Population HIV-1 dynamics in vivo: applicable models and inferential tools for virological data from AIDS clinical trials

A Bayesian approach for mixed effects state-space models under skewness and heavy tails

Human immunodeficiency virus (HIV) dynamics have been the focus of epidemiological and biostatistical research during the past decades to understand the progression of acquired immunodeficiency syndrome (AIDS) in the population. Although there are several approaches for modeling HIV dynamics, one of the most popular is based on Gaussian mixed-effects models because of its simplicity from the implementation and interpretation viewpoints. However, in some situations, Gaussian mixed-effects models cannot (a) capture serial correlation existing in longitudinal data, (b) deal with missing observations properly, and (c) accommodate skewness and heavy tails frequently presented in patients' profiles. For those cases, mixed-effects state-space models (MESSM) become a powerful tool for modeling correlated observations, including HIV dynamics, because of their flexibility in modeling the unobserved states and the observations in a simple way. Consequently, our proposal considers an MESSM where the observations' error distribution is a skew-t. This new approach is more flexible and can accommodate data sets exhibiting skewness and heavy tails. Under the Bayesian paradigm, an efficient Markov chain Monte Carlo algorithm is implemented. To evaluate the properties of the proposed models, we carried out some exciting simulation studies, including missing data in the generated data sets. Finally, we illustrate our approach with an application in the AIDS Clinical Trial Group Study 315 (ACTG-315) clinical trial data set.

Smoothed simulated pseudo-maximum likelihood estimation for nonlinear mixed effects models with censored responses

Nonlinear mixed effects models have been widely applied to analyses of data that arise from biological, agricultural, and environmental sciences. Estimation of and inference on parameters in nonlinear mixed effects models are often based on the specification of a likelihood function. Maximizing this likelihood function can be complicated by the specification of the random effects distribution, especially in the presence of multiple random effects. The implementation of nonlinear mixed effects models can be further complicated by left-censored responses, representing measurements from bioassays where the exact quantification below a certain threshold is not possible. Motivated by the need to characterize the nonlinear human immunodeficiency virus RNA viral load trajectories after the interruption of antiretroviral therapy, we propose a smoothed simulated pseudo-maximum likelihood estimation approach to fit nonlinear mixed effects models in the presence of left-censored observations. We establish the consistency and asymptotic normality of the resulting estimators. We develop testing procedures for the correlation among random effects and for testing the distributional assumptions on random effects against a specific alternative. In contrast to the existing variants of expectation-maximization approaches, the proposed methods offer flexibility in the specification of the random effects distribution and convenience in making inference about higher-order correlation parameters. We evaluate the finite-sample performance of the proposed methods through extensive simulation studies and illustrate them on a combined dataset from six AIDS Clinical Trials Group treatment interruption studies.

Varied Patterns of Decay of Intact Human Immunodeficiency Virus Type 1 Proviruses Over 2 Decades of Antiretroviral Therapy

Fourteen people with human immunodeficiency virus type 1 had longitudinal measurements of intact, defective, and total proviral DNA over the course of two decades of antiretroviral therapy. Three patterns of intact proviral DNA decay were revealed: (1) biphasic decline with markedly slower second-phase decline, (2) initial decline that transitions to a zero-slope plateau, and (3) initial decline followed by later increases in intact proviral DNA. Defective proviral DNA levels were essentially stable. Mechanisms of slowing or reversal of second-phase decay of intact proviral DNA may include the inability to clear cells with intact but transcriptionally silent proviruses and clonal expansion of cells with intact proviruses.

A simple model for viral decay dynamics and the distribution of infected cell life spans in SHIV-infected infant rhesus macaques

The dynamics of HIV viral load following the initiation of antiretroviral therapy is not well-described by simple, single-phase exponential decay. Several mathematical models have been proposed to describe its more complex behavior, the most popular of which is two-phase exponential decay. The underlying assumption in two-phase exponential decay is that there are two classes of infected cells with different lifespans. However, with the exception of CD4+ T cells, there is not a consensus on all of the cell types that can become productively infected, and the fit of the two-phase exponential decay to observed data from SHIV.C.CH505 infected infant rhesus macaques was relatively poor. Therefore, we propose a new model for viral decay, inspired by the Gompertz model where the decay rate itself is a dynamic variable. We modify the Gompertz model to include a linear term that modulates the decay rate. We show that this simple model performs as well as the two-phase exponential decay model on HIV and SIV data sets, and outperforms it for the infant rhesus macaque SHIV.C.CH505 infection data set. We also show that by using a stochastic differential equation formulation, the modified Gompertz model can be interpreted as being driven by a population of infected cells with a continuous distribution of cell lifespans, and estimate this distribution for the SHIV.C.CH505-infected infant rhesus macaques. Thus, we find that the dynamics of viral decay in this model of infant HIV infection and treatment may be explained by a distribution of cell lifespans, rather than two distinct cell types.

