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Hope to ask a bit about uniform shrinkage factor in updating the coefficients and intercept of prediction model:

I have built up a prediction model with "rms" and got the uniform (global) shrinkage factor of my model through its validate function. I hope to apply the uniform shrinkage factor to the coefficients of the model for better calibration to prevent overfitting in future data. I know I can simply multiple the uniform shrinkage factor to the original coefficients and get the updated coefficients. But I have trouble on getting the modified intercept after applying the uniform shrinkage factor.

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See Steyerberg's text Clinical Prediction Models 2nd edition. You have to go through an extra step to not penalize the intercept but to change it according to how you penalize the covariate effects. In general it is better to not assume constant shrinkage over covariates but instead to use something like ridge regression which the R rms package supports for linear and logistic models.

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