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InformationTheoretic ApproachFIGURE 14.3 Ovarian Cancer Data. Evaluation of triallevel surrogacy (using a twostage model) for a surrogacy setting with two timetoevent endpoints. True endpoint: overall survival. Surrogate endpoint: progressionfree survival. Individual and TrialLevel SurrogacyThe informationtheoretic approach was discussed in Chapters 9 and 10. For a multitrial setting, we consider two models for the true endpoint Tj:
Here, g is an appropriate link function. For the remainder of this section, we briefly discuss the surrogacy measures implemented in the Surrogate Shiny App. For an elaborate discussion about the modeling approach and the derivation of the surrogacy measures we refer to Chapter 9. An informationtheoretic measure for individuallevel surrogacy for a multitrial setting is given by
where L_{ki} is the —2 log likelihood of model M_{k}, k = 0,1 defined in (14.4), and Ui is the sample size of the ith trial. For a single trial setting (i.e., N = 1) the surrogacy measure is reduced to
To estimate the triallevel surrogacy measure, the following models are fitted: FIGURE 14.4 Ovarian Cancer Data. Evaluation of triallevel surrogacy (using a twostage model) for a surrogacy setting with two timetoevent endpoints. Estimation of triallevel surrogacy. At the second stage, the trialspecific parameter estimates obtained from generalized linear models defined in (14.5) are used to fit two linear regression models: A triallevel surrogacy measure is given by
where G^{2} is the likelihood ratio test statistic comparing the models M_{0} and M_{1} in (14.6) and N is the number of trials. 
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