Nonlinear mixed-effects models for HIV viral load trajectories before and after antiretroviral therapy interruption, incorporating left censoring

OBJECTIVES

Characterizing features of the viral rebound trajectories and identifying host, virological, and immunological factors that are predictive of the viral rebound trajectories are central to HIV cure research. We investigate if key features of HIV viral decay and CD4 trajectories during antiretroviral therapy (ART) are associated with characteristics of HIV viral rebound following ART interruption.

METHODS

Nonlinear mixed effect (NLME) models are used to model viral load trajectories before and following ART interruption, incorporating left censoring due to lower detection limits of viral load assays. A stochastic approximation EM (SAEM) algorithm is used for parameter estimation and inference. To circumvent the computational intensity associated with maximizing the joint likelihood, we propose an easy-to-implement three-step method.

RESULTS

We evaluate the performance of the proposed method through simulation studies and apply it to data from the Zurich Primary HIV Infection Study. We find that some key features of viral load during ART (e.g., viral decay rate) are significantly associated with important characteristics of viral rebound following ART interruption (e.g., viral set point).

CONCLUSIONS

The proposed three-step method works well. We have shown that key features of viral decay during ART may be associated with important features of viral rebound following ART interruption.

HIV-1 DNA decay dynamics in early treated individuals: practical considerations for clinical trial design

Background

Initiation of combination antiretroviral therapy (cART) soon after HIV-1 infection limits the establishment of viral reservoirs. Thus, early treated individuals are preferred candidates to evaluate novel viral remission strategies. However, their cART-dependent HIV-1 DNA decay dynamics are still poorly defined. This can hamper the design and interpretation of results from clinical trials intended to further reduce viral reservoirs.

Objectives

To clarify the duration of cART needed for the HIV-1 reservoir to be stabilized in early treated individuals.

Methods

We characterized the longitudinal decline of total HIV-1 DNA levels by droplet digital PCR in 21 individuals initiating cART within 6 months after estimated HIV-1 acquisition. Measurements were taken at cART initiation, after 6 months and annually until Year 4. Correlations between virological and clinical parameters were statistically analysed. Statistical modelling was performed applying a mixed-effects model.

Results

Total HIV-1 DNA experienced a median overall decrease of 1.43 log₁₀ units (IQR = 1.17–1.69) throughout the 4 years of follow-up. Baseline levels for total HIV-1 DNA, viral load, absolute CD4+ T cell count and CD4+/CD8+ ratio correlate with final HIV-1 DNA measurements (R² = 0.68, P < 0.001; R² = 0.54, P = 0.012; R² = −0.47, P = 0.031; and R² = −0.59, P = 0.0046, respectively). Statistical modelling shows that after 2 years on cART the viral reservoir had reached a set point.

Conclusions

A waiting period of 2 years on cART should be considered when designing interventions aiming to impact latent HIV-1 reservoir levels and viral rebound kinetics after cART discontinuation, in order to facilitate interpretation of results and enhance the chance of viral control.

Multiparameter one-sided tests for nonlinear mixed effects models with censored responses

Nonlinear mixed-effects (NLME) models are commonly used in longitudinal studies such as pharmacokinetics and HIV viral dynamics studies. NLME models are often derived based on underlying data-generating mechanisms, therefore the parameters in these models often have natural physical interpretations that may suggest reasonable constraints on certain parameters. For example, the HIV viral decay rates for populations receiving anti-HIV treatments may be reasonably expected to be nonnegative. Hypothesis testing for these parameters should incorporate practically reasonable constraints to increase statistical power. Motivated from HIV viral dynamic models, in this article we propose multiparameter one-sided or constrained tests for NLME models with censored responses, for example, viral dynamic models with viral loads subject to lower detection limits. We propose approximate likelihood-based tests that are computationally efficient. We evaluate the tests via simulations and show that the proposed tests are more powerful than the corresponding two-sided or unrestricted tests. We apply the proposed tests to two AIDS datasets with new findings.

Quantifying the Dynamics of HIV Decline in Perinatally Infected Neonates on Antiretroviral Therapy

BACKGROUND

Mathematical modeling has provided important insights into HIV infection dynamics in adults undergoing antiretroviral treatment (ART). However, much less is known about the corresponding dynamics in perinatally infected neonates initiating early ART.

SETTING

From 2014 to 2017, HIV viral load (VL) was monitored in 122 perinatally infected infants identified at birth and initiating ART within a median of 2 days. Pretreatment infant and maternal covariates, including CD4 T cell counts and percentages, were also measured.

METHODS

From the initial cohort, 53 infants demonstrated consistent decline and suppressed VL below the detection threshold (20 copies mL) within 1 year. For 43 of these infants with sufficient VL data, we fit a mathematical model describing the loss of short-lived and long-lived infected cells during ART. We then estimated the lifespans of infected cells and the time to viral suppression, and tested for correlations with pretreatment covariates.

