A comparison of some existing and novel methods for integrating historical models to improve estimation of coefficients in logistic regression.

Model integration refers to the process of incorporating a fitted historical model into the estimation of a current study to increase statistical efficiency. Integration can be challenging when the current model includes new covariates, leading to potential model misspecification. We present and evaluate seven existing and novel model integration techniques, which employ both likelihood constraints and Bayesian informative priors. Using a simulation study of logistic regression, we quantify how efficiency-assessed by bias and variance-changes with the sample sizes of both historical and current studies and in response to violations to transportability assumptions. We also apply these methods to a case study in which the goal is to use novel predictors to update a risk prediction model for in-hospital mortality among pediatric extracorporeal membrane oxygenation patients. Our simulation study and case study suggest that (i) when historical sample size is small, accounting for this statistical uncertainty is more efficient; (ii) all methods lose efficiency when there exist differences between the historical and current data-generating mechanisms; (iii) additional shrinkage to zero can improve efficiency in higher-dimensional settings but at the cost of bias in estimation.