This analytical study was conducted to predict the effect of vitamin D₃ supplements received 50,000 IU/week (provided by Zahravi Pharm. Co., Tabriz, Iran), for a period of 8 weeks, on the serum levels of vitamin D, TNF-α, TGF-β1, and TAC. In this study, research factors were obtained from women with breast cancer who were referred to the Shafa Specialty Cancer Diseases Hospital in Ahvaz, Khouzestan, the center of the southwest state of Iran [10]. Blood samples were collected for measurement of serum 25-hydroxyvitamin D [25(OH)D] concentrations before and after the intervention. Enzyme-linked immunosorbent assay (ELISA) method was used for measuring the serum levels of TNF-α, TGF-β1, and TAC [ELISA kits of bioactive diagnostic GmbH Company (Homburg, Germany)].

The baseline characteristics of the clinical trial participants in this study are shown in Table 1. Inclusion criteria included patients with breast cancer in stage I–III of the disease, age 30–60 years, and not receiving vitamin D supplements in the last 3 months. Patients with metastatic breast cancer or a precedent of other cancers, those who had a history of chemotherapy, radiotherapy, and hormone therapy for any reason other than the present disease, and people with chronic diarrhea and malabsorption were excluded from the study. Other exclusion factors included the use of corticosteroids, the patient’s known inflammatory disorders (such as acute bacterial or viral infections), and autoimmune diseases. The sample size was calculated based on a study with a confidence level of 95% and a power of 80% [32].

The mean serum levels of vitamin D, TNF-α, TGF-β1 and TAC before and after vitamin D₃ supplementation are indicated in Table 2.

The prediction model was developed using the breast cancer serum biomarkers including serum levels of vitamin D, TNF-α, TGF-β1, and TAC before and after vitamin D₃ supplementation. Moreover, patients’ demographic, anthropometric, and dietary information as the main features for supplement therapy in patients with breast cancer were selected [10]. Generally, the performance of the models was examined with random trials, including 188 rotation data in total training, validating, and testing execution phases for four serum levels predictor models. In this study, 90% of the data was used randomly to train the network, and the remnant was applied to determine the validation of the model in terms of its comprehensiveness and its ability to be generalized to other data.

An ANN framework is composed of several layers, i.e., the input layers, the hidden layers, and the output layers. ANNs have various kinds, such as multilayer perceptron (MLP), radial basis function, Hopfield, etc. In this study, the MLP neural network, which is a common type of neural network, was used to discover the relationship between input and output variables. To implement the proposed model, Matrix Laboratory (MATLAB) software version 2015b was used. The proposed model simulated the process of supplement therapy to predict the behavior of vitamin D in terms of its impact on the mentioned factors among women with breast cancer.

Modeling was performed with the Neural Net Fitting Section of MATLAB environment. The data were entered consisting of four input data related to before the intervention and one output data related to after the intervention in four-stage separately. The structure of the neural network used is presented in Figure 1.

The different architectures of the ANN were evaluated with diverse segmentation of data, disparate number of neurons and various training algorithms to achieve an optimal structure of the predictor model.

The data was divided into three forms: training, validation, and testing to adjust the network, measure the progress of the general network and evaluate the independent performance of the network, respectively. The disparate numbers of neurons were optimized by trial and error, including 5, 8, 10, 12, and 15 in various layers size. Moreover, the various training algorithms such as Levenberg-Marquardt, Bayesian Regularization, and Scaled Conjugate Gradient were also investigated to optimize the model performance.

Due to the limited number of available samples, the method of rotational placement was used with repetition in experiments of the proposed model to validate the model. Every designed model was evaluated 10 times using the training dataset. Moreover, the accuracy averages of all 10 runs in each pattern were calculated separately to specify the highest accuracy.

The performance of the ANNs models was evaluated using the mean squared error (MSE) through Equation 1. The MSE function was used to determine the error values in which the computing of three factors, including system output error, the square of the system error, and the mean of all the squared errors are possible.

The function formula is given below (Equation 1):

Where f_i is equivalent to the observed value, y_i is the corresponding predicted value for f_i, and N is the number of observations [23].

Oxidative stress means an imbalance in the systems of oxidants and antioxidants, and inflammation can be the result of oxidative stress in the body. Oxidative stress and inflammation suppress the immune system and cause the formation and growth of tumors and thus the progression of cancer [33, 34]. Vitamin D is a prohormone that is actuated through hydroxylation pathways to create 1,25-dihydroxyvitamin D₃ [35, 36]. Vitamin D, in addition to its well-known role in bone metabolism and calcium and phosphorus homeostasis, also has immune modulatory properties that play a role in cancer prevention and treatment [37]. Vitamin D has anti-inflammatory effects such as reducing the production of inflammatory cytokines [38]. VDRs have the aptitude to reduce the activity of nuclear factor-kappa B (NF-κB), a pro-inflammatory transcription factor [39, 40]. Vitamin D also exerts its antioxidant activity by binding to the VDR and adjusting gene expression. This vitamin increases the expression of antioxidant systems and restrains the release of reactive oxygen species [18].

