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

Influence Analysis of Digital Financial Risk in China's Economically Developed Regions Under COVID-19: Based on the Skew-Normal Panel Data Model

The rapid spread of COVID-19 worldwide makes an uncertain impact on the development of digital finance in China. In this background, the measurement of digital financial risk and analysis of influence factor become the focus of the financial field. Therefore, this article builds the indicator system of digital financial risk and uses the Lagrange multiplier method to obtain the optimal comprehensive weight of AHP and entropy weight. Then, this article measures the digital financial risk indexes of China's major regions with high-level economic development from 2013 to 2020. Furthermore, the maximum likelihood estimates of the unknown parameters of skew-normal panel data model are obtained based on the EM algorithm, and the comparative study of the normal and skew-normal panel data models is conducted under AIC and BIC. Finally, based on the result of the model, the influence factors of digital financial risk of China's economically developed regions under COVID-19 are analyzed to provide data support for the prevention and governance of digital financial risk.

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.

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.

Testing multiple hypotheses with skewed alternatives

In many practical cases of multiple hypothesis problems, it can be expected that the alternatives are not symmetrically distributed. If it is known a priori that the distributions of the alternatives are skewed, we show that this information yields high power procedures as compared to the procedures based on symmetric alternatives when testing multiple hypotheses. We propose a Bayesian decision theoretic rule for multiple directional hypothesis testing, when the alternatives are distributed as skewed, under a constraint on a mixed directional false discovery rate. We compare the proposed rule with a frequentist's rule of Benjamini and Yekutieli (2005) using simulations. We apply our method to a well-studied HIV dataset.

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 analysis of nonlinear mixed-effects mixture models for longitudinal data with heterogeneity and skewness

It is a common practice to analyze complex longitudinal data using nonlinear mixed-effects (NLME) models with normality assumption. The NLME models with normal distributions provide the most popular framework for modeling continuous longitudinal outcomes, assuming individuals are from a homogeneous population and relying on random-effects to accommodate inter-individual variation. However, the following two issues may standout: (i) normality assumption for model errors may cause lack of robustness and subsequently lead to invalid inference and unreasonable estimates, particularly, if the data exhibit skewness and (ii) a homogeneous population assumption may be unrealistically obscuring important features of between-subject and within-subject variations, which may result in unreliable modeling results. There has been relatively few studies concerning longitudinal data with both heterogeneity and skewness features. In the last two decades, the skew distributions have shown beneficial in dealing with asymmetric data in various applications. In this article, our objective is to address the simultaneous impact of both features arisen from longitudinal data by developing a flexible finite mixture of NLME models with skew distributions under Bayesian framework that allows estimates of both model parameters and class membership probabilities for longitudinal data. Simulation studies are conducted to assess the performance of the proposed models and methods, and a real example from an AIDS clinical trial illustrates the methodology by modeling the viral dynamics to compare potential models with different distribution specifications; the analysis results are reported.

SNP_NLMM: A SAS Macro to Implement a Flexible Random Effects Density for Generalized Linear and Nonlinear Mixed Models

Generalized linear and nonlinear mixed models (GMMMs and NLMMs) are commonly used to represent non-Gaussian or nonlinear longitudinal or clustered data. A common assumption is that the random effects are Gaussian. However, this assumption may be unrealistic in some applications, and misspecification of the random effects density may lead to maximum likelihood parameter estimators that are inconsistent, biased, and inefficient. Because testing if the random effects are Gaussian is difficult, previous research has recommended using a flexible random effects density. However, computational limitations have precluded widespread use of flexible random effects densities for GLMMs and NLMMs. We develop a SAS macro, SNP_NLMM, that overcomes the computational challenges to fit GLMMs and NLMMs where the random effects are assumed to follow a smooth density that can be represented by the seminonparametric formulation proposed by Gallant and Nychka (1987). The macro is flexible enough to allow for any density of the response conditional on the random effects and any nonlinear mean trajectory. We demonstrate the SNP_NLMM macro on a GLMM of the disease progression of toenail infection and on a NLMM of intravenous drug concentration over time.

