ABSTRACT
The purpose of explained variation and explained randomness is to be able to provide a quantifying measure of a model’s predictability. We would like to know how strong are predictive effects. Such a measure is immediately available via the regression coefficients themselves but, since these depend on the scale of the covariates, it is 488not possible to make simple comparisons on the basis of their magnitude. We would like to be able to make statements such as the following: treatment explains approximately 20% of survival but that, once we have taken account of some known prognostic factors, this figure drops to 5%, or that adding, say, tumor size to a model in which the main prognostic factors are already included the explained variation, or explained randomness, increases, say, from 32% to 33%. Simple situations may not be describable via nested models, for instance, how much do we lose (or gain) in terms of predictability by recoding some continuous prognostic variable into discrete classes on the basis of cutpoints.
