Goodness of fit

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Goodness of fit

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I have developed a risk scoring system that I'm trying to validate. It was
originally developed in one cohort, and I am now validating it in a new,
independent, cohort. However, I am unsure how to test for goodness-of-fit
using Hosmer-Lemeshow's test.

First question: When validating my score, is it not correct that I should use
the observed mortality (my endpoint) from the development cohort to estimate
the expected mortality in my validation cohort?

Second question: When calculating the Chi-square between the observed and
expected mortality, should my formula not be: (observed-expected)^2/
(expected*1-expected/N (in this stratum))?

Third question: How many degrees of freedome should I use? When I read the
book by Hosmer and Lemeshow (Applied logistic regression), in the section on
validation in an external cohort, I understand that the number of groups
equal the degrees of freedom, which in different from the ordinary method in
which the degrees of freedom is groups-2. Is this correct?