A Latent Class Approach to Modeling Trajectories of Health Care Cost in Pediatric Cystic Fibrosis

Introduction. Estimating costs of medical care attributable to treatments over time is difficult due to costs that cannot be explained solely by observed risk factors. Unobserved risk factors cannot be accounted for using standard econometric techniques, potentially leading to imprecise prediction. The goal of this work is to describe methodology to account for latent variables in the prediction of longitudinal costs. Methods. Latent class growth mixture models (LCGMMs) predict class membership using observed risk factors and class-specific distributions of costs over time. Our motivating example models cost of care for children with cystic fibrosis from birth to age 17. We compare a generalized linear mixed model (GLMM) with LCGMMs. Both models use the same covariates and distribution to predict average costs by combinations of observed risk factors. We adopt a Bayesian estimation approach to both models and compare results using the deviance information criterion (DIC). Results. The 3-class LCGMM model has a lower DIC than the GLMM. The LCGMM latent classes include a low-cost group where costs increase slowly over time, a medium-cost group with initial higher costs than the low-cost group and with more rapidly increasing costs at older ages, and a high-cost group with a U-shaped trajectory. The risk profile-specific mixtures of classes are used to predict costs over time. The LCGMM model shows more delineation of costs by age by risk profile and with less uncertainty than the GLMM model. Conclusions. The LCGMM approach creates flexible prediction models when using longitudinal cost data. The Bayesian estimation approach to LCGMM presented fits well into cost-effectiveness modeling where the estimated trajectories and class membership can be used for prediction.