Bayesian two-stage modeling of longitudinal and time-to-event data with an integrated fractional Brownian motion covariance structure.

It is difficult to characterize complex variations of biological processes, often longitudinally measured using biomarkers that yield noisy data. While joint modeling with a longitudinal submodel for the biomarker measurements and a survival submodel for assessing the hazard of events can alleviatemeasurement errorissues, the continuouslongitudinalsubmodel often usesrandomintercepts and slopesto estimate both betweenandwithin-patient heterogeneity in biomarkertrajectories.To overcome longitudinalsubmodel challenges,we replace randomslopeswith scaled integrated fractional Brownian motion (IFBM). As a more generalized version of integrated Brownian motion, IFBM reasonably depicts noisily measured biological processes. From thislongitudinal IFBM model, we derive novel target functionsto monitorthe risk ofrapid disease progression as real-time predictive probabilities. Predicted biomarker values from the IFBM submodel are used as inputs in a Coxsubmodel to estimate event hazard. This two-stage approach to fit the submodels is performed via Bayesian posterior computation and inference. We use the proposed approach to predict dynamic lung disease progression and mortality in women with a rare disease called lymphangioleiomyomatosis who were followed in a national patient registry. We compare our approach to those using integrated Ornstein-Uhlenbeck or conventional random intercepts-and-slopes terms for the longitudinal submodel. In the comparative analysis, the IFBM model consistently demonstrated superior predictive performance. [ABSTRACT FROM AUTHOR]