RESULTS

Most parameters governing the kinetics of VL decline were consistent with those obtained previously from adults and other infants. However, our estimates of the lifespan of short-lived infected cells were longer than published values. This difference may reflect sparse sampling during the early stages of VL decline, when the loss of short-lived cells is most apparent. In addition, infants with higher pretreatment CD4 percentage or lower pretreatment VL trended toward more rapid viral suppression.

CONCLUSIONS

HIV dynamics in perinatally infected neonates initiating early ART are broadly similar to those observed in other age groups. Accelerated viral suppression is also associated with higher CD4 percentage and lower VL.

Robust inference for skewed data in health sciences

Health data are often not symmetric to be adequately modeled through the usual normal distributions; most of them exhibit skewed patterns. They can indeed be modeled better through the larger family of skew-normal distributions covering both skewed and symmetric cases. Since outliers are not uncommon in complex real-life experimental datasets, a robust methodology automatically taking care of the noises in the data would be of great practical value to produce stable and more precise research insights leading to better policy formulation. In this paper, we develop a class of robust estimators and testing procedures for the family of skew-normal distributions using the minimum density power divergence approach with application to health data. In particular, a robust procedure for testing of symmetry is discussed in the presence of outliers. Two efficient computational algorithms are discussed. Besides deriving the asymptotic and robustness theory for the proposed methods, their advantages and utilities are illustrated through simulations and a couple of real-life applications for health data of athletes from Australian Institute of Sports and AIDS clinical trial data.

Bayesian joint modeling for partially linear mixed-effects quantile regression of longitudinal and time-to-event data with limit of detection, covariate measurement errors and skewness

Joint modeling analysis of longitudinal and time-to-event data has been an active area of statistical methodological study and biomedical research, but the majority of them are based on mean-regression. Quantile regression (QR) can characterize the entire conditional distribution of the outcome variable, and may be more robust to outliers/heavy tails and misspecification of error distribution. Additionally, a parametric specification may be insufficient and inflexible to capture the complicated longitudinal pattern of biomarkers. Thus, this study proposes novel QR-based partially linear mixed-effects joint models with three components (QR-based longitudinal response, longitudinal covariate, and time-to-event processes), and applies to Multicenter AIDS Cohort Study (MACS). Many common data features, including left-censoring due to a limit of detection, covariate measurement error, and asymmetric distribution, are considered to obtain reliable parameter estimates. Many interesting findings are discovered by the complicated joint models under Bayesian inference framework. Simulation studies are also implemented to assess the performance of the proposed joint models under different scenarios.

Efficient algorithms for covariate analysis with dynamic data using nonlinear mixed-effects model

Nonlinear mixed-effects modeling is one of the most popular tools for analyzing repeated measurement data, particularly for applications in the biomedical fields. Multiple integration and nonlinear optimization are the two major challenges for likelihood-based methods in nonlinear mixed-effects modeling. To solve these problems, approaches based on empirical Bayesian estimates have been proposed by breaking the problem into a nonlinear mixed-effects model with no covariates and a linear regression model without random effect. This approach is time-efficient as it involves no covariates in the nonlinear optimization. However, covariate effects based on empirical Bayesian estimates are underestimated and the bias depends on the extent of shrinkage. Marginal correction method has been proposed to correct the bias caused by shrinkage to some extent. However, the marginal approach appears to be suboptimal when testing covariate effects on multiple model parameters, a situation that is often encountered in real-world data analysis. In addition, the marginal approach cannot correct the inaccuracy in the associated p-values. In this paper, we proposed a simultaneous correction method (nSCEBE), which can handle the situation where covariate analysis is performed on multiple model parameters. Simulation studies and real data analysis showed that nSCEBE is accurate and efficient for both effect-size estimation and p-value calculation compared with the existing methods. Importantly, nSCEBE can be >2000 times faster than the standard mixed-effects models, potentially allowing utilization for high-dimension covariate analysis for longitudinal or repeated measured outcomes.

Comparison of empirical and dynamic models for HIV viral load rebound after treatment interruption

OBJECTIVE

To compare empirical and mechanistic modeling approaches for describing HIV-1 RNA viral load trajectories after antiretroviral treatment interruption and for identifying factors that predict features of viral rebound process.

METHODS

We apply and compare two modeling approaches in analysis of data from 346 participants in six AIDS Clinical Trial Group studies. From each separate analysis, we identify predictors for viral set points and delay in rebound. Our empirical model postulates a parametric functional form whose parameters represent different features of the viral rebound process, such as rate of rise and viral load set point. The viral dynamics model augments standard HIV dynamics models-a class of mathematical models based on differential equations describing biological mechanisms-by including reactivation of latently infected cells and adaptive immune response. We use Monolix, which makes use of a Stochastic Approximation of the Expectation-Maximization algorithm, to fit non-linear mixed effects models incorporating observations that were below the assay limit of quantification.

