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Table of Contents:
Validation Using the InformationTheory ApproachIndividualLevel SurrogacyThe informationtheoretic approach for the evaluation of surrogate endpoints (Alonso and Molenberghs, 2007) is discussed in detail in Chapters 8 and 9. Briefly, this approach allows us to evaluate surrogacy at the individual and trial levels in a general surrogacy setting. In this section, we briefly present the setting and illustrate the use of two SAS macros for a normalnormal and survivalbinary setting. We consider a multitrial setting and the following models for the true endpoint:
Let G^{2} be the likelihood ratio test statistic to compare models M_{0} and Mi in (12.50) within the ith trial. The association between both endpoints is quantified using the likelihood reduction factor (LRF) given by:
where N is the total number of the trials, and n* is trialspecific sample size. As pointed out in Chapter 9, the LRF ranges between 0 and 1. The case with LRF=0 indicates that the surrogate and the true endpoint are independent in each trial. TrialLevel SurrogacyTriallevel surrogacy can be estimated using a twostage approach. At the first stage, the following models are formulated for the two endpoints:
Here, p_{Ti} and p_{Si} are trialspecific intercepts and a* and в* are trialspecific treatment effects. Note that the models can be fitted with common intercepts (i.e., reduced fixedeffects models). At the second stage, the parameter estimates obtained from (12.52) are used to fit two linear regression models given by where the error terms e_{0}i and ?ц are normally distributed with zero mean and constant variance <г^{2} and where G^{2} is the likelihood ratio test statistic comparing the two models in (12.53). 
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