Semiparametric multivariate joint model for skewed-longitudinal and survival data: A Bayesian approach.

Joint models and statistical inference for longitudinal and survival data have been an active area of statistical research and have mostly coupled a longitudinal biomarker-based mixed-effects model with normal distribution and an event time-based survival model. In practice, however, the following issues may standout: (i) Normality of model error in longitudinal models is a routine assumption, but it may be unrealistically violating data features of subject variations. (ii) Data collected are often featured by the mixed types of multiple longitudinal outcomes which are significantly correlated, ignoring their correlation may lead to biased estimation. Additionally, a parametric model specification may be inflexible to capture the complicated patterns of longitudinal data. (iii) Missing observations in the longitudinal data are often encountered; the missing measures are likely to be informative (nonignorable) and ignoring this phenomenon may result in inaccurate inference. Multilevel item response theory (MLIRT) models have been increasingly used to analyze the multiple longitudinal data of mixed types (ie, continuous and categorical) in clinical studies. In this article, we develop an MLIRT-based semiparametric joint model with skew-t distribution that consists of an extended MLIRT model for the mixed types of multiple longitudinal data and a Cox proportional hazards model, linked through random-effects. A Bayesian approach is employed for joint modeling. Simulation studies are conducted to assess performance of the proposed models and method. A real example from primary biliary cirrhosis clinical study is analyzed to estimate parameters in the joint model and also evaluate sensitivity of parameter estimates for various plausible nonignorable missing data mechanisms.

Quantile-Adaptive Sufficient Variable Screening by Controlling False Discovery.

Sufficient variable screening rapidly reduces dimensionality with high probability in ultra-high dimensional modeling. To rapidly screen out the null predictors, a quantile-adaptive sufficient variable screening framework is developed by controlling the false discovery. Without any specification of an actual model, we first introduce a compound testing procedure based on the conditionally imputing marginal rank correlation at different quantile levels of response to select active predictors in high dimensionality. The testing statistic can capture sufficient dependence through two paths: one is to control false discovery adaptively and the other is to control the false discovery rate by giving a prespecified threshold. It is computationally efficient and easy to implement. We establish the theoretical properties under mild conditions. Numerical studies including simulation studies and real data analysis contain supporting evidence that the proposal performs reasonably well in practical settings.

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.

Estimation of the Outbreak Severity and Evaluation of Epidemic Prevention Ability of COVID-19 by Province in China.

Objectives. To compare the epidemic prevention ability of COVID-19 of each province in China and to evaluate the existing prevention and control capacity of each province.Methods. We established a quasi-Poisson linear mixed-effects model using the case data in cities outside Wuhan in Hubei Province, China. We adapted this model to estimate the number of potential cases in Wuhan and obtained epidemiological parameters. We estimated the initial number of cases in each province by using passenger flowrate data and constructed the extended susceptible-exposed-infectious-recovered model to predict the future disease transmission trends.Results. The estimated potential cases in Wuhan were about 3 times the reported cases. The basic reproductive number was 3.30 during the initial outbreak. Provinces with more estimated imported cases than reported cases were those in the surrounding provinces of Hubei, including Henan and Shaanxi. The regions where the number of reported cases was closer to the predicted value were most the developed areas, including Beijing and Shanghai.Conclusions. The number of confirmed cases in Wuhan was underestimated in the initial period of the outbreak. Provincial surveillance and emergency response capabilities vary across the country.

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.

Recurrence of Genital Infections With 9 Human Papillomavirus (HPV) Vaccine Types (6, 11, 16, 18, 31, 33, 45, 52, and 58) Among Men in the HPV Infection in Men (HIM) Study.

Background: The purpose of this study was to assess genital recurrence of human papillomavirus (HPV) genotypes included in the 9-valent vaccine and to investigate factors associated with recurrence among men in the HPV Infection in Men (HIM) Study. Methods: Men were followed every 6 months for a median of 3.7 years. HPV genotypes were detected using Roche linear array. Factors associated with type-specific HPV recurrence (infections occurring after a ≥12-month infection-free period) were assessed. Results: In type-specific analyses, 31% of prior prevalent and 20% of prior incident infections recurred. Among prevalent infections, HPV types 52, 45, 16, 58, and 6 and among incident infections, HPV types 58, 52, 18, 16, and 11 had the highest rates of recurrence. New sexual partners (male or female) and frequency of sexual intercourse with female partners were associated with HPV-6, -16, -31, and -58 infection recurrence. In grouped analyses, lifetime and new male sexual partners were associated with recurrence of prior incident infection with any of the 9 HPV types. Conclusions: Recurrence of genital HPV infections is relatively common among men and associated with high-risk sexual behavior. Further studies are needed to understand the role of HPV recurrence in the etiology of HPV-associated diseases.

Joint model-based clustering of nonlinear longitudinal trajectories and associated time-to-event data analysis, linked by latent class membership: with application to AIDS clinical studies.

