Accurate identification of optimal cut points in receiver operating characteristic (ROC) curve analysis is vital for diagnostic tests, especially with small or imbalanced samples. This thesis introduces a smoothed jackknife empirical likelihood (SJEL) method to estimate cut points for the Youden index, closest-to-(0,1) index, and concordance probability index, addressing limitations of traditional empirical likelihood and bootstrap methods. Utilizing a biquadratic kernel with an adaptive bandwidth and Wilks’ theorem, SJEL enhances the precision. Simulations across diverse scenarios with varying distributions and sample sizes demonstrated SJEL’s superior coverage probabilities and reduced confidence interval lengths compared to the bootstrap method. Applied to a prostate cancer dataset, SJEL consistently estimated a cut point, supported by narrow confidence intervals. SJEL proves robust for small-sample diagnostics, offering a promising approach for medical research, though future studies could explore alternative kernels to broaden its applicability.