Enhancing the prediction of vitamin D deficiency levels using an integrated approach of deep learning and evolutionary computing

Problem statement

Current studies on VDD prediction face key limitations, including reliance on limited feature sets, inadequate handling of temporal data, lack of advanced optimization techniques like genetic algorithms, and limited generalizability to benchmark datasets (Sambasivam, Amudhavel & Sathya, 2020; Kasyap et al., 2024). This study addresses these challenges by integrating CNN, BiLSTM, and GA, demonstrating enhanced predictive performance and robustness across benchmark dataset. Therefore, the main focus of this study is to accurately predict VDD level by developing a novel method that combines CNN+BiLSTM models and GAs. This work frames VDD level prediction as a multi-label problem and employs a dataset that is classified into four classes: “Adequate,” “Insufficient,” “Deficient,” and “Severely Deficient” in order to solve these challenges.

Research questions

Following research questions will be addressed in this work.

RQ1: How to perform prediction vitamin D deficiency (VDD) levels using CNN+BiLSTM with GA model?

RQ2: How effective is the suggested model in comparison to the ML and DL models that are currently in use?

RO3: How well the suggested approach predicts VDD levels compared to earlier similar works?

Research contributions

Following are the main research contributions of this work:

• 1)

  Development of a deep learning system based on CNN+BiLSTM for the diagnosis of vitamin D deficiency.

• 2)

  One notable contribution of this study is the use of evolutionary computing (GAs) to tune the architecture and parameters of the hybrid deep learning model (CNN+BILSTM). By employing evolutionary computing method, we systematically navigate through the vast configurations to pinpoint the optimal settings that boost model’s performance. Our approach showcases how GAs can optimize the process of hyper parameter adjustment leading to enhanced prediction accuracy.

• 3)

  The suggested approach outperforms classical machine learning techniques in the identification of VDD level.

• 4)

  Significant improvement in the accuracy of VDD level prediction as a result of the employed approach.

The study is structured as follows; In the Related Work section, previous research is reviewed. The Proposed Methodology section explains the suggested approach. Specific results and their analysis are presented in the Experimental Results and Discussion section. The Future Work and Conclusion sections discuss the limitations and possible extensions of the proposed method in future.

Research gap: limitations of existing models and need for advanced predictive approaches

While existing studies have explored machine learning and statistical models for predicting vitamin D deficiency, they exhibit significant limitations in generalizability, accuracy, and the ability to handle complex patterns inherent in health data. Most models fail to incorporate advanced architectures that combine spatial and sequential data, or optimization techniques like GAs, which can systematically enhance model performance. Furthermore, the global rise in vitamin D deficiency highlights the urgent need for scalable and precise prediction methods. This study addresses these critical gaps by proposing a hybrid CNN+BiLSTM model optimized with GA, providing a novel and effective approach to improve the predictive accuracy and practicality of vitamin D deficiency assessments.

Data acquisition

As per our research work, we acquired the dataset through a comprehensive survey of 1,700 participants to investigate vitamin D deficiency. The study received ethical approval from the Institutional Review Board of Faculty of Computing, Gomal University (FOC-GU-IRB), Pakistan, with the approval reference number FOC-GU-IRB/2024-01. Prior to data collection, written informed consent was obtained from all participants after explaining the purpose, procedures, risks, and benefits of the study. Participants were assured that their data would be kept confidential and used solely for research purposes. The dataset is made up of various socio-demographic and health-related factors such as age, sex, race, vitamin D levels (measured as ng/mL), body mass index (BMI), dietary calcium intake (mg), dietary vitamin D intake (IU), sun exposure (hours per week), location (urban, rural, or suburban), season of the year, medication usage, existing health conditions, lifestyle factors, and vitamin D deficiency levels categorized into the categories of adequate, insufficient, deficient, or severely deficient. The acquired dataset is attached in Supplemental Material. The data was collected through standardized questionnaires and clinical assessments and a diverse representation of the people was used which makes it easier to analyze the factors affecting the vitamin D status and its associated health implications. The dataset covered factors such as age, gender, BMI, body fat and vitamin D levels. Factors like sun exposure and milk intake were also considered to assess their impact on vitamin D levels. Our statistical analysis revealed correlations (p value < 0.05) among these variables and vitamin D levels underscoring the importance of understanding one’s vitamin D status. We discovered that a quarter of the participants were deficient in vitamin D, indicating health concerns. The study elaborates on these findings and the prevalence of vitamin D levels in Table 1.

