extension of the random effects bent-cable Tobit model that incorporates a mixture of true undetectable observations and those values from a skew-normal distribution for a response with left-censoring, skewness and phasic patterns. The proposed methods are illustrated using real data from an AIDS clinical study.

Joint bent-cable Tobit models for longitudinal and time-to-event data

In this article, we show how to estimate a transition period for the evolvement of drug resistance to antiretroviral (ARV) drug or other related treatments in the framework of developing a Bayesian method for jointly analyzing time-to-event and longitudinal data. For HIV/AIDS longitudinal data, developmental trajectories of viral loads tend to show a gradual change from a declining trend after initiation of treatment to an increasing trend without an abrupt change. Such characteristics of trajectories are also associated with a time-to-event process. To assess these clinically important features, we develop a joint bent-cable Tobit model for the time-to-event and left-censored response variable with skewness and phasic developments. Random effects are used to determine the stochastic dependence between the time-to-event process and response process. The proposed method is illustrated using real data from an AIDS clinical study.

Bayesian Two-Part Tobit Models with Left-Censoring, Skewness, and Nonignorable Missingness

In a longitudinal HIV/AIDS study with response data, observations may be missing because of patient dropouts due to drug intolerance or other problems, resulting in nonignorable missing data. In addition to nonignorable missingness, there are also problems of skewness and left-censoring in the response variable because of a lower limit of detection (LOD). There has been relatively little work published simultaneously dealing with these features of longitudinal data. In particular, one of the features may sometimes be the existence of a larger proportion of left-censored data falling below LOD than expected under a usually assumed log-normal distribution. When this happens, an alternative model that can account for a high proportion of censored data should be considered. We present an extension of the random effects Tobit model that incorporates a mixture of true undetectable observations and the values from a skew-normal distribution for an outcome with left-censoring, skewness, and nonignorable missingness. A unifying modeling approach is used to assess the impact of left-censoring, skewness, nonignorable missingness and measurement error in covariates on a Bayesian inference. The proposed methods are illustrated using real data from an AIDS clinical study.

Extending multivariate- t linear mixed models for multiple longitudinal data with censored responses and heavy tails

The analysis of complex longitudinal data is challenging due to several inherent features: (i) more than one series of responses are repeatedly collected on each subject at irregularly occasions over a period of time; (ii) censorship due to limits of quantification of responses arises left- and/or right- censoring effects; (iii) outliers or heavy-tailed noises are possibly embodied within multiple response variables. This article formulates the multivariate- t linear mixed model with censored responses (MtLMMC), which allows the analysts to model such data in the presence of the above described features simultaneously. An efficient expectation conditional maximization either (ECME) algorithm is developed to carry out maximum likelihood estimation of model parameters. The implementation of the E-step relies on the mean and covariance matrix of truncated multivariate- t distributions. To enhance the computational efficiency, two auxiliary permutation matrices are incorporated into the procedure to determine the observed and censored parts of each subject. The proposed methodology is demonstrated via a simulation study and a real application on HIV/AIDS data.

Piecewise Growth Mixture Tobit Models: Application to AIDS Studies

Piecewise growth models are very flexible methods for assessing distinct phases of development or progression in longitudinal data. As an extension of these models, this paper presents piecewise growth mixture Tobit models (PGMTMs) for describing phasic changes of individual trajectories over time where the longitudinal data has a mixture of subpopulations and where left censoring due to a lower limit of detection (LOD) is also observed. There has been relatively little work done simultaneously modeling heterogeneous growth trajectories, segmented phases of progression, and left-censoring with skewed responses. The proposed methods are illustrated using real data from an AIDS clinical study. Analysis results suggested two classes of viral load growth trajectories: Class 1 started with a decline in viral load after treatment but rebound after change-point; Class 2 had a decrease the same as the Class 1 and continued a slower decrease over time.

Performance of Six Different Ritonavir-Boosted Protease Inhibitor–Based Regimens in Heavily Antiretroviral-Experienced HIV-Infected Patients

BACKGROUND

Regimens based on ritonavir-boosted protease inhibitors (PI/r) are often used as rescue interventions. It is unclear whether significant differences exist between distinct PI/r.

