Alternative methods to evaluate trial level surrogacy.
BACKGROUND
The evaluation and validation of surrogate endpoints have been extensively studied in the last decade. Prentice [1] and Freedman, Graubard and Schatzkin [2] laid the foundations for the evaluation of surrogate endpoints in randomized clinical trials. Later, Buyse et al. [5] proposed a meta-analytic methodology, producing different methods for different settings, which was further studied by Alonso and Molenberghs [9], in their unifying approach based on information theory.


OBJECTIVE
In this article, we focus our attention on the trial-level surrogacy and propose alternative procedures to evaluate such surrogacy measure, which do not pre-specify the type of association. A promising correction based on cross-validation is investigated. As well as the construction of confidence intervals for this measure.


METHODS
In order to avoid making assumption about the type of relationship between the treatment effects and its distribution, a collection of alternative methods, based on regression trees, bagging, random forests, and support vector machines, combined with bootstrap-based confidence interval and, should one wish, in conjunction with a cross-validation based correction, will be proposed and applied. We apply the various strategies to data from three clinical studies: in opthalmology, in advanced colorectal cancer, and in schizophrenia.


RESULTS
The results obtained for the three case studies are compared; they indicate that using random forest or bagging models produces larger estimated values for the surrogacy measure, which are in general stabler and the confidence interval narrower than linear regression and support vector regression. For the advanced colorectal cancer studies, we even found the trial-level surrogacy is considerably different from what has been reported.


CONCLUSIONS
In general the alternative methods are more computationally demanding, and specially the calculation of the confidence intervals, require more computational time that the delta-method counterpart.


CONCLUSIONS
First, more flexible modeling techniques can be used, allowing for other type of association. Second, when no cross-validation-based correction is applied, overly optimistic trial-level surrogacy estimates will be found, thus cross-validation is highly recommendable. Third, the use of the delta method to calculate confidence intervals is not recommendable since it makes assumptions valid only in very large samples. It may also produce range-violating limits. We therefore recommend alternatives: bootstrap methods in general. Also, the information-theoretic approach produces comparable results with the bagging and random forest approaches, when cross-validation correction is applied. It is also important to observe that, even for the case in which the linear model might be a good option too, bagging methods perform well too, and their confidence intervals were more narrow.
Center for Statistics, Hasselt University, Campus Diepenbeek, B3590 Diepenbeek, Belgium. jose.cortinas@uhasselt.be
Josè Cortiñas
JC
Abrahantes
Ziv
Z
Shkedy
Geert
G
Molenberghs
D000465:Algorithms; D015415:Biomarkers / Q000032:analysis; D002986:Clinical Trials as Topic / Q000706:statistics & numerical data*; D015179:Colorectal Neoplasms / Q000188:drug therapy; D016001:Confidence Intervals; D023381:Endpoint Determination / Q000706:statistics & numerical data*; D006801:Humans; D016014:Linear Models; D008268:Macular Degeneration / Q000628:therapy; D015233:Models, Statistical; D012559:Schizophrenia / Q000188:drug therapy
D015415:Biomarkers