Parkinson's disease (PD), a degenerative disorder of the central nervous system, is commonly diagnosed using functional medical imaging techniques such as single-photon emission computed tomography (SPECT). In this study, we utilized two SPECT data sets (n = 634 and n = 202) from different hospitals to develop a model capable of accurately predicting PD stages, a multiclass classification task. We used the entire three-dimensional (3D) brain images as input and experimented with various model architectures. Initially, we treated the 3D images as sequences of two-dimensional (2D) slices and fed them sequentially into 2D convolutional neural network (CNN) models pretrained on ImageNet, averaging the outputs to obtain the final predicted stage. We also applied 3D CNN models pretrained on Kinetics-400. Additionally, we incorporated an attention mechanism to account for the varying importance of different slices in the prediction process. To further enhance model efficacy and robustness, we simultaneously trained the two data sets using weight sharing, a technique known as cotraining. Our results demonstrated that 2D models pretrained on ImageNet outperformed 3D models pretrained on Kinetics-400, and models utilizing the attention mechanism outperformed both 2D and 3D models. The cotraining technique proved effective in improving model performance when the cotraining data sets were sufficiently large.