METHOD

All HIV+ patients who had experienced PI failure at two HIV clinics and were rescued with a regimen based on saquinavir (SQV)/r 1000/100 mg bid, indinavir (IDV)/r 800/100 mg bid, lopinavir (LPV)/r 400/100 mg bid, amprenavir (APV)/r 600/100 mg bid, atazanavir (ATV)/r 300/100 mg qd, or tipranavir (TPV)/r 500/200 mg bid were retrospectively examined. A significant virological response (VR) was defined as >1 log reduction in plasma HIV-RNA or to <50 copies/mL at week 24.

RESULTS

A total of 389 patients were included in the analysis: 139 on SQV/r, 35 on IDV/r, 129 on LPV/r, 35 on APV/r, 29 on ATV/r, and 22 on TPV/r. No significant differences in HIV-RNA and CD4 counts at baseline were recognized between groups. In a multivariate analysis, only the total number of protease resistance mutations was associated with a lower VR (odds ratio [OR] = 0.77, 95% CI 0.68-0.87, p < .001). The presence of <5 or > or =5 protease resistance mutations at baseline was the best threshold to discriminate the achievement of VR in any treatment group. In an intent-to-treat analysis, for individuals with 5 protease resistance mutations, the rates of VR were 64% with TPV/r, 47% with LPV/r, 46% with SQV/r, 33% with ATV/r, 25% with IDV/r, and 16% with APV/r. Adverse events leading to treatment withdrawal occurred more frequently using IDV/r (22.8%) than others (p = .03).

CONCLUSION

The rate of VR in salvage therapy using PI/r-based regimens is relatively high in PI-experienced patients. The efficacy is greatly influenced by the number of baseline protease resistance mutations; 5 mutations is the best threshold to predict the chances of VR to any PI/r-based regimen.

Mixed-Effects Models with Skewed Distributions for Time-Varying Decay Rate in HIV Dynamics

After initiation of treatment, HIV viral load has multiphasic changes, which indicates that the viral decay rate is a time-varying process. Mixed-effects models with different time-varying decay rate functions have been proposed in literature. However, there are two unresolved critical issues: (i) it is not clear which model is more appropriate for practical use, and (ii) the model random errors are commonly assumed to follow a normal distribution, which may be unrealistic and can obscure important features of within- and among-subject variations. Because asymmetry of HIV viral load data is still noticeable even after transformation, it is important to use a more general distribution family that enables the unrealistic normal assumption to be relaxed. We developed skew-elliptical (SE) Bayesian mixed-effects models by considering the model random errors to have an SE distribution. We compared the performance among five SE models that have different time-varying decay rate functions. For each model, we also contrasted the performance under different model random error assumption such as normal, Student-t, skew-normal or skew-t distribution. Two AIDS clinical trial data sets were used to illustrate the proposed models and methods. The results indicate that the model with a time-varying viral decay rate that has two exponential components is preferred. Among the four distribution assumptions, the skew-t and skew-normal models provided better fitting to the data than normal or Student-t model, suggesting that it is important to assume a model with a skewed distribution in order to achieve reasonable results when the data exhibit skewness.

Bayesian bivariate linear mixed-effects models with skew-normal/independent distributions, with application to AIDS clinical studies

Bivariate correlated (clustered) data often encountered in epidemiological and clinical research are routinely analyzed under a linear mixed-effected (LME) model with normality assumptions for the random-effects and within-subject errors. However, those analyses might not provide robust inference when the normality assumptions are questionable if the data set particularly exhibits skewness and heavy tails. In this article, we develop a Bayesian approach to bivariate linear mixed-effects (BLME) models replacing the Gaussian assumptions for the random terms with skew-normal/independent (SNI) distributions. The SNI distribution is an attractive class of asymmetric heavy-tailed parametric structure which includes the skew-normal, skew-t, skew-slash, and skew-contaminated normal distributions as special cases. We assume that the random-effects and the within-subject (random) errors, respectively, follow multivariate SNI and normal/independent (NI) distributions, which provide an appealing robust alternative to the symmetric normal distribution in a BLME model framework. The method is exemplified through an application to an AIDS clinical data set to compare potential models with different distribution specifications, and clinically important findings are reported.

