Mixtures of Self-Modelling Regressions

A shape invariant model for functions f1,...,fn specifies that each individual function fi can be related to a common shape function g through the relation fi(x) = aig(cix + di) + bi. We consider a flexible mixture model that allows multiple shape functions g1,...,gK, where each fi is a shape invariant transformation of one of those gK. We derive an MCMC algorithm for fitting the model using Bayesian Adaptive Regression Splines (BARS), propose a strategy to improve its mixing properties and utilize existing model selection criteria in semiparametric mixtures to select the number of distinct shape functions. We discuss some of the computational difficulties that arise. The method is illustrated using synaptic transmission data, where the groups of functions may indicate different active zones in a synapse

Semiparametric Mixed Models for Nested Repeated Measures Applied to Ambulatory Blood Pressure Monitoring Data

Semiparametric mixed models are increasingly popular for statistical analysis of medical device studies in which long sequences of repeated measurements are recorded. Monitoring these sequences at different periods over time on the same individual, such as before and after an intervention, results in nested repeated measures (NRM). Covariance models to account for NRM and simultaneously address mean profile estimation with penalized splines via semiparametric regression are considered with application to a prospective study of 24-hour ambulatory blood pressure and the impact of surgical intervention on obstructive sleep apnea

Flexible semiparametric joint modeling: an application to estimate individual lung function decline and risk of pulmonary exacerbations in cystic fibrosis.

BACKGROUND: Epidemiologic surveillance of lung function is key to clinical care of individuals with cystic fibrosis, but lung function decline is nonlinear and often impacted by acute respiratory events known as pulmonary exacerbations. Statistical models are needed to simultaneously estimate lung function decline while providing risk estimates for the onset of pulmonary exacerbations, in order to identify relevant predictors of declining lung function and understand how these associations could be used to predict the onset of pulmonary exacerbations. METHODS: Using longitudinal lung function (FEV1) measurements and time-to-event data on pulmonary exacerbations from individuals in the United States Cystic Fibrosis Registry, we implemented a flexible semiparametric joint model consisting of a mixed-effects submodel with regression splines to fit repeated FEV1 measurements and a time-to-event submodel for possibly censored data on pulmonary exacerbations. We contrasted this approach with methods currently used in epidemiological studies and highlight clinical implications. RESULTS: The semiparametric joint model had the best fit of all models examined based on deviance information criterion. Higher starting FEV1 implied more rapid lung function decline in both separate and joint models; however, individualized risk estimates for pulmonary exacerbation differed depending upon model type. Based on shared parameter estimates from the joint model, which accounts for the nonlinear FEV1 trajectory, patients with more positive rates of change were less likely to experience a pulmonary exacerbation (HR per one standard deviation increase in FEV1 rate of change = 0.566, 95% CI 0.516-0.619), and having higher absolute FEV1 also corresponded to lower risk of having a pulmonary exacerbation (HR per one standard deviation increase in FEV1 = 0.856, 95% CI 0.781-0.937). At the population level, both submodels indicated significant effects of birth cohort, socioeconomic status and respiratory infections on FEV1 decline, as well as significant effects of gender, socioeconomic status and birth cohort on pulmonary exacerbation risk. CONCLUSIONS: Through a flexible joint-modeling approach, we provide a means to simultaneously estimate lung function trajectories and the risk of pulmonary exacerbations for individual patients; we demonstrate how this approach offers additional insights into the clinical course of cystic fibrosis that were not possible using conventional approaches

Integrating latent classes in the Bayesian shared parameter joint model of longitudinal and survival outcomes

Cystic fibrosis is a chronic lung disease requiring frequent lung-function monitoring to track acute respiratory events (pulmonary exacerbations). The association between lung-function trajectory and time-to-first exacerbation can be characterized using joint longitudinal-survival modeling. Joint models specified through the shared parameter framework quantify the strength of association between such outcomes but do not incorporate latent sub-populations reflective of heterogeneous disease progression. Conversely, latent class joint models explicitly postulate the existence of sub-populations but do not directly quantify the strength of association. Furthermore, choosing the optimal number of classes using established metrics like deviance information criterion is computationally intensive in complex models. To overcome these limitations, we integrate latent classes in the shared parameter joint model through a fully Bayesian approach. To choose the optimal number of classes, we construct a mixture model assuming more latent classes than present in the data, thereby asymptotically “emptying” superfluous latent classes, provided the Dirichlet prior on class proportions is sufficiently uninformative. Model properties are evaluated in simulation studies. Application to data from the US Cystic Fibrosis Registry supports the existence of three sub-populations corresponding to lung-function trajectories with high initial forced expiratory volume in 1 s (FEV1), rapid FEV1 decline, and low but steady FEV1 progression. The association between FEV1 and hazard of exacerbation was negative in each class, but magnitude varied

