3 types of residuals to check model fit
- residuals
- key tool to assess model fit
- calculated for each data point (e.g. patient)
- actual value vs model-predicted value
- calculation of residuals a little different from linear or logistic regression (mainly due to censoring)
Schoenfeld residual
- Cox doesn’t care about what shape of the hazard function is (i.e. risk of death over time)
- all that matters is if two hazard functions are parallel, or “proportional”
- Schoenfeld residual tests this
- example: hazard function for males vs females
- if residuals for gender does not correlate with follow-up time since hospital admission, good news,
- i.e. residuals are indepenent of time, proportional assumption valid
Martingale residual
- tests whether continuous predictor (e.g. age), has linear relation with outcome (time of death),
- or if transforming the continuous variable will make relationship linear (e.g. age^2, log(age))
- Martingale has mean of 0, range -inf to 1
- MR of 1 = patients died earlier than predicted
- MR of -50 = patients died later than predicted
- valid assumption should see a straight line near 0
Deviance residual
- normalized transformation of Martingale residuals
- mean 0, sd 1
- used to spot influential points
- data points that have large effect on model coefficients (HRs)
- (similar to how outliers in linear regression can change line of best fit dramatically)
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