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Abstract:
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The identification of surrogate endpoints is a hot area of research in medicine. Most of the existing methodologies are based on the assumption of parametric Archimedean copula models that are utilized to quantify the association between the surrogate endpoints and the true endpoint (overall survival) using Kendall’s ? correlation coefficient. However, this parametric assumption ignores the inherent joint conditional distribution. Therefore, it is of major interest to estimate Kendall’s ? by using the nonparametric estimation method. Let us assume that (Ti, Si) and (Tj, Sj) be bivariate random vectors denoting progression-free survival (PFS) and overall survival (OS). Here, we introduce the bivariate extension of Wilcoxon-Mann-Whitney effect p = P[(Ti>Tj),(Si>Sj)]+0.5P[(Ti=Tj),( Si=Sj)] to estimate Kendall’s ? and derive its consistent variance estimator. Parametric Archimedean copulas-based methods, generalized semi-Markov model, and the rank-based nonparametric models are investigated and their performance was compared with extensive simulations. The methods are illustrated on 11 post-docetaxel trials (10,735 patients) in men with metastatic castration-resistant prostate cancer.
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