Bayesian method for comparing F1 scores in the absence of a gold standard

In the field of medicine, evaluating the diagnostic performance of new diagnostic methods can be challenging, especially in the absence of a gold standard. This study proposes a methodology for assessing the performance of diagnostic tests by estimating the posterior distribution of the $F_1$ score using latent class analysis, without relying on a gold standard. The proposed method utilizes Markov Chain Monte Carlo sampling to estimate the posterior distribution of the $F_1$ score, enabling a comprehensive evaluation of diagnostic test methods. By applying this method to internet addiction, we demonstrate how latent class analysis can be effectively used to assess diagnostic performance, offering a practical solution for situations where no gold standard is available. The effectiveness of the proposed approach was evaluated through simulation studies by examining the coverage probability of the 95% highest density interval of the estimated posterior distributions.