RESULTS

Among the 346 participants, the median age at treatment interruption was 42. Ninety-three percent of participants were male and sixty-five percent, white non-Hispanic. Both models provided a reasonable fit to the data and can accommodate atypical viral load trajectories. The median set points obtained from two approaches were similar: 4.44 log10 copies/mL from the empirical model and 4.59 log10 copies/mL from the viral dynamics model. Both models revealed that higher nadir CD4 cell counts and ART initiation during acute/recent phase were associated with lower viral set points and identified receiving a non-nucleoside reverse transcriptase inhibitor (NNRTI)-based pre-ATI regimen as a predictor for a delay in rebound.

CONCLUSION

Although based on different sets of assumptions, both models lead to similar conclusions regarding features of viral rebound process.

A flexible nonlinear mixed effects model for HIV viral load rebound after treatment interruption

Characterization of HIV viral rebound after the discontinuation of antiretroviral therapy is central to HIV cure research. We propose a parametric nonlinear mixed effects model for the viral rebound trajectory, which often has a rapid rise to a peak value followed by a decrease to a viral load set point. We choose a flexible functional form that captures the shapes of viral rebound trajectories and can also provide biological insights regarding the rebound process. Each parameter can incorporate a random effect to allow for variation in parameters across individuals. Key features of viral rebound trajectories such as viral set points are represented by the parameters in the model, which facilitates assessment of intervention effects and identification of important pretreatment interruption predictors for these features. We employ a stochastic expectation-maximization (StEM) algorithm to incorporate HIV-1 RNA values that are below the lower limit of assay quantification. We evaluate the performance of our model in simulation studies and apply the proposed model to longitudinal HIV-1 viral load data from five AIDS Clinical Trials Group treatment interruption studies.

Quantile regression-based Bayesian joint modeling analysis of longitudinal-survival data, with application to an AIDS cohort study

In longitudinal studies, it is of interest to investigate how repeatedly measured markers are associated with time to an event. Joint models have received increasing attention on analyzing such complex longitudinal-survival data with multiple data features, but most of them are mean regression-based models. This paper formulates a quantile regression (QR) based joint models in general forms that consider left-censoring due to the limit of detection, covariates with measurement errors and skewness. The joint models consist of three components: (i) QR-based nonlinear mixed-effects Tobit model using asymmetric Laplace distribution for response dynamic process; (ii) nonparametric linear mixed-effects model with skew-normal distribution for mismeasured covariate; and (iii) Cox proportional hazard model for event time. For the purpose of simultaneously estimating model parameters, we propose a Bayesian method to jointly model the three components which are linked through the random effects. We apply the proposed modeling procedure to analyze the Multicenter AIDS Cohort Study data, and assess the performance of the proposed models and method through simulation studies. The findings suggest that our QR-based joint models may provide comprehensive understanding of heterogeneous outcome trajectories at different quantiles, and more reliable and robust results if the data exhibits these features.

Differential decay of intact and defective proviral DNA in HIV-1-infected individuals on suppressive antiretroviral therapy

BACKGROUNDThe relative stabilities of the intact and defective HIV genomes over time during effective antiretroviral therapy (ART) have not been fully characterized.METHODSWe used the intact proviral DNA assay (IPDA) to estimate the rate of change of intact and defective proviruses in HIV-infected adults on ART. We used linear spline models with a knot at seven years and a random intercept and slope up to the knot. We estimated the influence of covariates on rates of change.RESULTSWe studied 81 individuals for a median of 7.3 (IQR 5.9-9.6) years. Intact genomes declined more rapidly from initial suppression through seven years (15.7% per year decline; 95% CI -22.8%, -8.0%) and more slowly after seven years (3.6% per year; 95% CI -8.1%, +1.1%). The estimated half-life of the reservoir was 4.0 years (95% CI 2.7-8.3) until year seven and 18.7 years (95% CI 8.2-infinite) thereafter. There was substantial variability between individuals in the rate of decline until year seven. Intact provirus declined more rapidly than defective provirus (P < 0.001) and showed a faster decline in individuals with higher CD4+ T cell nadirs.CONCLUSIONThe biology of the replication-competent (intact) reservoir differs from that of the replication-incompetent (non-intact) pool of proviruses. The IPDA will likely be informative when investigating the impact of interventions targeting the reservoir.FUNDINGDelaney AIDS Research Enterprise, UCSF/Gladstone Institute of Virology & Immunology CFAR, CFAR Network of Integrated Systems, amfAR Institute for HIV Cure Research, I4C and Beat-HIV Collaboratories, Howard Hughes Medical Institute, Gilead Sciences, Bill and Melinda Gates Foundation.

ushr: Understanding suppression of HIV in R

BACKGROUND

HIV/AIDS is responsible for the deaths of one million people every year. Although mathematical modeling has provided many insights into the dynamics of HIV infection, there is still a lack of accessible tools for researchers unfamiliar with modeling techniques to apply them to their own clinical data.

