  In clinical prediction modeling, model updating refers to the practice of
modifying a prediction model before it is used in a new setting. In the context
of logistic regression for a binary outcome, one of the simplest updating
methods is a fixed odds-ratio transformation of predicted risks to improve
calibration-in-the-large. Previous authors have proposed equations for
calculating this odds-ratio based on the discrepancy between the prevalence in
the original and the new population, or between the average of predicted and
observed risks. We show that this method fails to consider the
non-collapsibility of odds-ratio. Consequently, it under-corrects predicted
risks, especially when predicted risks are more dispersed (i.e., for models
with good discrimination). We suggest an approximate equation for recovering
the conditional odds-ratio from the mean and variance of predicted risks. Brief
simulations and a case study show that this approach reduces under-correction,
sometimes substantially. R code for implementation is provided.
