In randomized clinical trials, the primary outcome, often requires long term follow-up and/or is costly to measure. For such settings, it is desirable to use a surrogate marker to infer about the treatment effect on the outcome. Identifying such an surrogate marker and quantifying the proportion of treatment effect on the outcome explained (PTE) by the treatment effect on the surrogate marker are thus of great importance. Most existing methods for quantifying the PTE are model-based and may yield biased estimates under model mis-specification. We will propose a set of non-parametric methods for estimating the PTE under different conditions. Additionally, optimal use of the surrogate marker to estimate the treatment effect on the primary outcome is important in practice. We will discuss the optimal transformation of the surrogate marker and its tight relationship with PTE. We will illustrate our methods with real data examples.