RESULTS

Here we present ushr, a free and open-source R package that models the decline of HIV during antiretroviral treatment (ART) using a popular mathematical framework. ushr can be applied to longitudinal data of viral load measurements, and provides processing tools to prepare it for computational analysis. By mathematically fitting the data, important biological parameters can then be estimated, including the lifespans of short and long-lived infected cells, and the time to reach viral suppression below a defined detection threshold. The package also provides visualization and summary tools for fast assessment of model results.

CONCLUSIONS

ushr enables researchers without a strong mathematical or computational background to model the dynamics of HIV using longitudinal clinical data. Increasing accessibility to such methods may facilitate quantitative analysis across a broader range of independent studies, so that greater insights on HIV infection and treatment dynamics may be gained.

A novel quantification of information for longitudinal data analyzed by mixed-effects modeling

Nonlinear mixed-effects (NLME) modeling is one of the most powerful tools for analyzing longitudinal data especially under the sparse sampling design. The determinant of the Fisher information matrix is a commonly used global metric of the information that can be provided by the data under a given model. However, in clinical studies, it is also important to measure how much information the data provide for a certain parameter of interest under the assumed model, for example, the clearance in population pharmacokinetic models. This paper proposes a new, easy-to-interpret information metric, the "relative information" (RI), which is designed for specific parameters of a model and takes a value between 0% and 100%. We establish the relationship between interindividual variability for a specific parameter and the variance of the associated parameter estimator, demonstrating that, under a "perfect" experiment (eg, infinite samples or/and minimum experimental error), the RI and the variance of the model parameter estimator converge, respectively, to 100% and the ratio of the interindividual variability for that parameter and the number of subjects. Extensive simulation experiments and analyses of three real datasets show that our proposed RI metric can accurately characterize the information for parameters of interest for NLME models. The new information metric can be readily used to facilitate study designs and model diagnosis.

A quick and accurate method for the estimation of covariate effects based on empirical Bayes estimates in mixed-effects modeling: Correction of bias due to shrinkage

Nonlinear mixed-effects modeling is a popular approach to describe the temporal trajectory of repeated measurements of clinical endpoints collected over time in clinical trials, to distinguish the within-subject and the between-subject variabilities, and to investigate clinically important risk factors (covariates) that may partly explain the between-subject variability. Due to the complex computing algorithms involved in nonlinear mixed-effects modeling, estimation of covariate effects is often time-consuming and error-prone owing to local convergence. We develop a fast and accurate estimation method based on empirical Bayes estimates from the base mixed-effects model without covariates, and simple regressions outside of the nonlinear mixed-effect modeling framework. Application of the method is illustrated using a pharmacokinetic dataset from an anticoagulation drug for the prevention of major cardiovascular events in patients with acute coronary syndrome. Both the application and extensive simulations demonstrated that the performance of this high-throughput method is comparable to the commonly used maximum likelihood estimation in nonlinear mixed-effects modeling.

Mixed Effects Models with Censored Covariates, with Applications in HIV/AIDS Studies

Mixed effects models are widely used for modelling clustered data when there are large variations between clusters, since mixed effects models allow for cluster-specific inference. In some longitudinal studies such as HIV/AIDS studies, it is common that some time-varying covariates may be left or right censored due to detection limits, may be missing at times of interest, or may be measured with errors. To address these “incomplete data“ problems, a common approach is to model the time-varying covariates based on observed covariate data and then use the fitted model to “predict” the censored or missing or mismeasured covariates. In this article, we provide a review of the common approaches for censored covariates in longitudinal and survival response models and advocate nonlinear mechanistic covariate models if such models are available.

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.

Probability of atrial fibrillation after ablation: Using a parametric nonlinear temporal decomposition mixed effects model

Atrial fibrillation is an arrhythmic disorder where the electrical signals of the heart become irregular. The probability of atrial fibrillation (binary response) is often time varying in a structured fashion, as is the influence of associated risk factors. A generalized nonlinear mixed effects model is presented to estimate the time-related probability of atrial fibrillation using a temporal decomposition approach to reveal the pattern of the probability of atrial fibrillation and their determinants. This methodology generalizes to patient-specific analysis of longitudinal binary data with possibly time-varying effects of covariates and with different patient-specific random effects influencing different temporal phases. The motivation and application of this model is illustrated using longitudinally measured atrial fibrillation data obtained through weekly trans-telephonic monitoring from an NIH sponsored clinical trial being conducted by the Cardiothoracic Surgery Clinical Trials Network.