Spiritual Struggle in Parents of Children with Cystic Fibrosis Increases Odds of Depression

Objective. Spiritual struggle (SS) is associated with poorer health outcomes including depression. The study’s main objectives were to characterize change in depression over time, examine longitudinal associations between SS and depression, and determine the extent to which experiencing SS at baseline was predictive of developing depression at follow-up. Methods. A two-site study collected questionnaire responses of parents (N=112; 72% female) of children with cystic fibrosis followed longitudinally. Generalized linear mixed effects modeling examined the association between depression and SS over time and assessed potential mediators, moderators, and confounders. Results. Prevalence of depression increased from baseline to follow-up (OR: 3.6, P<0.0001), regardless of degree of SS. Parents with Moderate/Severe SS were more likely to have depressive symptoms, compared to parents without SS (OR: 15.2, P=0.0003) and parents who had Mild SS (OR: 10.2, P=0.0001). Being female and feeling less “at peace” also significantly predicted increased depression (OR: 2.5, P=0.0397, and OR: 1.15, P=0.0419, resp.). Experiencing SS at baseline was not predictive of having depression subsequently at follow-up. Conclusions. Parents experiencing SS were significantly more likely to report depressive symptoms. Interventions to reduce SS have shown efficacy and may be considered

Efficiently analyzing large patient registries with Bayesian joint models for longitudinal and time-to-event data

The joint modeling of longitudinal and time-to-event outcomes has become a popular tool infollow-up studies. However, fitting Bayesian joint models to large datasets, such as patientregistries, can require extended computing times. To speed up sampling, we divided a patient registry dataset into subsamples, analyzed them in parallel, and combined the resultingMarkov chain Monte Carlo draws into a consensus distribution. We used a simulation studyto investigate how different consensus strategies perform with joint models. In particular,we compared grouping all draws together with using equal- and precision-weighted averages.We considered scenarios reflecting different sample sizes, numbers of data splits, and processor characteristics. Parallelization of the sampling process substantially decreased the timerequired to run the model. We found that the weighted-average consensus distributions forlarge sample sizes were nearly identical to the target posterior distribution. The proposedalgorithm has been made available in an R package for joint models, JMbayes2. This workwas motivated by the clinical interest in investigating the association between ppFEV1, acommonly measured marker of lung function, and the risk of lung transplant or death, using data from the US Cystic Fibrosis Foundation Patient Registry (35,153 individuals with372,366 years of cumulative follow-up). Splitting the registry into five subsamples resultedin an 85% decrease in computing time, from 9.22 to 1.39 hours. Splitting the data and finding a consensus distribution by precision-weighted averaging proved to be a computationallyefficient and robust approach to handling large datasets under the joint modeling framework

Efficiently analyzing large patient registries with Bayesian joint models for longitudinal and time-to-event data

The joint modeling of longitudinal and time-to-event outcomes has become a popular tool infollow-up studies. However, fitting Bayesian joint models to large datasets, such as patientregistries, can require extended computing times. To speed up sampling, we divided a patient registry dataset into subsamples, analyzed them in parallel, and combined the resultingMarkov chain Monte Carlo draws into a consensus distribution. We used a simulation studyto investigate how different consensus strategies perform with joint models. In particular,we compared grouping all draws together with using equal- and precision-weighted averages.We considered scenarios reflecting different sample sizes, numbers of data splits, and processor characteristics. Parallelization of the sampling process substantially decreased the timerequired to run the model. We found that the weighted-average consensus distributions forlarge sample sizes were nearly identical to the target posterior distribution. The proposedalgorithm has been made available in an R package for joint models, JMbayes2. This workwas motivated by the clinical interest in investigating the association between ppFEV1, acommonly measured marker of lung function, and the risk of lung transplant or death, using data from the US Cystic Fibrosis Foundation Patient Registry (35,153 individuals with372,366 years of cumulative follow-up). Splitting the registry into five subsamples resultedin an 85% decrease in computing time, from 9.22 to 1.39 hours. Splitting the data and finding a consensus distribution by precision-weighted averaging proved to be a computationallyefficient and robust approach to handling large datasets under the joint modeling framework