Bayesian inference for skew-normal mixture models with left-censoring

Assays to measure concentration of antibody after vaccination are often subject to left-censoring due to a lower detection limit (LDL), leading to a high proportion of observations below the detection limit. Not accounting for such left-censoring appropriately can lead to biased parameter estimates. To properly adjust for left-censoring and a high proportion of observations at LDL, this article proposes a mixture model combining a point mass below LDL and a Tobit model with skew-elliptical error distribution. We show that skew-elliptical distributions, where the skew-normal and skew-t are special cases, have great flexibility for simultaneously handling left-censoring, skewness, and heaviness in the tails of a distribution of a response variable with left-censored data. A Bayesian procedure is used to estimate model parameters. Two real data sets from a study of the measles vaccine and an HIV/AIDS study are used to illustrate the proposed models.

Jointly modeling time-to-event and longitudinal data: A Bayesian approach

This article explores Bayesian joint models of event times and longitudinal measures with an attempt to overcome departures from normality of the longitudinal response, measurement errors, and shortages of confidence in specifying a parametric time-to-event model. We allow the longitudinal response to have a skew distribution in the presence of measurement errors, and assume the time-to-event variable to have a nonparametric prior distribution. Posterior distributions of the parameters are attained simultaneously for inference based on Bayesian approach. An example from a recent AIDS clinical trial illustrates the methodology by jointly modeling the viral dynamics and the time to decrease in CD4/CD8 ratio in the presence of CD4 counts with measurement errors and to compare potential models with various scenarios and different distribution specifications. The analysis outcome indicates that the time-varying CD4 covariate is closely related to the first-phase viral decay rate, but the time to CD4/CD8 decrease is not highly associated with either the two viral decay rates or the CD4 changing rate over time. These findings may provide some quantitative guidance to better understand the relationship of the virological and immunological responses to antiretroviral treatments.

Bayesian semiparametric mixture Tobit models with left censoring, skewness, and covariate measurement errors

Common problems to many longitudinal HIV/AIDS, cancer, vaccine, and environmental exposure studies are the presence of a lower limit of quantification of an outcome with skewness and time-varying covariates with measurement errors. There has been relatively little work published simultaneously dealing with these features of longitudinal data. In particular, left-censored data falling below a limit of detection may sometimes have a proportion larger than expected under a usually assumed log-normal distribution. In such cases, alternative models, which can account for a high proportion of censored data, should be considered. In this article, we present an extension of the Tobit model that incorporates a mixture of true undetectable observations and those values from a skew-normal distribution for an outcome with possible left censoring and skewness, and covariates with substantial measurement error. To quantify the covariate process, we offer a flexible nonparametric mixed-effects model within the Tobit framework. A Bayesian modeling approach is used to assess the simultaneous impact of left censoring, skewness, and measurement error in covariates on inference. The proposed methods are illustrated using real data from an AIDS clinical study. .

Mixed-Effects Tobit Joint Models for Longitudinal Data with Skewness, Detection Limits, and Measurement Errors

Complex longitudinal data are commonly analyzed using nonlinear mixed-effects (NLME) models with a normal distribution. However, a departure from normality may lead to invalid inference and unreasonable parameter estimates. Some covariates may be measured with substantial errors, and the response observations may also be subjected to left-censoring due to a detection limit. Inferential procedures can be complicated dramatically when such data with asymmetric characteristics, left censoring, and measurement errors are analyzed. There is relatively little work concerning all of the three features simultaneously. In this paper, we jointly investigate a skew-tNLME Tobit model for response (with left censoring) process and a skew-tnonparametric mixed-effects model for covariate (with measurement errors) process under a Bayesian framework. A real data example is used to illustrate the proposed methods.

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.

A DYNAMIC BAYESIAN NONLINEAR MIXED-EFFECTS MODEL OF HIV RESPONSE INCORPORATING MEDICATION ADHERENCE, DRUG RESISTANCE AND COVARIATES()

