Consider a risk prediction model developed on one population. When transporting this model to another population, the calibration can be off. There are several strategies for recalibration. One is to fit a new logistic regression model with an intercept only and an offset term for the linear predictor (coefficients from developed model times new data). The resulting linear predictor is considered the recalibrated risk (Steyerberg, Clinical Predictions Models, Chapter 20). What is the exact logic of this approach? I can imagine if there is only a difference in prevalence, then the intercept will be something like the average difference across scores.
Specifically, what is the exact interpretation of the linear predictor resulting from the logistic regression of an intercept only with offset and why?