Central precocious puberty (CPP) is the most common type of precocious puberty and has a significant effect on children. A gonadotropin-releasing hormone (GnRH)-stimulation test is the gold standard for confirming CPP. This test, however, is costly and unpleasant for patients. Therefore, it is critical to developing alternative methods for CPP diagnosis in order to alleviate patient suffering. This study aims to develop an artificial intelligence (AI) diagnostic system for predicting response to the GnRH-stimulation test using data from laboratory tests, electronic health records (EHRs), and pelvic ultrasonography and left-hand radiography reports. The challenges are in integrating these multimodal features into a comprehensive deep learning model in order to achieve an accurate diagnosis while also accounting for the missing or incomplete modalities. To begin, we developed a dynamic multimodal variational autoencoder (DMVAE) that can exploit intrinsic correlations between different modalities to impute features for missing modalities. Next, we combined features from all modalities to predict the outcome of a CPP diagnosis. The experimental results (AUROC 0.9086) demonstrate that our DMVAE model is superior to standard methods. Additionally, we showed that by setting appropriate operating thresholds, clinicians could diagnose about two-thirds of patients with confidence (1.0 specificity). Only about one-third of patients require confirmation of their diagnoses using GnRH (or GnRH analog)-stimulation tests. To interpret the results, we implemented an explainer Shapley additive explanation (SHAP) to analyze the local and global feature attributions.