Dirichlet process mixture models to estimate outcomes for individuals with missing predictor data: application to predict optimal type 2 diabetes therapy in electronic health record data
Authors: Cardoso Pedro , Dennis John M. , Bowden Jack , Shields Beverley M. , McKinley Trevelyan J. 
Published: July 2022

Background

Missing data is a common problem in regression modelling. Much of the literature focuses on handling missing outcome variables, but there are also challenges when dealing with missing predictor information, particularly when trying to build prediction models for use in practice.

Methods

We develop a flexible Bayesian approach for handling missing predictor information in regression models. For prediction this provides practitioners with full posterior predictive distributions for both the missing predictor information and the outcome variable, conditional on the observed predictors. We apply our approach to a previously proposed treatment selection model for type 2 diabetes second-line therapies. Our approach combines a regression model and a Dirichlet process mixture model (DPMM), where the former defines the treatment selection model and the latter provides a flexible way to model the joint distribution of the predictors.

Results

We show that under missing-completely-at-random (MCAR) and missing-at-random (MAR) assumptions (with respect to the missing predictors), the DPMM can model complex relationships between predictor variables, and predict missing values conditionally on existing information. We also demonstrate that in the presence of multiple missing predictors, the DPMM model can be used to explore which variable(s), if collected, could provide the most additional information about the likely outcome.

Conclusions

Our approach can provide practitioners with supplementary information to aid treatment selection decisions in the presence of missing data, and can be readily extended to other types of response model.

Key Messages

Missing predictor variables present a significant challenge when building and implementing prediction models in clinical practice.

Removing individuals with missing information and performing a complete case analysis can lead to imprecision and bias. Multiple imputation approaches typically translate uncertainty through prediction model parameter standard errors, as opposed to a consistent joint probability model.

Alternatively, a Bayesian approach using Dirichlet process mixture models (DPMMs) offers a flexible way to model complex joint distributions of predictor variables, which can be used to estimate posterior (predictive) distributions for the missing predictors, conditional on the observed predictors.

Using a DPMM, in this way allows uncertainties around missing predictor data to be propagated through to a prediction model of interest using a Bayesian hierarchical framework. This allows prediction models to be developed using datasets with incomplete predictor information (assuming missing-completely-at-random/missing-at-random). Furthermore, predictions can be made on new individuals even if they have incomplete predictor information (under the same assumptions).

This approach provides full posterior predictive probability distributions for both missing predictor variables and the outcome variable, allowing a wide range of probabilistic models outputs to be derived to support clinical decision making.