BAYESIAN GROWTH MIXTURE MODELS: AN APPLICATION TO MODEL COST OF CARE IN PEDIATRIC CYSTIC FIBROSIS

Purpose: In cost-effectiveness analyses, heterogeneity in costs outcomes are frequently encountered. One standard approach to account for heterogeneity are generalized linear models, but these are not entirely adequate to address all variation. Bayesian Growth Mixture Models (GMMs) are a technique to account for this additional heterogeneity. We describe how GMMs can inform cost estimates for cost-effectiveness studies addressing uncertainty, including microsimulations.  Our approach is applied to total direct cost of care data from a clinical trial population of 73 children with Cystic Fibrosis followed over 21 years.

Method: A GMM consists of two sub-models, a multinomial logistic model, predicting latent class membership, and a class-specific trajectory model, describing each classes' unique trajectory. We model the probability of latent class membership using three observed binary disease characteristics known at birth with the different combinations of characteristics represent distinct “risk profiles”. The class-specific cost trajectories were modeled using age and age-squared as covariates with random intercepts and slopes to account for individual variability. The posterior distributions of multinomial logistic probabilities and costs by age are easily incorporated into a microsimulation model. In this study we simulate patients with different risk profiles and estimate their costs as following different trajectories proportional to their risk profiles' median posterior probability of class membership.

Results: Figure 1 describes the three-class model with a random intercept for age and age-squared used in the cost model for the entire sample.  The median cost trajectory and corresponding 90% Credibility Intervals are displayed. Class 1 and 2 represent higher utilization with different shaped trajectories (increasing vs U-shaped) and overall median posterior probabilities of membership of 16.4% and 58.9% respectively. Class 3, which represents less utilization, had a median posterior probability of 24.6%. The risk profile median probability and 90% credibility interval of Class 3 membership of patients with all three disease characteristics, is 0.8% [0.09% - 2%] while the same probability for patients with none of the characteristics is 81.1% [71.4% - 89.9%].   

Conclusion: GMMs can model cost of care in highly heterogeneous cost diseases when observables are not sufficient to model costs.  Results from the model can inform inputs to a micro or discrete event simulations incorporating costs.