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.

Bayesian quantile regression-based partially linear mixed-effects joint models for longitudinal data with multiple features

In longitudinal AIDS studies, it is of interest to investigate the relationship between HIV viral load and CD4 cell counts, as well as the complicated time effect. Most of common models to analyze such complex longitudinal data are based on mean-regression, which fails to provide efficient estimates due to outliers and/or heavy tails. Quantile regression-based partially linear mixed-effects models, a special case of semiparametric models enjoying benefits of both parametric and nonparametric models, have the flexibility to monitor the viral dynamics nonparametrically and detect the varying CD4 effects parametrically at different quantiles of viral load. Meanwhile, it is critical to consider various data features of repeated measurements, including left-censoring due to a limit of detection, covariate measurement error, and asymmetric distribution. In this research, we first establish a Bayesian joint models that accounts for all these data features simultaneously in the framework of quantile regression-based partially linear mixed-effects models. The proposed models are applied to analyze the Multicenter AIDS Cohort Study (MACS) data. Simulation studies are also conducted to assess the performance of the proposed methods under different scenarios.

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 joint analysis of heterogeneous- and skewed-longitudinal data and a binary outcome, with application to AIDS clinical studies

In medical studies, heterogeneous- and skewed-longitudinal data with mis-measured covariates are often observed together with a clinically important binary outcome. A finite mixture of joint models is currently used to fit heterogeneous-longitudinal data and binary outcome, in which these two parts are connected by the individual latent class membership. The skew distributions, such as skew-normal and skew-t, have shown beneficial in dealing with asymmetric data in various applications in literature. However, there has been relatively few studies concerning joint modeling of heterogeneous- and skewed-longitudinal data and a binary outcome. In this article, we propose a joint model in which a flexible finite mixture of nonlinear mixed-effects models with skew distributions is connected with binary logistic model by a latent class membership indicator. Simulation studies are conducted to assess the performance of the proposed models and method, and a real example from an AIDS clinical trial study illustrates the methodology by modeling the viral dynamics to compare potential models with different distribution specifications; the analysis results are reported.

Bayesian quantile regression for nonlinear mixed-effects joint models for longitudinal data in the presence of mismeasured covariate errors

Quantile regression (QR) models have recently received increasing attention in longitudinal studies where measurements of the same individuals are taken repeatedly over time. When continuous (longitudinal) responses follow a distribution that is quite different from a normal distribution, usual mean regression (MR)-based linear models may fail to produce efficient estimators, whereas QR-based linear models may perform satisfactorily. To the best of our knowledge, there have been very few studies on QR-based nonlinear models for longitudinal data in comparison to MR-based nonlinear models. In this article, we study QR-based nonlinear mixed-effects (NLME) joint models for longitudinal data with non-central location and outliers and/or heavy tails in response, and non-normality and measurement errors in covariate under Bayesian framework. The proposed QR-based modeling method is compared with an MR-based one by an AIDS clinical dataset and through simulation studies. The proposed QR joint modeling approach can be not only applied to AIDS clinical studies, but also may have general applications in other fields as long as relevant technical specifications are met.

Parameter and state estimation in a Neisseria meningitidis model: A study case of Niger

Neisseria meningitidis (Nm) is a major cause of bacterial meningitidis outbreaks in Africa and the Middle East. The availability of yearly reported meningitis cases in the African meningitis belt offers the opportunity to analyze the transmission dynamics and the impact of control strategies. In this paper, we propose a method for the estimation of state variables that are not accessible to measurements and an unknown parameter in a Nm model. We suppose that the yearly number of Nm induced mortality and the total population are known inputs, which can be obtained from data, and the yearly number of new Nm cases is the model output. We also suppose that the Nm transmission rate is an unknown parameter. We first show how the recruitment rate into the population can be estimated using real data of the total population and Nm induced mortality. Then, we use an auxiliary system called observer whose solutions converge exponentially to those of the original model. This observer does not use the unknown infection transmission rate but only uses the known inputs and the model output. This allows us to estimate unmeasured state variables such as the number of carriers that play an important role in the transmission of the infection and the total number of infected individuals within a human community. Finally, we also provide a simple method to estimate the unknown Nm transmission rate. In order to validate the estimation results, numerical simulations are conducted using real data of Niger.

