Ovarian Cancer Data. Evaluation of trial-level surrogacy (using a two-stage model) for a surrogacy setting with two time-to-event endpoints. True endpoint: overall survival. Surrogate endpoint: progression-free survival.
Individual- and Trial-Level Surrogacy
The information-theoretic approach was discussed in Chapters 9 and 10. For a multi-trial 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 information-theoretic measure for individual-level surrogacy for a multi-trial setting is given by
where Lki is the —2 log likelihood of model Mk, 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 trial-level surrogacy measure, the following models are fitted:
Ovarian Cancer Data. Evaluation of trial-level surrogacy (using a two-stage model) for a surrogacy setting with two time-to-event endpoints. Estimation of trial-level surrogacy.
At the second stage, the trial-specific parameter estimates obtained from generalized linear models defined in (14.5) are used to fit two linear regression models:
A trial-level surrogacy measure is given by
where G2 is the likelihood ratio test statistic comparing the models M0 and M1 in (14.6) and N is the number of trials.