HIV dynamic studies have contributed significantly to the understanding of HIV pathogenesis and antiviral treatment strategies for AIDS patients. Establishing the relationship of virologic responses with clinical factors and covariates during long-term antiretroviral (ARV) therapy is important to the development of effective treatments. Medication adherence is an important predictor of the effectiveness of ARV treatment, but an appropriate determinant of adherence rate based on medication event monitoring system (MEMS) data is critical to predict virologic outcomes. The primary objective of this paper is to investigate the effects of a number of summary determinants of MEMS adherence rates on virologic response measured repeatedly over time in HIV-infected patients. We developed a mechanism-based differential equation model with consideration of drug adherence, interacted by virus susceptibility to drug and baseline characteristics, to characterize the long-term virologic responses after initiation of therapy. This model fully integrates viral load, MEMS adherence, drug resistance and baseline covariates into the data analysis. In this study we employed the proposed model and associated Bayesian nonlinear mixed-effects modeling approach to assess how to efficiently use the MEMS adherence data for prediction of virologic response, and to evaluate the predicting power of each summary metric of the MEMS adherence rates. In particular, we intend to address the questions: (i) how to summarize the MEMS adherence data for efficient prediction of virologic response after accounting for potential confounding factors such as drug resistance and covariates, and (ii) how to evaluate treatment effect of baseline characteristics interacted with adherence and other clinical factors. The approach is applied to an AIDS clinical trial involving 31 patients who had available data as required for the proposed model. Results demonstrate that the appropriate determinants of MEMS adherence rates are important in order to more efficiently predict virologic response, and investigations of adherence to ARV treatment would benefit from measuring not only adherence rate but also its summary metric assessment. Our study also shows that the mechanism-based dynamic model is powerful and effective to establish a relationship of virologic responses with medication adherence, virus resistance to drug and baseline covariates.

Skew-normal Bayesian nonlinear mixed-effects models with application to AIDS studies

Studies of HIV dynamics in AIDS research are very important in understanding the pathogenesis of HIV-1 infection and also in assessing the effectiveness of antiviral therapies. Nonlinear mixed-effects (NLME) models have been used for modeling between-subject and within-subject variations in viral load measurements. Mostly, normality of both within-subject random error and random-effects is a routine assumption for NLME models, but it may be unrealistic, obscuring important features of between-subject and within-subject variations, particularly, if the data exhibit skewness. In this paper, we develop a Bayesian approach to NLME models and relax the normality assumption by considering both model random errors and random-effects to have a multivariate skew-normal distribution. The proposed model provides flexibility in capturing a broad range of non-normal behavior and includes normality as a special case. We use a real data set from an AIDS study to illustrate the proposed approach by comparing various candidate models. We find that the model with skew-normality provides better fit to the observed data and the corresponding estimates of parameters are significantly different from those based on the model with normality when skewness is present in the data. These findings suggest that it is very important to assume a model with skew-normal distribution in order to achieve robust and reliable results, in particular, when the data exhibit skewness.

Predictive value of pharmacokinetics-adjusted phenotypic susceptibility on response to ritonavir-enhanced protease inhibitors (PIs) in human immunodeficiency virus-infected subjects failing prior PI therapy

The activities of protease inhibitors in vivo may depend on plasma concentrations and viral susceptibility. This nonrandomized, open-label study evaluated the relationship of the inhibitory quotient (IQ [the ratio of drug exposure to viral phenotypic susceptibility]) to the human immunodeficiency virus type 1 (HIV-1) viral load (VL) change for ritonavir-enhanced protease inhibitors (PIs). Subjects on PI-based regimens replaced their PIs with ritonavir-enhanced indinavir (IDV/r) 800/200 mg, fosamprenavir (FPV/r) 700/100 mg, or lopinavir (LPV/r) 400/200 mg twice daily. Pharmacokinetics were assessed at day 14; follow-up lasted 24 weeks. Associations between IQ and VL changes were examined. Fifty-three subjects enrolled, 12 on IDV/r, 33 on FPV/r, and 8 on LPV/r. Median changes (n-fold) (FC) of 50% inhibitory concentrations (IC(50)s) to the study PI were high. Median 2-week VL changes were -0.7, -0.1, and -1.0 log(10) for IDV/r, FPV/r, and LPV/r. With FPV/r, correlations between the IQ and the 2-week change in VL were significant (Spearman's r range, -0.39 to -0.50; P < or = 0.029). The strongest correlation with response to FPV/r was the IC(50) FC (r = 0.57; P = 0.001), which improved when only adherent subjects were included (r = 0.68; P = 0.001). In multivariable analyses of the FPV/r arm that included FC, one measure of the drug concentration, corresponding IQ, baseline VL, and CD4, the FC to FPV was the only significant predictor of VL decline (P < 0.001). In exploratory analyses of all arms, the area under the concentration-time curve IQ was correlated with the week 2 VL change (r = -0.72; P < 0.001). In conclusion, in PI-experienced subjects with highly resistant HIV-1, short-term VL responses to RTV-enhanced FPV/r correlated best with baseline susceptibility. The IQ improved correlation in analyses of all arms where a greater range of virologic responses was observed.

