Understanding Prostate Cancer Risk Using Statistical and Machine Learning Approaches: A Comparative Methodological Analysis

Regression models are fundamental statistical tools used to examine the relationships between dependent and independent variables. These models require different assumptions depending on the structure of the data and the characteristics of the variables. In this context, logistic regression (LR) is a widely used, powerful, and flexible method for analyzing binary outcome variables (1, 2).

One of the main advantages of LR is that it is not strictly bound by classical parametric assumptions such as normal distribution, linear relationships, or homogeneity of variances (2, 3). This makes it highly reliable in fields such as clinical research, where complex data structures are common (4). Moreover, LR allows for the simultaneous evaluation of multiple independent variables and enables statistical testing of their individual and combined effects on the dependent variable (5).

In recent years, the increasing computational power and accessibility of large datasets have brought machine learning (ML) techniques to the forefront as alternatives to traditional statistical methods. First introduced in the 1950s, ML encompasses mathematical models that enable computers to learn from data and make predictions (6). Today, ML algorithms are widely used across various disciplines, including finance, engineering, and healthcare, due to their high accuracy, flexibility, and modeling capacity (7, 8).

ML is generally categorized into supervised, unsupervised, and semi-supervised learning approaches (6, 9). Supervised learning is applied when the outcome variable in the dataset is known and includes methods such as support vector machines (SVM), decision trees, and classification algorithms. Unsupervised learning aims to uncover hidden patterns or groupings in the data without any labeled outcome variable. Semi-supervised learning, on the other hand, is a hybrid model that utilizes both labeled and unlabeled data (10).

Today, the increasing volume and complexity of clinical data-especially in multifactorial diseases such as cancer-have created a need for more effective tools for risk prediction. Accordingly, ML algorithms have become valuable tools in healthcare for early diagnosis, treatment planning, and personalized medicine.

Prostate cancer is the second most common malignancy among men worldwide and ranks second in cancer-related mortality (11). Similar epidemiological trends have been observed in Türkiye. This highlights the critical public health importance of early detection and accurate identification of risk factors.

This study aims to comparatively evaluate the performance of binary LR and various ML algorithms, including SVM, K-nearest neighbors (KNN), chi-squared automatic interaction detection (CHAID), and C5.0, in identifying risk factors for prostate cancer and predicting disease status. By combining traditional statistical methods with modern ML approaches, this study reflects an integrated modeling strategy that can contribute to the development of effective clinical decision support systems.

This article is derived from the doctoral dissertation titled “a study on determining prostate cancer risk factors with LR analysis and ML algorithms”, completed at İstanbul University-Cerrahpaşa, Institute of Health Sciences.

This study utilized a cross-sectional design involving 501 male participants: 248 diagnosed with prostate cancer and 253 without prostate cancer. Participants were recruited from the Urology Outpatient Clinic of Göztepe Training and Research Hospital in İstanbul between April 2021 and September 2021. Data were collected face-to-face using a structured questionnaire, and informed consent was obtained from all participants through a signed consent form prior to participation.

The questionnaire was developed based on a review of current clinical guidelines and epidemiological literature on prostate cancer risk. It consisted of 20 items grouped into three domains: (i) sociodemographic characteristics (e.g., age, education level, marital status), (ii) clinical and urological symptoms (e.g., urinary frequency, hematuria, erectile dysfunction), and (iii) lifestyle-related and behavioral factors (e.g., smoking status, physical activity level, alcohol use, dietary fat intake). The questionnaire was reviewed by two urologists and a biostatistician for content relevance and clinical appropriateness before implementation.

Sample size determination was based on the rule of having at least ten cases per independent variable for LR analysis (1, 12). After excluding incomplete or inconsistent data, the final sample comprised 501 individuals. Ethics approval was obtained from the University of Health Sciences Türkiye, Hamidiye Scientific Research Ethics Committee (approval number: 21/125, dated: 19.03.2021).

Statistical Analysis

All analyses were conducted using IBM SPSS Statistics for Windows, Version 25.0 (IBM Corp., Armonk, NY, USA) and its Modeler module. Descriptive statistics were calculated for all variables. Categorical variables were summarized using frequencies and percentages, while continuous variables were presented as means and standard deviations.