Longitudinal and time-to-event data are often observed together. Finite mixture models are currently used to analyze nonlinear heterogeneous longitudinal data, which, by releasing the homogeneity restriction of nonlinear mixed-effects (NLME) models, can cluster individuals into one of the pre-specified classes with class membership probabilities. This clustering may have clinical significance, and be associated with clinically important time-to-event data. This article develops a joint modeling approach to a finite mixture of NLME models for longitudinal data and proportional hazard Cox model for time-to-event data, linked by individual latent class indicators, under a Bayesian framework. The proposed joint models and method are applied to a real AIDS clinical trial data set, followed by simulation studies to assess the performance of the proposed joint model and a naive two-step model, in which finite mixture model and Cox model are fitted separately.

Generalizability analysis for clinical trials: a simulation study.

Subjects are rarely selected on a random basis from a well-defined patient population of interest into a clinical trial, with women, children, the elderly, and those with common comorbidities who are frequently underrepresented. Decades of clinical experience have demonstrated that the application of trial findings to individual patients is permissible by using efficacy as a measure of effectiveness and assuming that the characteristics of patients are sufficiently similar. In order to investigate this issue in greater depth, we simulated a patient population with treatment effect size of 0.5 (Cohen's d) and five covariates that included gender, health insurance, comorbidity, age, and motivation. To demonstrate how selection of patients for a clinical trial can bias the results when treatment effect varies across individuals, we created 50 nonrandom clinical trials based on this patient population and showed relative bias to range from 1.68% to 99.70%. We calculated and evaluated three indexes: C-statistics, standardized mean difference (SMD), and Tipton's index (ß) of generalization for the 50 nonrandom trials. Findings indicated that (i) the ranges were 0.56-0.98, 0.23-11.17, and 0.99-0.73 for C-statistics, SMD, and ß, respectively, when treatment effect bias increased from 1.68% to 99.70% and (ii) C-statistics < 0.86, SMD < 1.95, and ß > 0.91 when treatment effect bias <50%. Recommendations are made using existing generalization indexes on the basis of our simulation results. An example from a real clinical trial is provided for illustration. Copyright © 2017 John Wiley & Sons, Ltd.

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.

Sequential Acquisition of Anal Human Papillomavirus (HPV) Infection Following Genital Infection Among Men Who Have Sex With Women: The HPV Infection in Men (HIM) Study.

BACKGROUND: The purpose of this study was to assess the risk of sequential acquisition of anal human papillomavirus (HPV) infection following a type-specific genital HPV infection for the 9-valent vaccine HPV types and investigate factors associated with sequential infection among men who have sex with women (MSW). METHODS: Genital and anal specimens were available for 1348 MSW participants, and HPV genotypes were detected using the Roche Linear Array assay. Sequential risk of anal HPV infection was assessed using hazard ratios (HRs) among men with prior genital infection, compared with men with no prior genital infection, in individual HPV type and grouped HPV analyses. RESULTS: In individual analyses, men with prior HPV 16 genital infections had a significantly higher risk of subsequent anal HPV 16 infections (HR, 4.63; 95% confidence interval [CI], 1.41-15.23). In grouped analyses, a significantly higher risk of sequential type-specific anal HPV infections was observed for any of the 9 types (adjusted HR, 2.80; 95% CI, 1.32-5.99), high-risk types (adjusted HR, 2.65; 95% CI, 1.26, 5.55), and low-risk types (adjusted HR, 5.89; 95% CI, 1.29, 27.01). CONCLUSIONS: MSW with prior genital HPV infections had a higher risk of a subsequent type-specific anal infection. The higher risk was not explained by sexual intercourse with female partners. Autoinoculation is a possible mechanism for the observed association.

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.

A mixture of hierarchical joint models for longitudinal data with heterogeneity, non-normality, missingness, and covariate measurement error.

Longitudinal data arise frequently in medical studies and it is a common practice to analyze such complex data with nonlinear mixed-effects (NLME) models. However, the following four issues may be critical in longitudinal data analysis. (i) A homogeneous population assumption for models may be unrealistically obscuring important features of between-subject and within-subject variations; (ii) normality assumption for model errors may not always give robust and reliable results, in particular, if the data exhibit skewness; (iii) the responses may be missing and the missingness may be nonignorable; and (iv) some covariates of interest may often be measured with substantial errors. When carrying out statistical inference in such settings, it is important to account for the effects of these data features; otherwise, erroneous or even misleading results may be produced. Inferential procedures can be complicated dramatically when these four data features arise. In this article, the Bayesian joint modeling approach based on a finite mixture of NLME joint models with skew distributions is developed to study simultaneous impact of these four data features, allowing estimates of both model parameters and class membership probabilities at population and individual levels. A real data example is analyzed to demonstrate the proposed methodologies, and to compare various scenarios-based potential models with different specifications of distributions.

Impact of Adolescent Personality Disorders on Obesity 17 Years Later.