Identifying significant covariates for anti-HIV treatment response: mechanism-based differential equation models and empirical semiparametric regression models

In this paper, the mechanism-based ordinary differential equation (ODE) model and the flexible semiparametric regression model are employed to identify the significant covariates for antiretroviral response in AIDS clinical trials. We consider the treatment effect as a function of three factors (or covariates) including pharmacokinetics, drug adherence and susceptibility. Both clinical and simulated data examples are given to illustrate these two different kinds of modeling approaches. We found that the ODE model is more powerful to model the mechanism-based nonlinear relationship between treatment effects and virological response biomarkers. The ODE model is also better in identifying the significant factors for virological response, although it is slightly liberal and there is a trend to include more factors (or covariates) in the model. The semiparametric mixed-effects regression model is very flexible to fit the virological response data, but it is too liberal to identify correct factors for the virological response; sometimes it may miss the correct factors. The ODE model is also biologically justifiable and good for predictions and simulations for various biological scenarios. The limitations of the ODE models include the high cost of computation and the requirement of biological assumptions that sometimes may not be easy to validate. The methodologies reviewed in this paper are also generally applicable to studies of other viruses such as hepatitis B virus or hepatitis C virus.

Design of long-term HIV dynamic studies using semiparametric mixed-effects models

Studies of HIV dynamics in AIDS research are very important in understanding the pathogenesis of HIV-1 infection and also in assessing the effectiveness of antiviral therapies. There are many AIDS clinical trials on HIV dynamics currently in development worldwide, giving rise to many design issues yet to be addressed. For example, most studies are focused on short-term viral dynamics and the existing models may not be applicable to describe long-term virologic response. In this paper, we use a simulation-based approach to study the designs of long-term viral dynamics under semiparametric nonlinear mixed-effects models. These models not only can preserve the meaningful interpretation of the short-term HIV dynamics, but also characterize the long-term virologic responses to antiretroviral (ARV) treatment. We investigate a number of feasible clinical protocol designs similar to those currently used in AIDS clinical trials. In particular, we evaluate whether earlier samplings can result in more useful information about the viral response trajectory; we also evaluate the effectiveness of two strategies: more frequent samplings per subject with fewer subjects versus fewer samplings per subject with more subjects while keeping the total number of samplings constant. The results of our investigation provide quantitative guidance for designing and selecting ARV therapy.

Bayesian Experimental Design for Long-Term Longitudinal HIV Dynamic Studies

The study of HIV dynamics is one of the most important developments in recent AIDS research for understanding the pathogenesis of HIV-1 infection and antiviral treatment strategies. Currently a large number of AIDS clinical trials on HIV dynamics are in development worldwide. However, many design issues that arise from AIDS clinical trials have not been addressed. In this paper, we use a simulation-based approach to deal with design problems in Bayesian hierarchical nonlinear (mixed-effects) models. The underlying model characterizes the long-term viral dynamics with antiretroviral treatment where we directly incorporate drug susceptibility and exposure into a function of treatment efficacy. The Bayesian design method is investigated under the framework of hierarchical Bayesian (mixed-effects) models. We compare a finite number of feasible candidate designs numerically, which are currently used in AIDS clinical trials from different perspectives, and provide guidance on how a design might be chosen in practice.

Steady-state pharmacokinetic and safety profiles of voriconazole and ritonavir in healthy male subjects