Segmental modeling of viral load changes for HIV longitudinal data with skewness and detection limits

Although it is a common practice to analyze complex HIV longitudinal data using nonlinear mixed-effects or nonparametric mixed-effects models in literature, the following issues may standout. (i) In clinical practice, the profile of each subject's viral response may follow a 'broken-stick'-like trajectory, indicating multiple phases of decline and increase in response. Such multiple phases (change points) may be an important indicator to help quantify treatment effect and improve management of patient care. To estimate change points, nonlinear mixed-effects or nonparametric mixed-effects models become a challenge because of complicated structures of model formulations. (ii) The commonly assumed distribution for model random errors is normal, but this assumption may unrealistically obscure important features of subject variations. (iii) The response observations (viral load) may be subject to left censoring due to a limit of detection. Inferential procedures can be complicated dramatically when data with asymmetric (skewed) characteristics and left censoring are observed in conjunction with change points as unknown parameters into models. There is relatively little work concerning all these features simultaneously. This article proposes segmental mixed-effects models with skew distributions for the response process (with left censoring) under a Bayesian framework. A real data example is used to illustrate the proposed methods.

Skew-normal/independent linear mixed models for censored responses with applications to HIV viral loads

Often in biomedical studies, the routine use of linear mixed-effects models (based on Gaussian assumptions) can be questionable when the longitudinal responses are skewed in nature. Skew-normal/elliptical models are widely used in those situations. Often, those skewed responses might also be subjected to some upper and lower quantification limits (QLs; viz., longitudinal viral-load measures in HIV studies), beyond which they are not measurable. In this paper, we develop a Bayesian analysis of censored linear mixed models replacing the Gaussian assumptions with skew-normal/independent (SNI) distributions. The SNI is an attractive class of asymmetric heavy-tailed distributions that includes the skew-normal, skew-t, skew-slash, and skew-contaminated normal distributions as special cases. The proposed model provides flexibility in capturing the effects of skewness and heavy tail for responses that are either left- or right-censored. For our analysis, we adopt a Bayesian framework and develop a Markov chain Monte Carlo algorithm to carry out the posterior analyses. The marginal likelihood is tractable, and utilized to compute not only some Bayesian model selection measures but also case-deletion influence diagnostics based on the Kullback-Leibler divergence. The newly developed procedures are illustrated with a simulation study as well as an HIV case study involving analysis of longitudinal viral loads.

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.

Combining structural and functional measurements to improve detection of glaucoma progression using Bayesian hierarchical models

PURPOSE

To present and evaluate a new methodology for combining longitudinal information from structural and functional tests to improve detection of glaucoma progression and estimation of rates of change.

METHODS

This observational cohort study included 434 eyes of 257 participants observed for an average of 4.2 ± 1.1 years and recruited from the Diagnostic Innovations in Glaucoma Study (DIGS). The subjects were examined annually with standard automated perimetry, optic disc stereophotographs, and scanning laser polarimetry with enhanced corneal compensation. Rates of change over time were measured using the visual field index (VFI) and average retinal nerve fiber layer thickness (TSNIT average). A bayesian hierarchical model was built to integrate information from the longitudinal measures and classify individual eyes as progressing or not. Estimates of sensitivity and specificity of the bayesian method were compared with those obtained by the conventional approach of ordinary least-squares (OLS) regression.

RESULTS

The bayesian method identified a significantly higher proportion of the 405 glaucomatous and suspect eyes as having progressed when compared with the OLS method (22.7% vs. 12.8%; P < 0.001), while having the same specificity of 100% in 29 healthy eyes. In addition, the bayesian method identified a significantly higher proportion of eyes with progression by optic disc stereophotographs compared with the OLS method (74% vs. 37%; P = 0.001).

CONCLUSIONS

A bayesian hierarchical modeling approach for combining functional and structural tests performed significantly better than the OLS method for detection of glaucoma progression. (ClinicalTrials.gov number, NCT00221897.).