Marginal Versus Conditional Odds Ratios When Updating Risk Prediction Models

Risk prediction models often need to be updated when applied to new settings. A simple updating method involves fixed odds ratio transformation of predicted risks to adjust the model for outcome prevalence in the new setting. When a sample from the target population is available, the gold standard is to use a logistic regression model to estimate this odds ratio. A simpler method has been proposed that calculates this odds ratio from the prevalence estimates in the original and new samples. We show that the marginal odds ratio estimated in this way is generally closer to one than the correct (conditional) odds ratio; thus, the simpler method should be avoided when individual-level data are available. When such data are not available, we suggest an approximate method for recovering the conditional odds ratio from the variance of predicted risks in the development sample. Brief simulations and examples show that this approach reduces undercorrection, often substantially.