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A Continuous (Normally Distributed) and a Survival EndpointModel FormulationThe twostage approach for a continuous (normally distributed) and a survival endpoints was discussed in Chapter 7. It is assumed that the true endpoint, T, is a failuretime random variable and the surrogate, S, is a normally distributed continuous variable. Briefly, the first stage consists of the classical linear regression model for FIGURE 12.36 Data structure. the surrogate given by
where e®j is normally distributed with mean zero and variance of. The proportional hazard model for the true endpoints given by
where в* are trialspecific effects of treatment Z and A® (t), is a trialspecific baseline hazard function. If a parametric (e.g., Weibulldistributionbased) baseline hazard is used in (12.37), the joint distribution function defined by the copula and the marginal models (12.36) and (12.37) allows us to construct the likelihood function for the observed data and obtain estimates of the treatment effects a® and в*. Individuallevel surrogacy can be evaluated by using Kendall’s т or Spearman’s p (see Section 5.2). Triallevel surrogacy is assessed using the correlation coefficient between the estimated treatment effects a® and в®. 
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