  Predicting risks of chronic diseases has become increasingly important in
clinical practice. When a prediction model is developed in a given source
cohort, there is often a great interest to apply the model to other cohorts.
However, due to potential discrepancy in baseline disease incidences between
different cohorts and shifts in patient composition, the risk predicted by the
original model often under- or over-estimates the risk in the new cohort. The
remedy of such a poorly calibrated prediction is needed for proper medical
decision-making. In this article, we assume the relative risks of predictors
are the same between the two cohorts, and propose a novel weighted estimating
equation approach to re-calibrating the projected risk for the targeted
population through updating the baseline risk. The recalibration leverages the
knowledge about the overall survival probabilities for the disease of interest
and competing events, and the summary information of risk factors from the
targeted population. The proposed re-calibrated risk estimators gain efficiency
if the risk factor distributions are the same for both the source and target
cohorts, and are robust with little bias if they differ. We establish the
consistency and asymptotic normality of the proposed estimators. Extensive
simulation studies demonstrate that the proposed estimators perform very well
in terms of robustness and efficiency in finite samples. A real data
application to colorectal cancer risk prediction also illustrates that the
proposed method can be used in practice for model recalibration.