Variables with a p-value less than 0.05 in univariate analysis were entered into the multivariate logistic regression model using the enter method. All statistical tests were two-sided, and p-values less than 0.05 were considered statistically significant.

Binary Logistic Regression: Binary logistic regression analysis was conducted to identify significant predictors of prostate cancer. Variables with a p-value less than 0.05 in univariate analysis were entered into the multivariate model using the enter method. Odds ratios (ORs), 95% confidence intervals (CIs), and p-values were reported.

SVM: The SVM model used a radial basis function kernel. Hyperparameters were optimized using a grid search approach combined with 10-fold cross-validation. Performance was assessed based on accuracy, sensitivity, specificity, and area under the curve (AUC) values.

KNN: The KNN model was implemented with k values ranging from 3 to 15. The optimal value of k was determined through cross-validation. The Euclidean distance metric was used for classification.

CHAID Decision Tree: The CHAID algorithm was used to construct a decision tree. Splits were based on chi-square tests with Bonferroni-adjusted significance levels. The model provided interpretable decision rules for classification.

C5.0 Decision Tree: The C5.0 model employed boosting and pruning to improve performance. This algorithm generated a set of classification rules and a decision tree to predict prostate cancer status. Model accuracy and AUC values were used for evaluation.

Model Evaluation: The dataset was randomly split into training (70%) and testing (30%) subsets. The performance of each model was evaluated on the test set using classification accuracy, sensitivity, specificity, and receiver operating characteristic (ROC) curves. AUC values were computed to assess discriminative power. Statistical significance was evaluated at a 95% confidence level.

The demographic characteristics and clinical features of the participants are summarized in Table 1. Patients with prostate cancer had a significantly higher mean age (72±8.74 years) compared to healthy individuals (46±9.92 years). A significantly higher proportion of prostate cancer patients reported smoking, a family history of cancer, and urinary symptoms compared to the control group, as shown in Table 1.

Binary logistic regression identified several statistically significant risk factors: age (OR =1.103, p<0.001), smoking (OR =5.624, p<0.001), family history of cancer (OR =2.517, p=0.016), urinary frequency (OR =2.484 to 3.763, p<0.05), sedentary lifestyle (OR =2.672, p=0.004), and presence of blood in semen (OR =11.432, p<0.001). Binary logistic regression analysis revealed several statistically significant predictors of prostate cancer. Age was positively associated with cancer risk; each additional year of age increased the odds of prostate cancer by 10.3% (OR =1.103; 95% CI: 1.078-1.128; p=0.001). Smoking was one of the strongest predictors, increasing the risk more than fivefold (OR =5.624; 95% CI: 2.752-11.494; p=0.001). A positive family history of cancer doubled the likelihood of diagnosis (OR =2.517; 95% CI: 1.189-5.329; p=0.016).

Urinary frequency was another significant predictor. Compared to individuals who urinated five or fewer times per day, those who urinated 5-10 times had 2.48 times higher odds (OR =2.484; 95% CI: 1.095-5.637; p=0.029), and those who urinated more than 10 times had 3.76 times higher odds (OR =3.763; 95% CI: 1.491-9.496; p=0.005).

Sedentary behavior significantly increased the risk; individuals with sedentary behavior had 2.67 times higher odds compared to those who regularly exercised (OR =2.672; 95% CI: 1.638-14.487; p=0.004).

Notably, the presence of blood in semen was associated with an elevenfold increase in prostate cancer risk (OR =11.432; 95% CI: 2.763-47.289; p=0.001). The regression coefficients and full model statistics are presented in Table 2. Model fit was acceptable according to the Hosmer-Lemeshow test (c² =12.112; p=0.146), and model performance metrics are shown in Figures 1 and 2.

The detailed regression coefficients and ORs are provided in Table 2. Each model identified overlapping but distinct sets of predictive variables. While age, smoking, and family history of cancer were common variables across models, SVM also included variables like fat consumption and chronic disease status, CHAID considered erectile dysfunction, and C5.0 emphasized urinary frequency and daily lifestyle. The variables identified by each model are summarized in Table 3.

