Quantifying the effect of the surrogate marker by information gain

Statistical validation of a surrogate marker has been studied for more than a decade. Recently, Alonso et al. (2004, Biometrics 60, 724-728) proposed a quantity called the likelihood reduction factor (LRF) to evaluate the validity of a surrogate marker. However, as pointed out in the present article, the LRF may not correctly validate a surrogate marker. Therefore, a new quantity, the proportion of information gain (PIG) using the Kullback-Leibler information, is proposed. Simulations show that under some model assumptions, the PIG precisely reflects the role of a surrogate marker.