How to use data

The acquired dataset, initially stored in a spreadsheet format, got transformed into CSV files for using the “pd.read_csv” command from the Pandas library. By utilizing sklearns data splitting feature, we assigned 80% of the data for training purposes and set aside 20% for testing. The training dataset, which is comprised of 80% of the data, contained both input variables and outcome labels, crucial for the models learning phase. To evaluate the model, the remaining data was used as a testing dataset, with samples to assess algorithm performance. In addition, 10% of the data is especially designated as to address issues, such as overfitting and validation to fine-tune model parameters. This structured technique has divided data within 10-10-80 split, for testing, validation and training, which assisted in the model’s training process to ensure accuracy and generality of classification model.

Preprocessing

Data preprocessing plays an important role in predictive modeling by improving the effectiveness of the models training and reducing the overfitting chances (RushiLongadge & Malik, 2013). This importance includes handling missing data points, which can be caused by problems such as error in recording and non-responses. Strategies to manage missing data contain using the mean to replace known values or make known a random value. The method we chosen involves replacing the entries with the most recent valid value in the dataset, ensuring a more reliable dataset for training model.

Label encoding and data balancing

The dataset has different attributes, such as marital status, gender. Here preprocessing is needed for deep learning (DL) algorithms. which work with data in numerical form (Raza et al., 2024). To transform categorical attributes into numerical representations suitable for deep learning models, we applied three encoding methods: label encoding, One-Hot Encoding (OHE), and Leave-One-Out Encoding (LOOE). Label encoding assigns a unique integer to each category, while OHE creates a binary vector representation, ensuring non-ranking categorical features. LOOE encodes categories based on their target-dependent means, capturing nuanced inter-category relationships. These methods were selected to explore their respective abilities to represent categorical data in ways that could improve the CNN+BiLSTM model’s performance. OHE avoids ordinality bias, while LOOE incorporates category-level information relevant to the target variable. Each encoding method was applied independently during preprocessing, and the resulting datasets were fed into the CNN+BiLSTM pipeline for performance evaluation. Additionally, the dataset is unbalanced with most cases, showing + ive results for VDD. To address this issue, we apply oversampling to balance the representation of the categories and improve the model’s ability to correctly classify the two subgroups. This adjustment resulted in a dataset of 9,722 cases, equally distributed across both categories, thereby increasing the reliability and out model performance.

In addition to label encoding, OHE and LOOE were evaluated to explore alternative categorical feature representation strategies. These encoding methods were incorporated to evaluate their impact on the CNN+BiLSTM model’s performance. Our empirical analysis (see Results section) indicated that while OHE showed comparable performance to label encoding, LOOE yielded a marginal improvement in accuracy due to its ability to integrate category-specific predictive power.

Applying CNN+BiLSTM model

After completing the preprocessing step, we applied CNN+BiLSTM model to classify VDD levels into different categories. The model contains layers, including Dropout, Embedding, Maxpooling, convolutional, BiLSTM and an output layer. To facilitate a clearer understanding of the CNN+BiLSTM architecture, Fig. 2 illustrates the structural flow and interaction among the layers, including the embedding, convolutional, BiLSTM, and output layers.

Output layer

Finally, outcome from the BiLSTM layer acts as the input for the output layer (see Fig. 3). To classify suicidal ideations, the softmax function is employed. The overall input is determined using Eq. (22);

(22) $${\mathrm{o}}_{\mathrm{k}}=\sum _{\mathrm{i}}^{\mathrm{n}}{\mathrm{j}}_{\mathrm{i}}{\mathrm{m}}_{\mathrm{i}}+\mathrm{p}.$$

In this scenario, we have the input vector denoted as m, the weight vector represented by j, and the bias value is indicated as p.

The softmax function is calculated using Eq. (23) as follows.

(23) $$\mathrm{\sigma }\left({\mathrm{o}}_{\mathrm{k}}\right)={\mathrm{e}}^{{\mathrm{o}}_{\mathrm{k}}}/{\sum }_{\mathrm{l}=1}^{\mathrm{t}}{\mathrm{e}}^{{\mathrm{o}}_{\mathrm{l}}}.$$

Applied example for predicting VDD levels

The softmax technique was employed to determine the probability of each category: “VDD1,” “VDD2,” “VDD3,” and “VDD4.” The process begins by calculating the total input, as demonstrated by Eq. (23).

