A Resampling Based Grid Search Method to Improve Reliability and Robustness of Mixture-Item Response Theory Models of Multimorbid High-Risk Patients

There are many statistics available to the applied statistician for assessing model fit and even more methods for assessing internal and external validity. We detail a useful approach using a grid search technique that balances the internal model consistency with generalizability and can be used with models that naturally lend themselves to multiple assessment techniques. Our method relies on resampling and a simple grid search method over 3 commonly used statistics that are simple to calculate. We apply this method in a latent traits framework using a mixture Item Response Theory (MIXIRT) model of common chronic health conditions. Model fit is assessed using Akaike's Information Criteria (AIC), latent class similarity is measured with the Variance of Information (VI), and the consistency of condition complexity and prevalence across latent classes is compared using Kendall's τ rank order statistic. From two patient cohorts at high risk for hospitalization in 2014 and 2018, we generated 19 MIXIRT models (allowing 2-20 latent classes) on 21 common comorbid conditions identified via healthcare encounter diagnosis codes. We ran these models on 100 bootstrap samples of size 10% for each cohort. Among the resulting models, combined AIC and VI statistics identified 5-7 latent classes, but the rank order correlation of condition complexity revealed that only the 5 class solutions had consistent condition complexity. The 5 class solutions were combined to produce a single parsimonious MIXIRT solution that balanced clinical significance with model fit, cluster similarity, and consistency of condition complexity.