An inverse relationship between the serum level of vitamin D and the development and progression of breast cancer has been shown; indeed, the reduction of the serum vitamin D level leads to an increase in the risk of relapse and premature death of these patients [41]. Several studies have shown the effect of vitamin D on intended factors in cancer patients [10, 20, 21]. Mohseni et al. [10] investigated the effects of vitamin D supplementation on serum vitamin D levels, inflammatory factors (TNF-α, TGF-β1), and TAC. Although the results of this study showed that vitamin D supplementation significantly increased the serum levels of vitamin D and TAC in patients with breast cancer, some studies have shown an insignificant relationship between vitamin D supplements and the risk of breast cancer according to the results of mammography density [42]. These conflicting results arrived from different factors in the studies such as the dose of vitamin D, the age of the studied population, and the condition of intervention. Moreover, in this study, the effects of vitamin D on the inflammatory factors were considered. In contrast, in previous studies, mammography density was reported as a positive factor for the risk of breast cancer. The changes in the serum levels of inflammatory factors, including TNF-α and TGF-β1, were not significant notwithstanding the reduction [10]. In other studies, Wesselink et al. [20] examined the association between circulating levels of vitamin D and inflammatory markers, including TNF-α, in patients with colorectal cancer. The results of this study showed a reverse correlation between the levels of vitamin D and TNF-α [20]. Another study by Qin et al. [21] examined the effect of vitamin D supplementation on serum TGF-β1 levels in women at high risk for breast cancer. The results showed that treatment with a dose of 400 IU of vitamin D for one month was effective in reducing the serum level of TGF-β1 [21].

In accordance with the above studies on the anti-inflammatory and antioxidant effects of vitamin D on the serum levels of vitamin D, inflammatory factors, and TAC in the treatment of cancer and due to the effect of increasing TNF-α and TGF-β1 [43, 44] and decreasing serum levels of TAC [45] and vitamin D in the progression of breast cancer, using the methods that can predict these effects accelerate the healing process and reduce mortality [34, 46]. In the current study, according to the existing correlation and its importance, some changes in the serum levels of the variables under the influence of vitamin D supplementation in patients with breast cancer were shown to be predictable.

The application of artificial intelligence methods and clinical decision-making algorithms can accelerate the process of analyzing information related to patients, interpreting data, and predicting treatment results [47, 48], which also leads to the reduction of expenses related to the disease [49]. The results of the present study showed that the ANN can predict the effect of vitamin D₃ supplementation on serum levels of vitamin D, TGF-β1, and TAC with high accuracy including 85.4%, 89.5%, and 88.1%, respectively. The average accuracy of the developed model for the TNF-α variable was 40%, which showed that there was not a significant correlation between the input variables and the TNF-α changes in the patient with vitamin D supplementation therapy.

Recently, studies have also been conducted to predict the effects of supplements using the ANN methods [23, 30, 31]. In a study conducted by Jamshidnezhad et al. [23] the effect of coenzyme Q10 (Q10) supplementation on inflammatory markers in women with breast cancer was investigated using a machine-learning predictive model. In this study, a MLP neural network was used, and the results showed that the use of an ANN could predict the levels of the impact of Q10 supplementation on inflammatory factors, including interleukin 6 (IL-6), IL-8, and vascular endothelial growth factor (VEGF) with an accuracy of 96%, 88%, and 92%, respectively [23].

Hosseini et al. [30] also conducted a study to predict the effect of saffron supplementation on the treatment of patients with asthma and allergies using the ANN method. In this study, the use of the ANN genetic algorithm method could accurately predict the levels of effects of saffron supplementation on anti-inflammatory factors [anti-heat shock protein (Hsp) and C-reactive protein (CRP)] in asthma with an accuracy of 96.5% and 98.9%. The results confirmed the effectiveness of the ANN in predicting the effect of the supplement on the treatment of patients with asthma [30].

In another study, Allahyari et al. [31] examined the prediction of response to vitamin D supplementation and changes in serum vitamin D levels based on neurophysiological factors in adolescent girls using the ANN. The results showed that the ANN algorithm with sigmoid transfer function could effectively predict the response to vitamin D supplementation with sensitivity and specificity between 60–70% [31].

In agreement with our project, studies have confirmed that machine learning methods such as ANN can predict the effect of different supplements on diseases. The application of these methods can help patients by saving time and economizing the costs during the periods of treatment. In general, studies have shown that we can use artificial intelligence algorithms instead of implementing old computational methods, to improve the performance of models in data analysis and understand patterns in them [50]. In the present study, we used the ANN and MATLAB software to predict the effect of vitamin D supplementation in women with breast cancer. The results of the present study highlight the importance of predicting the effect of vitamin D supplementation on the serum levels of vitamin D, inflammatory factors, and TAC in women with breast cancer using an ANN.

In the present study, the ANN was used to predict the effect of vitamin D supplementation on serum levels of vitamin D, inflammatory markers, and TAC in women with breast cancer. Given that the considered factors are effective in the progression of breast cancer, the results of this research can help to meliorate the treatment process of patients.

These techniques can help specialists improve the treatment procedure by predicting the effect of vitamin D supplementation on the factors affecting the progression of breast cancer in different people to prescribe vitamin D supplementation with greater confidence.

As study limitations, an exploration of more alternative machine learning approaches warrants consideration. Incorporating more data from diverse centers could augment result quality and real-world relevance. Furthermore, independent evaluation of treatment methodologies and their impacts on patients with cancer, alongside a deeper probe into drug effects through machine learning, beckon as promising avenues for future research in this domain.