multiple-trial or meta-analysis setting. In the next subsection, validation methods will be discussed multiple-trial setting. Validation of surrogate endpoints in multiple-trial setting In the multiple-trial setting, the surrogate endpoint and final true endpoint are collected in multiple trials and both individual patient data and trial data are assumed to be available for the analysis. Both fixed effect models and random effect models with treatment as an independent variable are suggested in the literature (Buyse and Molenberghs 1998) in the validating the surrogate endpoint, the method is called meta-analytic approach (Buyse and Molenberghs 1998). The two-stage fixed effect model is illustrated as below. At the first stage, the surrogate endpoint and true final endpoint are assumed to be jointly Normally distributed with treatment effect model presented in both surrogate endpoint and true endpoint in a linear model. Sij = + 7.12 µSi +αiZij εSij Tij = µTi + + 7.13 βi Zij εTij where µSi and µTi are the intercepts for the linear regressions respectively. Here, and are the αi βi corresponding treatment effect with being the error term for effect of true effect on surrogate εj endpoint. and are correlated errors εSij εTij, , where At second stage, it assumes the µSi, µTi, and are a mixture of fixed and random effects, so αi βi ,
multiple-trial or meta-analysis setting. In the next subsection, validation methods will be discussed multiple-trial setting. Validation of surrogate endpoints in multiple-trial setting In the multiple-trial setting, the surrogate endpoint and final true endpoint are collected in multiple trials and both individual patient data and trial data are assumed to be available for the analysis. Both fixed effect models and random effect models with treatment as an independent variable are suggested in the literature (Buyse and Molenberghs 1998) in the validating the surrogate endpoint, the method is called meta-analytic approach (Buyse and Molenberghs 1998). The two-stage fixed effect model is illustrated as below. At the first stage, the surrogate endpoint and true final endpoint are assumed to be jointly Normally distributed with treatment effect model presented in both surrogate endpoint and true endpoint in a linear model. Sij = µSi +αiZij + εSij 7.12 Tij = µTi + βi Zij + εTij 7.13 where µSi and µTi are the intercepts for the linear regressions respectively. Here, αi and βi are the corresponding treatment effect with εj being the error term for effect of true effect on surrogate endpoint. εSij and εTij, are correlated errors , where At second stage, it assumes the µSi, µTi, αi and βi are a mixture of fixed and random effects, so ,
PhD%20Dissertation%20Feng%20Liu%20Final%20Clean.docx