A note on bias of measures of explained variation for survival data.

Papers evaluating measures of explained variation, or similar indices, almost invariably use independence from censoring as the most important criterion. And they always end up suggesting that some measures meet this criterion, and some do not, most of the time leading to a conclusion that the first is better than the second. As a consequence, users are offered measures that cannot be used with time-dependent covariates and effects, not to mention extensions to repeated events or multi-state models. We explain in this paper that the aforementioned criterion is of no use in studying such measures, because it simply favors those that make an implicit assumption of a model being valid everywhere. Measures not making such an assumption are disqualified, even though they are better in every other respect. We show that if these, allegedly inferior, measures are allowed to make the same assumption, they are easily corrected to satisfy the 'independent-from-censoring' criterion. Even better, it is enough to make such an assumption only for the times greater than the last observed failure time τ, which, in contrast with the 'preferred' measures, makes it possible to use all the modeling flexibility up to τ and assume whatever one wants after τ. As a consequence, we claim that some of the measures being preferred as better in the existing reviews are in fact inferior.