OBJECTIVES: To investigate associations between adolescent personality disorder (PD) and obesity 17 years later. METHODS: The Children in the Community is a longitudinal study based on a randomly sampled cohort of families, in effect since 1975. PDs were assessed in youths by self-report and mother report in 1985 to 1986, when participants were at an average age of 16 years. Obesity was assessed in 2001 to 2004 when participants were an average age of 33 years (n = 621). RESULTS: Prevalence of obesity was 16.59% (103/621) at an average age of 33 years. Prevalence of any adolescent PD was 17.55% (109/621) at an average age of 16 years. Adolescents who had any PD were 1.84 (95% confidence interval [CI] = 1.05-3.22) times as likely to be obese 17 years later after adjusting for demographic variables and known risk factors. Paranoid, histrionic, and obsessive-compulsive PDs in adolescence were significantly associated with obesity in adulthood, with odds ratios of 3.45 (95% CI = 1.46-8.17), 4.49 (95% CI = 1.91-10.53), and 6.80 (95% CI = 2.50-18.55), respectively. CONCLUSIONS: This is the first study to report a significant independent long-term association based on prospective data between adolescent PDs and adult obesity in a community-based sample. Findings will contribute to the design of preventive measures against the development of obesity.

A Bayesian mixture of semiparametric mixed-effects joint models for skewed-longitudinal and time-to-event data.

In longitudinal studies, it is of interest to investigate how repeatedly measured markers in time are associated with a time to an event of interest, and in the mean time, the repeated measurements are often observed with the features of a heterogeneous population, non-normality, and covariate measured with error because of longitudinal nature. Statistical analysis may complicate dramatically when one analyzes longitudinal-survival data with these features together. Recently, a mixture of skewed distributions has received increasing attention in the treatment of heterogeneous data involving asymmetric behaviors across subclasses, but there are relatively few studies accommodating heterogeneity, non-normality, and measurement error in covariate simultaneously arose in longitudinal-survival data setting. Under the umbrella of Bayesian inference, this article explores a finite mixture of semiparametric mixed-effects joint models with skewed distributions for longitudinal measures with an attempt to mediate homogeneous characteristics, adjust departures from normality, and tailor accuracy from measurement error in covariate as well as overcome shortages of confidence in specifying a time-to-event model. The Bayesian mixture of joint modeling offers an appropriate avenue to estimate not only all parameters of mixture joint models but also probabilities of class membership. Simulation studies are conducted to assess the performance of the proposed method, and a real example is analyzed to demonstrate the methodology. The results are reported by comparing potential models with various scenarios.

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.

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.

Jointly Modeling Event Time and Skewed-Longitudinal Data with Missing Response and Mismeasured Covariate for AIDS Studies.

In longitudinal studies it is often of interest to investigate how a repeatedly measured marker in time is associated with a time to an event of interest. This type of research question has given rise to a rapidly developing field of biostatistics research that deals with the joint modeling of longitudinal and time-to-event data. Normality of model errors in longitudinal model is a routine assumption, but it may be unrealistically obscuring important features of subject variations. Covariates are usually introduced in the models to partially explain between- and within-subject variations, but some covariates such as CD4 cell count may be often measured with substantial errors. Moreover, the responses may encounter nonignorable missing. Statistical analysis may be complicated dramatically based on longitudinal-survival joint models where longitudinal data with skewness, missing values, and measurement errors are observed. In this article, we relax the distributional assumptions for the longitudinal models using skewed (parametric) distribution and unspecified (nonparametric) distribution placed by a Dirichlet process prior, and address the simultaneous influence of skewness, missingness, covariate measurement error, and time-to-event process by jointly modeling three components (response process with missing values, covariate process with measurement errors, and time-to-event process) linked through the random-effects that characterize the underlying individual-specific longitudinal processes in Bayesian analysis. The method is illustrated with an AIDS study by jointly modeling HIV/CD4 dynamics and time to viral rebound in comparison with potential models with various scenarios and different distributional specifications.

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.

The efficacy of religious service attendance in reducing depressive symptoms.

PURPOSE: To examine whether religiosity may help people ward off depression, we investigated the association between religious service attendance and depressive symptom scores in a community-based 30-year follow-up longitudinal study. METHODS: This study used data on 754 subjects followed over 30 years and evaluated at four time points. Linear mixed effects models were used to assess the association between religious service attendance and depressive symptoms development; frequency of attendance and age also were used as predictors. Demographic factors, life-time trauma, family socioeconomic status, and recent negative events were considered as control variables. RESULTS: Depressive symptom scores were reduced by an average of 0.518 units (95 % CI from -0.855 to -0.180, p < 0.005) each year in subjects who attended religious services as compared with subjects who did not. The more frequent the religious service attendance, the stronger the influence on depressive symptoms when compared with non-attendance. Yearly, monthly, and weekly religious service attendance reduced depression scores by 0.474 (95 % CI from -0.841 to -0.106, p < 0.01), 0.495 (95 % CI from -0.933 to -0.057, p < 0.05) and 0.634 (95 % CI from -1.056 to -0.212, p < 0.005) units on average, respectively, when compared with non-attendance after controlling for other covariates. CONCLUSION: Religious service attendance may reduce depressive symptoms significantly, with more frequent attendance having an increasingly greater impact on symptom reduction in this 30-year community-based longitudinal study.

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.