## 4 Discussion
In this same study, 4/27 studies were performed on more than one scanner from the same vendor, 2/27 were performed on scanners by two vendors, and only one study used multi-institutional image data. Another meta-analysis of 12 studies using machine learning for the identification of hrPCA similarly showed that all studies originated from a single institution or image data repository (the Cancer Imaging Archive) [40]. The large majority of the machine learning prostate MRI papers cited in this paper used Siemens 3T scanner systems. Given our results, it is likely that the accuracy of these models would decrease if tested on image data from a different scanner; further training and testing of these models on image data from other scanners would likely be required. Homogeneity in training image datasets will also be a function of patient population cohorts, including race, gender, and disease prevalence. It is well-recognized that the performance of a medical diagnostic test can vary in a subgroup of patients according to the severity and clinical presentation of the disease (spectrum effect) [41; 42]. As such, homogeneous patient racial, gender, socioeconomic status (which are known to impact disease prevalence) within training sets will also impact the broader performance of these models. The local institutional patient population consisted of approximately 40% African Americans; African Americans have a higher incidence of prostate cancer and present with more advanced disease [43]. While the ProstateX dataset did not include patient racial demographics, it is unlikely that the Dutch medical center had such a patient cohort. Racial bias within medical models is recognized [44], with various medicolegal avenues for mitigation [45]. All these factors have led to the development of the field of federated machine learning, which provides the computing architecture for the construction of multi-institutional models using de-centralized and de-identified patient data [46]. Federated learning in medical algorithms is in its early stages and requires additional inter-institutional computing infrastructure or use of commercial platforms [47; 48; 49]. Despite the multitude of differences between the two institutional image datasets in our study, the multi-institutionally trained modelPXL regained high AUCs (0.83-0.96) when it was trained and tested on image datasets from both institutions. In effect, the algorithm was able to \"learn\" around the differences between the two image datasets and classify lesions with high accuracy. The multi-institutionally trained models (modelPXL) maintained relatively high AUCs (0.85-0.99) when tested on single-institutional image data, although there were statistically significant differences in performance between multi- and single-institutional testing sets (\(p<0.01\)). ModelPXLT2 had higher AUCs when tested on single-institutional image data compared to multi-institutional data (0.92-0.83). ModelPXLDC had higher AUCs when tested on multi-institutional image data compared with single-institutional data (0.98-0.85). Additionally, it is important to note these increases in performance occurred with only a small amount of additional data (50 Local lesions added to the 89 PX2 lesions), which showcases that even a small proportion of heterogeneous training data serves to make a model more generalizable. These findings also have important implications for federated learning: it suggests that training on heterogeneous multi-institutional image data may have associated cost or benefits for model performance when tested on single-institutional image data. A few published studies using algorithms with federated learning models have outperformed local institutional algorithms in prostate segmentation [21; 50]. These results do not aim to limit the development of models on one or two datasets; however, they hope to encourage consideration for the heterogeneity and patient population when applying clinical models.