Variable selection for joint models with time-varying coefficients

Many clinical studies collect longitudinal and survival data concurrently. Joint models combining these two types of outcomes through shared random effects are frequently used in practical data analysis. The standard joint models assume that the coefficients for the longitudinal and survival components are time-invariant. In many applications, the assumption is overly restrictive. In this research, we extend the standard joint model to include time-varying coefficients, in both longitudinal and survival components, and we present a data-driven method for variable selection. Specifically, we use a B-spline decomposition and penalized likelihood with adaptive group LASSO to select the relevant independent variables and to distinguish the time-varying and time-invariant effects for the two model components. We use Gaussian-Legendre and Gaussian-Hermite quadratures to approximate the integrals in the absence of closed-form solutions. Simulation studies show good selection and estimation performance. Finally, we use the proposed procedure to analyze data generated by a study of primary biliary cirrhosis.

Predicting Time to Reclassification for English Learners: A Joint Modeling Approach

The development of academic English proficiency and the time it takes to reclassify to fluent English proficient status are key issues in English learner (EL) policy. This article develops a shared random effects model (SREM) to estimate English proficiency development and time to reclassification simultaneously, treating student-specific random effects as latent covariates in the time to reclassification model. Using data from a large Arizona school district, the SREM resulted in predictions of time to reclassification that were 93% accurate compared to 85% accuracy from a conventional discrete-time hazard model used in prior literature. The findings suggest that information about English-language development is critical for accurately predicting the grade an EL will reclassify.

Longitudinal associations between different dementia diagnoses and medication use jointly accounting for dropout

ABSTRACTBackground:Longitudinal studies of older adults are characterized by high dropout rates, multimorbid conditions, and multiple medication use, especially proximal to death. We studied the association between multiple medication use and incident dementia diagnoses including Alzheimer's disease (AD), vascular dementia (VD), and Lewy-body dementia (LBD), simultaneously accounting for dropout.Methods:Using the National Alzheimer's Coordinating Center data with three years of follow-up, a set of covariate-adjusted models that ignore dropout was fit to complete-case data, and to the whole-cohort data. Additionally, covariate-adjusted joint models with shared random effects accounting for dropout were fit to the whole-cohort data. Multiple medication use was defined as polypharmacy (⩾ five medications), hyperpolypharmacy (⩾ ten medications), and total number of medications.Results:Incident diagnoses were 2,032 for AD, 135 for VD, and 139 for LBD. Percentages of dropout at the end of follow-up were as follows: 71.8% for AD, 81.5% for VD, and 77.7% for LBD. The odds ratio (OR) estimate for hyperpolypharmacy among those with LBD versus AD was 2.19 (0.78, 6.15) when estimated using complete-case data and 3.00 (1.66, 5.40) using whole-cohort data. The OR reduced to 1.41 (0.76, 2.64) when estimated from the joint model accounting for dropout. The OR for polypharmacy using complete-case data differed from the estimates using whole-cohort data. The OR for dementia diagnoses on total number of medications was similar, but non-significant when estimated using complete-case data.Conclusion:Reasons for dropout should be investigated and appropriate statistical methods should be applied to reduce bias in longitudinal studies among high-risk dementia cohorts.

Bayesian multi-scale modeling for aggregated disease mapping data

In disease mapping, a scale effect due to an aggregation of data from a finer resolution level to a coarser level is a common phenomenon. This article addresses this issue using a hierarchical Bayesian modeling framework. We propose four different multiscale models. The first two models use a shared random effect that the finer level inherits from the coarser level. The third model assumes two independent convolution models at the finer and coarser levels. The fourth model applies a convolution model at the finer level, but the relative risk at the coarser level is obtained by aggregating the estimates at the finer level. We compare the models using the deviance information criterion (DIC) and Watanabe-Akaike information criterion (WAIC) that are applied to real and simulated data. The results indicate that the models with shared random effects outperform the other models on a range of criteria.

Combination of longitudinal biomarkers in predicting binary events

In disease screening, the combination of multiple biomarkers often substantially improves the diagnostic accuracy over a single marker. This is particularly true for longitudinal biomarkers where individual trajectory may improve the diagnosis. We propose a pattern mixture model (PMM) framework to predict a binary disease status from a longitudinal sequence of biomarkers. The marker distribution given the disease status is estimated from a linear mixed effects model. A likelihood ratio statistic is computed as the combination rule, which is optimal in the sense of the maximum receiver operating characteristic (ROC) curve under the correctly specified mixed effects model. The individual disease risk score is then estimated by Bayes’ theorem, and we derive the analytical form of the 95% confidence interval. We show that this PMM is an approximation to the shared random effects (SRE) model proposed by Albert (2012. A linear mixed model for predicting a binary event from longitudinal data under random effects mis-specification. Statistics in Medicine31(2), 143–154). Further, with extensive simulation studies, we found that the PMM is more robust than the SRE model under wide classes of models. This new PPM approach for combining biomarkers is motivated by and applied to a fetal growth study, where the interest is in predicting macrosomia using longitudinal ultrasound measurements.