The classification results for each algorithm are presented in Table 4. Additionally, confusion matrix-based classification metrics, such as sensitivity, specificity, accuracy, and approximate AUC values, are shown in Table 5.

Figure 1 shows the ROC curves for each classification model. logistic regression achieved the highest AUC value (0.922), indicating superior discriminative performance in distinguishing patients with and without prostate cancer. The CHAID model followed with an AUC of 0.914, while SVM and KNN showed comparable performance with AUCs of 0.897 and 0.884, respectively. The C5.0 model yielded the lowest AUC (0.885), which is still considered to have acceptable predictive power.

Figure 2 presents the cumulative gain chart for the classification models. Logistic regression demonstrated the steepest cumulative gain curve, indicating the most effective identification of true positive cases within a smaller portion of the population. This further supports the model’s robustness in clinical screening contexts. SVM and CHAID also showed strong performance, while C5.0 and KNN were relatively less efficient in early-stage detection based on gain curve profiles.

This study compared the predictive capabilities and risk factor identification accuracy of logistic regression analysis and several ML algorithms in the context of prostate cancer. Logistic regression emerged as the most effective method based on classification accuracy, which can be attributed to the linear nature of relationships in the dataset. These findings align with existing literature emphasizing the strength of logistic regression in clinical applications where model interpretability and probabilistic outcomes are essential (13). This is in line with findings from Morote et al. (14), who highlighted logistic regression’s interpretability and robustness when applied to structured clinical datasets.

Nevertheless, ML methods provided additional insights by capturing non-linear interactions and incorporating a broader range of features. For instance, the SVM model identified variables such as dietary fat consumption and chronic illnesses, which were not prominent in the logistic regression model. This suggests that ML models may offer advantages in uncovering hidden patterns that are not easily detected by traditional statistical approaches (9). Similar results were reported by Chen et al. (15), who found that SVM and other ML models could identify non-linear relationships and less obvious predictors in prostate cancer datasets.

The CHAID and C5.0 decision tree algorithms also performed well, with CHAID achieving over 91% accuracy. These algorithms provide intuitive, rule-based outputs that can be useful in clinical settings, especially for decision support tools. KNN, while simpler, still demonstrated solid performance, though it may be less scalable with larger datasets or higher dimensionality (16).

Our findings are consistent with previous studies that support the integration of ML in medical diagnostics. Our identification of age, smoking, and family history as significant predictors aligns with well-established risk factors reported in epidemiological studies (17). However, one must consider the complexity and interpretability of ML models when applying them in clinical practice. Logistic regression retains value due to its transparency and ease of implementation, particularly when working with structured and relatively low-dimensional datasets (3).

A limitation of this study includes the sample size, which may affect the generalizability of the results. Additionally, imbalanced age distributions between patient and control groups may have influenced model performance. It is acknowledged that the observed age disparity between groups is inherent to the epidemiology of prostate cancer, as the disease predominantly affects older males (4). However, the strong predictive power of age might have overshadowed other relevant variables in both logistic regression and ML models. Future studies might benefit from age-stratified analyses to assess the isolated contribution of additional predictors.

This study demonstrated that both logistic regression and ML algorithms are effective in identifying significant risk factors and predicting prostate cancer. Logistic regression showed the highest overall classification accuracy and remains a robust choice for structured clinical data.

Key risk factors identified across models included age, smoking, family history of cancer, urinary frequency, and blood in semen. These findings highlight the importance of early detection and suggest that integrating both statistical and ML methods could enhance decision-making in prostate cancer screening and diagnosis.

Future studies should focus on expanding data diversity, improving model interpretability, and integrating additional clinical and genetic variables to support more personalized healthcare strategies. In light of these findings, the integration of hybrid analytical frameworks that combine traditional statistical models with ML algorithms should be encouraged in clinical settings. Such a blended approach can facilitate earlier risk stratification, support personalized decision-making, and contribute to the development of more effective prostate cancer screening protocols. Future research may also explore the implementation of these models into real-world clinical decision support systems to assess their practical utility and scalability.

Ultimately, blending statistical rigor with the predictive depth of ML may help transform prostate cancer screening from a reactive to a more proactive approach.