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Survival variables were estimated using the Kaplan-Meier method and compared by the log-rank test.
The distribution of the time-to-event variables were estimated using the Kaplan-Meier method with log-rank testing.
To account for the effect of shared common ancestry [ 9], "independent contrasts" [ 10] for these two variables were estimated using the program CAIC [ 11] based on a composite tree of the sampled species (supplementary Fig. S2 [see Additional file 1]).
Independent contrasts for these two variables were estimated using the program CAIC [ 11] based on a composite tree of the sampled species that was constructed from recent molecular phylogenies for the major clades of vertebrates (supplementary Fig. S2 [see Additional file 1]).
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The significance of the independent variables was estimated using the Wald test.
The strength of the association between the studied variables was estimated using the Spearman rank correlation coefficient (R).
The impact of continuous variables was estimated using the Mann-Whitney U-test.
The association with some baseline influencing factors between healing and candidate surrogate variables was estimated using the odds ratio and the 95% CIs in binary logistic regression.
The skewness of the explanatory variable was estimated using the skewness function in the e1071 package.
The relative importance of each variable was estimated using the jack-knife method.
For patients whose baseline serum creatinine level was unknown, this variable was estimated using the Modification of Diet in Renal Disease (MDRD) formula [ 16, 17].
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