A Meta-analysis of MBL2 Polymorphisms and Tuberculosis Risk

MBL2 gene encodes mannose-binding lectin, is a member of innate immune system. Earlier studies revealed that MBL2 gene variants, rs1800451, rs1800450, rs5030737, rs7096206, rs11003125 and rs7095891 are associated with impaired serum level and susceptibility to TB, but their results are inconsistent. A meta-analysis was performed by including 22 studies (7095 TB-patients and 7662 controls) and data were analyzed with respect to associations between alleles, genotypes and minor allele carriers to evaluate the potential association between MBL2 polymorphisms and TB risk. Statistically significant results were found only for the homozygous variant genotype (CC vs. AA: p = 0.045; OR = 0.834, 95% CI = 0.699 to 0.996) of rs1800451 and showed reduced risk of TB in overall population. However, other genetic models of rs1800450, rs5030737, rs7096206, rs11003125, rs7095891 and combined rs1800450, rs1800451, rs5030737 polymorphisms of MBL2 gene did not reveal any association with TB risk. Stratified analysis by ethnicity showed decreased risk of TB in African population for rs1800450 and rs1800451. Whereas, no association was observed between other MBL2 polymorphisms and TB risk in all the evaluated ethnic populations. In conclusion, MBL2 rs1800450 and rs1800451 polymorphisms play a protective role in TB infection and reinforce their critical significance as a potential genetic marker for TB resistance.

Bayesian quantile regression-based nonlinear mixed-effects joint models for time-to-event and longitudinal data with multiple features

This article explores Bayesian joint models for a quantile of longitudinal response, mismeasured covariate and event time outcome with an attempt to (i) characterize the entire conditional distribution of the response variable based on quantile regression that may be more robust to outliers and misspecification of error distribution; (ii) tailor accuracy from measurement error, evaluate non-ignorable missing observations, and adjust departures from normality in covariate; and (iii) overcome shortages of confidence in specifying a time-to-event model. When statistical inference is carried out for a longitudinal data set with non-central location, non-linearity, non-normality, measurement error, and missing values as well as event time with being interval censored, it is important to account for the simultaneous treatment of these data features in order to obtain more reliable and robust inferential results. Toward this end, we develop Bayesian joint modeling approach to simultaneously estimating all parameters in the three models: quantile regression-based nonlinear mixed-effects model for response using asymmetric Laplace distribution, linear mixed-effects model with skew-t distribution for mismeasured covariate in the presence of informative missingness and accelerated failure time model with unspecified nonparametric distribution for event time. We apply the proposed modeling approach to analyzing an AIDS clinical data set and conduct simulation studies to assess the performance of the proposed joint models and method. Copyright © 2016 John Wiley & Sons, Ltd.

HIV-1-RNA Decay and Dolutegravir Concentrations in Semen of Patients Starting a First Antiretroviral Regimen

BACKGROUND

The objective of this study was to quantify human immunodeficiency virus (HIV) type 1 RNA decay and dolutegravir (DTG) concentrations in the semen of HIV-infected patients receiving DTG-based first-line therapy.

METHODS

This was a prospective, single-arm, open-label study including 15 HIV-1-infected, antiretroviral therapy-naive men starting once-daily treatment with DTG (50 mg) plus abacavir-lamivudine (600/300 mg). HIV-1 RNA was measured in seminal plasma (SP) and blood plasma (BP) at baseline, on days 3, 7, and 14, and at weeks 4, 12, and 24. The HIV-1 RNA decay rate was assessed using nonlinear mixed-effects models. Total and free DTG concentrations were quantified 24 hours after the dose at weeks 4 and 24 by means of a validated liquid chromatography-tandem mass spectrometry method.

RESULTS

Viral decay was faster in BP than in SP in the first decay phase (half-life, 4.5 vs 8.6 days; P = .001) with no statistically significant differences in the second phase. HIV-1 RNA suppression (<40 copies/mL) was reached earlier in SP (4 vs 12 weeks; P = .008) due to lower baseline HIV-1 RNA levels. The median total DTG 24 hours after the dose in SP was 119.1 ng/mL (range, 27.2-377 ng/mL), which represents 7.8% of BP exposure. The median DTG free-fraction in SP was 48% of the total drug. Seminal protein-unbound DTG concentrations exceeded the in vitro 50% inhibitory concentration (0.21 ng/mL) by a median of 214-fold.

CONCLUSIONS

DTG concentrations in SP are sufficient to contribute to rapid seminal HIV-1 RNA suppression.

Predicting virological decay in patients starting combination antiretroviral therapy

OBJECTIVE

Model trajectories of viral load measurements from time of starting combination antiretroviral therapy (cART), and use the model to predict whether patients will achieve suppressed viral load (≤200 copies/ml) within 6-months of starting cART.

DESIGN

Prospective cohort study including HIV-positive adults (UK Collaborative HIV Cohort Study).

METHODS

Eligible patients were antiretroviral naive and started cART after 1997. Random effects models were used to estimate viral load trends. Patients were randomly selected to form a validation dataset with those remaining used to fit the model. We evaluated predictions of suppression using indices of diagnostic test performance.

