## 2 Materials and Methods
### Statistical Analysis  
Data processing was performed for both pre-clinical and clinical data, using SPSS 25 (IBM Corporation, New York, NY, US) and the free statistical software R (R Core Team, 2019). These tests were performed in 46 patients and for 10 phantom values. To estimate the area under the curve (AUC) for prediction, making use of multiple variables together with the existence of prostate cancer, receiver operating characteristic (ROC) curve analysis was conducted. In this study, we adopted three multivariate approaches. PCA is one of the most commonly used statistical methodologies to investigate patterns in large, correlated datasets [16]. PCA explores the structures in the dataset and extracts principal components by mapping the original data to their equivalent components in the rotated space. It represents unsupervised modelling with no associated response, i.e., PCA will rotate and scale the image. PCA obtains a set of vectors (principal components) which are then used to measure the variability of the dataset, i.e., plotting the first and the second principal components will show the variation in the multidimensional dataset in a 2D plane. Discriminant analysis of principal component (DAPC) was conducted to identify and describe clusters without the influence of the response [17]. DAPC seeks to find differences between groups while minimising the variation within clusters. DAPC transforms the data first using PCA, which are then used to identify the existing clusters. DCA was also considered to test the hypothesis of separation between the two groups, cancerous and healthy tissues [18]. DCA maximises the component axis for class separation. Unlike the previous methods, it is considered as supervised modelling. Thus, the response influences the components. Therefore, DCA is useful, not only as a support for PCA, but to also predict future samples. In addition, univariate and multivariate logistic regression was used to assess the association of clinical characteristics and laboratory parameters to determine the best predictors of prostate cancer. The analysis started with all variables in the model, i.e., backward elimination. This allowed for the construction of the optimal regression equation to help determine the level of importance of each predictor variable. Two evaluation techniques were considered: AIC and [PERSON]'s pseudo-R-squared. AIC estimates the likelihood of a model to predict future values ([PERSON], 1974), which, in turn, can be used to evaluate a model [19]. A model with a lower AIC, among all other models, is considered to have a good fit. [PERSON]'s pseudo-R-squared measures the goodness-of-fit of models. The test can range from 0 to 1, although it can never reach 1 because of its calculation. According to [PERSON]: \"while R\({}^{2}\) index is a more familiar concept to planners who are experienced in ordinary regression analysis, it is not well-behaved a statistic as the R\({}^{2}\) measure, for maximum likelihood estimation. Those unfamiliar with R\({}^{2}\) should be forewarned that its values tend to be considerably lower than those of the R\({}^{2}\) index and should not be judged by the standards for a 'good fit' in ordinary regression analysis. For example, values of 0.2 to 0.4 for R\({}^{2}\) represent an excellent fit\" [20]. Two-step logistic regression was performed to identify explanatory variables of significant prostate cancer. Mean, median, mode, standard deviation, sample variance minimum and maximum were individually entered into a univariate logistic regression model where the outcome was defined as having significant prostate cancer or not. Statistically significant variables were then entered into the multivariate logistic regression model. Odds ratio (OR), 95% confidence interval (95% CI) of odds ratio, and \(p\) values were recorded in Table S2. The reproducibility of the radiomic measurements was assessed in a subgroup of 10 randomly selected phantoms by three observers.