Combining chains of Bayesian models with Markov melding

A challenge for practitioners of Bayesian inference is specifying a model that incorporates multiple relevant, heterogeneous data sets. It may be easier to instead specify distinct submodels for each source of data, then join the submodels together. We consider chains of submodels, where submodels directly relate to their neighbours via common quantities which may be parameters or deterministic functions thereof. We propose chained Markov melding, an extension of Markov melding, a generic method to combine chains of submodels into a joint model. One challenge we address is appropriately capturing the prior dependence between common quantities within a submodel, whilst also reconciling differences in priors for the same common quantity between two adjacent submodels. Estimating the posterior of the resulting overall joint model is also challenging, so we describe a sampler that uses the chain structure to incorporate information contained in the submodels in multiple stages, possibly in parallel. We demonstrate our methodology using two examples. The first example considers an ecological integrated population model, where multiple data sets are required to accurately estimate population immigration and reproduction rates. We also consider a joint longitudinal and time-to-event model with uncertain, submodel-derived event times. Chained Markov melding is a conceptually appealing approach to integrating submodels in these settings.

Improving suicide risk prediction via targeted data fusion: proof of concept using medical claims data

OBJECTIVE

Reducing suicidal behavior among patients in the healthcare system requires accurate and explainable predictive models of suicide risk across diverse healthcare settings.

MATERIALS AND METHODS

We proposed a general targeted fusion learning framework that can be used to build a tailored risk prediction model for any specific healthcare setting, drawing on information fusion from a separate more comprehensive dataset with indirect sample linkage through patient similarities. As a proof of concept, we predicted suicide-related hospitalizations for pediatric patients in a limited statewide Hospital Inpatient Discharge Dataset (HIDD) fused with a more comprehensive medical All-Payer Claims Database (APCD) from Connecticut.

RESULTS

We built a suicide risk prediction model for the source data (APCD) and calculated patient risk scores. Patient similarity scores between patients in the source and target (HIDD) datasets using their demographic characteristics and diagnosis codes were assessed. A fused risk score was generated for each patient in the target dataset using our proposed targeted fusion framework. With this model, the averaged sensitivities at 90% and 95% specificity improved by 67% and 171%, and the positive predictive values for the combined fusion model improved 64% and 135% compared to the conventional model.

DISCUSSION AND CONCLUSIONS

We proposed a general targeted fusion learning framework that can be used to build a tailored predictive model for any specific healthcare setting. Results from this study suggest we can improve the performance of predictive models in specific target settings without complete integration of the raw records from external data sources.