Since there is a likelihood of coadministration of voriconazole and ritonavir, two studies were conducted to evaluate the potential of drug interaction. Study A was a randomized, placebo-controlled, two-period, parallel-group trial (n = 34). Study B had the same design without the placebo group (n = 17). In period 1, subjects received 200 mg voriconazole or placebo twice daily (BID) for 3 days (400 mg BID on day 1). In period 2, following a 7-day washout, subjects received ritonavir alone at 400 mg BID (study A) or 100 mg BID (study B) for 10 days (days 11 to 20), and then ritonavir was coadministered with 200 mg BID voriconazole or placebo for the next 10 days (days 21 to 30). Serial plasma samples were collected on days 3, 20, and 30, and safety data were collected throughout the study. High-dose (400 mg BID) ritonavir substantially reduced the steady-state mean voriconazole exposure (area under the concentration-time curve from 0 to 12 h [AUC(0-12)], -82%; maximum concentration [C(max)], -66%). However, the effect of low-dose (100 mg BID) ritonavir was less pronounced (AUC(0-12), -39%; C(max), -24%). The decrease in voriconazole exposure was probably due to the induction of CYP2C19 and CYP2C9 by ritonavir. It is interesting that one subject in each study exhibited the opposite effect of ritonavir on voriconazole exposure (a 2.5- to 3-fold increase), probably due to lack of CYP2C19. Voriconazole had no apparent effect on the exposure of high-dose ritonavir but slightly decreased the exposure of low-dose ritonavir (AUC(0-12), -14%; C(max), -24%). The safety profile of combination therapy was not notably different from that of voriconazole or ritonavir alone. Due to the significant effect of ritonavir on voriconazole exposure, coadministration of voriconazole with 400 mg BID ritonavir is contraindicated; coadministration with 100 mg BID ritonavir should be avoided, unless an assessment of the benefit/risk to the patient justifies the use.

Analysis of relation between virologic responses and immunologic responses, patient's factors in AIDS clinical trials using a semiparametric mixed-effects model

In this article we propose to use a semiparametric mixed-effects model based on an exploratory analysis of clinical trial data for a study of the relation between virologic responses and immunologic markers such as CD4+ and CD8 counts, and host-specific factors in AIDS clinical trials. The regression spline technique, used for inference for parameters in the model, reduces the unknown nonparametric components to parametric functions. It is simple and straightforward to implement the procedures using readily available software, and parameter inference can be developed from standard parametric models. We apply the model and the proposed method to an AIDS clinical study. Our findings indicate that viral load level is positively related to baseline viral load level, negatively related to CD4+ cell counts, but unrelated to CD8 cell counts and patient's age neither.

Modeling the short-, middle- and long-term viral load responses for comparing estimated dynamic parameters

A virologic marker, the number of HIV RNA copies or viral load, is currently used to evaluate antiviral therapies in AIDS clinical trials. This marker can be used to assess the antiviral potency of therapies, but is easily affected by drug exposures, drug resistance and other factors during the long-term treatment evaluation process. The study of HIV dynamics is one of the most important development in recent AIDS research for understanding the pathogenesis of HIV-1 infection and antiviral treatment strategies. Although many HIV dynamic models have been proposed by AIDS researchers in the last decade, they have only been used to quantify short-term viral dynamics and do not correctly describe long-term virologic responses to antiretroviral treatment. In other words, these simple viral dynamic models can only be used to fit short-term viral load data for estimating dynamic parameters. In this paper, a mechanism-based differential equation models is introduced for characterizing the long-term viral dynamics with antiretroviral therapy. We applied this model to fit different segments of the viral load trajectory data from a simulation experiment and an AIDS clinical trial study, and found that the estimates of dynamic parameters from our modeling approach are very consistent. We may conclude that our model can not only characterize long-term viral dynamics, but can also quantify short- and middle-term viral dynamics. It suggests that if there are enough data in the early stage of the treatment, the results from our modeling based on short-term information can be used to capture the performance of long-term care with HIV-1 infected patients.

Ritonavir-Boosted Protease Inhibitors: Impact of Ritonavir on Toxicities in Treatment-Experienced Patients

The purpose of this review is to discuss the basis for ritonavir boosting of protease inhibitors as well as the complications and benefits associated with ritonavir boosting when designing an antiretroviral regimen for treatment-experienced patients. Such patients have fewer viable options because of cross-resistance arising from previous regimen failures. Ritonavir administered at a low dose to boost another protease inhibitor may be a useful strategy for achieving virological efficacy while minimizing the toxicities associated with full-dose ritonavir. There may be an increased risk of adverse events associated with increased plasma concentration of the concurrent protease inhibitor. Still, the incidence of these adverse events is generally low, and clinical trials have suggested that they rarely result in discontinuation or alteration of the regimen. In highly treatment-experienced patients in particular, the potential benefits associated with ritonavir boosting usually outweigh the risks.