# A comparison of Bayesian and frequentist approaches to incorporating clinical and biological information for the prediction of response to standardized pediatric colitis therapy

## TL;DR

This study compares Bayesian and frequentist models to predict treatment outcomes in pediatric ulcerative colitis patients.

## Contribution

The study evaluates Bayesian and BART models as alternatives to frequentist approaches for predicting clinical outcomes in pediatric UC.

## Key findings

- Bayesian and BART models showed similar or better predictive performance compared to frequentist models.
- Bayesian and BART models provided narrower credible intervals and better precision in AUC estimation.
- BART models identified nonlinear associations not captured by traditional methods.

## Abstract

The prospective cohort study PROTECT is the largest study in pediatric ulcerative colitis (UC) with standardized treatments, providing valuable data for predicting clinical outcomes. PROTECT and previous studies have identified characteristics associated with clinical outcomes. In this study, we aimed to compare predictive modeling between Bayesian analysis including machine learning and frequentist analysis.

The key outcomes for this analysis were week 4, 12 and 52 corticosteroid (CS)-free remission following standardized treatment from diagnosis. We developed predictive modeling with multivariable Bayesian logistic regression (BLR), Bayesian additive regression trees (BART) and frequentist logistic regression (FLR). The effect estimate of each risk factor was estimated and compared between the BLR and FLR models. The predictive performance of the models was assessed including area under curve (AUC) of the receiver operating characteristic (ROC) curve. Ten-fold cross-validation was performed for internal validation of the models. The estimation contained 95% credible (or confidence) interval (CI).

The statistically significant associations between the risk factors and early or late outcomes were consistent between all BLR and FLR models. The model performance was similar while BLR and BART models had narrower credible intervals of AUCs. To predict week 4 CS-free remission, the BLR model had AUC of 0.69 (95% CI 0.67–0.70), the BART model had AUC of 0.70 (0.67–0.72), and the FLR had AUC of 0.70 (0.65–0.76). To predict week 12 CS-free remission, the BLR model had AUC of 0.78 (0.77–0.79), the BART model had AUC of 0.78 (0.77–0.79), and the FLR model had AUC of 0.79 (0.74–0.83). To predict week 52 CS-free remission, the BLR model had AUC of 0.69 (0.68–0.70), the BART model had AUC of 0.69 (0.67–0.70), and the FLR model had AUC of 0.69 (0.64–0.74). The BART model identified nonlinear associations.

BLR and BART models had intuitive interpretation on interval estimation, better precision in estimating the AUC and can be alternatives for predicting clinical outcomes in pediatric patients with UC. BART model can estimate nonlinear nonparametric association.