RESULTS

Of 9562 eligible patients 6435 were used to fit the model and 3127 for validation. Mean log10 viral load trajectories declined rapidly during the first 2 weeks post-cART, moderately between 2 weeks and 3 months, and more slowly thereafter. Higher pretreatment viral load predicted steeper declines, whereas older age, white ethnicity, and boosted protease inhibitor/non-nucleoside reverse transcriptase inhibitors based cART-regimen predicted a steeper decline from 3 months onwards. Specificity of predictions and the diagnostic odds ratio substantially improved when predictions were based on viral load measurements up to the 4-month visit compared with the 2 or 3-month visits. Diagnostic performance improved when suppression was defined by two consecutive suppressed viral loads compared with one.

CONCLUSIONS

Viral load measurements can be used to predict if a patient will be suppressed by 6-month post-cART. Graphical presentations of this information could help clinicians decide the optimum time to switch treatment regimen during the first months of cART.

A multiphase non-linear mixed effects model: An application to spirometry after lung transplantation

In medical sciences, we often encounter longitudinal temporal relationships that are non-linear in nature. The influence of risk factors may also change across longitudinal follow-up. A system of multiphase non-linear mixed effects model is presented to model temporal patterns of longitudinal continuous measurements, with temporal decomposition to identify the phases and risk factors within each phase. Application of this model is illustrated using spirometry data after lung transplantation using readily available statistical software. This application illustrates the usefulness of our flexible model when dealing with complex non-linear patterns and time-varying coefficients.

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.

Meta-analysis reveals PTPN22 1858C/T polymorphism confers susceptibility to rheumatoid arthritis in Caucasian but not in Asian population

The PTPN22 1858C/T polymorphism is associated with rheumatoid arthritis (RA). However, reports from the Asian populations are conflicting in nature and lacks consensus. The aim of our study was to evaluate the association between the PTPN22 1858C/T polymorphism and RA in Asian and Caucasian subjects by carrying out a meta-analysis of Asian and Caucasian data. A total of 27 205 RA cases and 27 677 controls were considered in the present meta-analysis involving eight Asian and 35 Caucasian studies. The pooled odds ratios (ORs) were performed for the allele, dominant, and recessive genetic model. No statistically significant association was found between the PTPN22 1858C/T polymorphism and risk of RA in Asian population (allele genetic model: OR = 1.217, 95% confidence interval (CI) = 0.99-1.496, p value 0.061; dominant genetic model: OR = 1.238, 95% CI = 0.982-1.562, p value 0.071; recessive genetic model: OR = 1.964, 95% CI = 0.678-5.693, p value 0.213). A significant association with risk of RA in Caucasian population suggesting that T-- allele does confer susceptibility to RA in this subgroup was observed (allele genetic model: OR = 1.638, 95% CI = 1.574-1.705, p value < 0.0001; dominant genetic model: OR = 1.67, 95% CI = 1.598-1.745, p value < 0.0001; recessive genetic model: OR = 2.65, 95% CI = 2.273-3.089, p value < 0.0001). The PTPN22 1858C/T polymorphism is not associated with RA risk in Asian populations. However, our meta-analysis confirms that the PTPN22 1858C/T polymorphism is associated with RA susceptibility in Caucasians.

Tumor necrosis factor (TNF)-α -308G/A (rs1800629) polymorphism distribution in North India and its association with pemphigus: Case-control study and meta-analysis

Pemphigus is an autoimmune blistering disorder of skin and/or mucosal surfaces characterized by intraepithelial lesions and immunoglobulin-G autoantibodies against desmogleins (proteins critical in cell-to-cell adhesion). Genetic, immunological, hormonal, and environmental factors are known to contribute to its etiology. Tumor necrosis factor-alpha (TNF-α) which plays a key role in pathogenesis of many infectious and inflammatory diseases has been found in high levels in lesional skin and sera of pemphigus patients. However, studies on association of single nucleotide polymorphism (SNP) in promoter region of TNF-α at position -308 affecting G to A transition with pemphigus has been scarce. This study was conducted to evaluate the TNF-α -308G/A SNP distribution in North Indian cohort, and to define the association between the TNF-α -308G/A SNP distribution and pemphigus, globally, by means of meta-analysis. TNF-α -308G/A SNP in pemphigus patients was investigated by cytokine genotyping using genomic DNA by PCR with sequence-specific primers. Meta-analysis of the data, including four previously published studies from other populations, was performed to generate a meaningful relationship. The results of our case-control study indicate non-significant differences between patients and controls in TNF-α -308G/A SNP. The meta-analysis also revealed that TNF-α -308G/A SNP is not associated with pemphigus risk in population at large; however, it may be contributing towards autoimmune phenomenon in pemphigus by being a part of its multi-factorial etiology. This study provides evidence that the TNF-α -308G/A polymorphism is not associated with overall pemphigus susceptibility. Nevertheless, further studies on specific ethnicity and pemphigus variants are necessary to validate the findings.