The aim of this study was to investigate the relationship between image patterns in cephalometric radiographs and the diagnosis of orthognathic surgery and propose a method to improve the accuracy of predictive models according to the depth of the neural networks. The study included 640 and 320 patients requiring non-surgical and surgical orthodontic treatments, respectively. The data of 150 patients were exclusively classified as a test set. The data of the remaining 810 patients were split into five groups and a five-fold cross-validation was performed. The convolutional neural network models used were ResNet-18, 34, 50, and 101. The number in the model name represents the difference in the depth of the blocks that constitute the model. The accuracy, sensitivity, and specificity of each model were estimated and compared. The average success rate in the test set for the ResNet-18, 34, 50, and 101 was 93.80%, 93.60%, 91.13%, and 91.33%, respectively. In screening, ResNet-18 had the best performance with an area under the curve of 0.979, followed by ResNets-34, 50, and 101 at 0.974, 0.945, and 0.944, respectively. This study suggests the required characteristics of the structure of an artificial intelligence model for decision-making based on medical images.