For the first decision feature, “VDD1” represents the class label for “Adequate.” The formula for VDD1 is as follows:

$$\begin{array}{rl}& VD{D}_1=l_1\times U_1+l_2\times U_2+w=0.4\times 0.6+0.3\times 0.4+0.7=0.24+0.12+0.7=1.06\\ & VD{D}_2=l_1\times U_1+l_2\times U_2+w=0.2\times 0.6+0.8\times 0.4+0.7=0.12+0.32+0.7=1.14\\ & \mathrm{V}\mathrm{D}\mathrm{D}3=l_1\times U_1+l_2\times U_2+w=0.6\times 0.6+0.3\times 0.4+0.7=0.36+0.12+0.7=1.18\\ & \mathrm{V}\mathrm{D}\mathrm{D}4=l_1\times U_1+l_2\times U_2+w=0.5\times 0.6+0.5\times 0.4+0.7=0.3+0.2+0.7=1.2\end{array}$$

The Softmax function is then applied to calculate the probabilities. The Softmax function is defined as:

$$\mathrm{\sigma }\left(\mathrm{V}\mathrm{D}{\mathrm{D}}_{\mathrm{k}}\right)={\mathrm{e}}^{\mathrm{V}\mathrm{D}{\mathrm{D}}_{\mathrm{k}}}/{\sum }_{\mathrm{j}=1}^4{\mathrm{e}}^{\mathrm{V}\mathrm{D}{\mathrm{D}}_{\mathrm{j}}}$$

First, calculate ${\mathrm{e}}^{\mathrm{V}\mathrm{D}{\mathrm{D}}_{\mathrm{k}}}$ for each class:

${\mathrm{e}}^{\mathrm{V}\mathrm{D}{\mathrm{D}}_1}$ = ${\mathrm{e}}^{1.06}\approx 2.88$, ${\mathrm{e}}^{\mathrm{V}\mathrm{D}{\mathrm{D}}_2}={\mathrm{e}}^{1.14}\approx 3.13$, ${\mathrm{e}}^{\mathrm{V}\mathrm{D}{\mathrm{D}}_3}={\mathrm{e}}^{1.18}\approx 3.25$, ${\mathrm{e}}^{\mathrm{V}\mathrm{D}{\mathrm{D}}_4}={\mathrm{e}}^{1.2}\approx 3.32$

Now, sum these values:

${\sum }_{\mathrm{j}=1}^4{\mathrm{e}}^{\mathrm{V}\mathrm{D}{\mathrm{D}}_{\mathrm{j}}}=2.887+3.13+3.32+3.32=12.587$

Finally, calculate the Softmax probabilities for each class:

• 1)

  For VDD1: $\mathrm{\sigma }\left(\mathrm{V}\mathrm{D}{\mathrm{D}}_1\right)={\mathrm{e}}^{1.06}/12.587\approx 0.229$

• 2)

  For VDD2: $\mathrm{\sigma }\left(\mathrm{V}\mathrm{D}{\mathrm{D}}_2\right)={\mathrm{e}}^{1.14}/12.587\approx 0.249$

• 3)

  For VDD3: $\mathrm{\sigma }\left(\mathrm{V}\mathrm{D}{\mathrm{D}}_3\right)={\mathrm{e}}^{1.2}/12.587\approx 0.258$

• 4)

  For VDD4: $\mathrm{\sigma }\left(\mathrm{V}\mathrm{D}{\mathrm{D}}_4\right)={\mathrm{e}}^{1.2}/12.587\approx 0.264$

These probabilities are computed using the Softmax function (see Fig. 4).

Incorporating genetic algorithm for the optimization of CNN+BiLSTM model

Integrating GAs into the performance enhancement of the proposed a deep learning model (CNN+BiLSTM) to forecast vitamin D insufficiency requires a series of steps. The subsequent subsections offer a method for applying a GA to refine the structure and parameters of the proposed prediction model.

The parameter set of the CNN+BiLSTM model is denoted as $\mathrm{P}=\left\{\mathrm{p}1,\mathrm{p}2,...,\mathrm{p}\mathrm{n}\right\}$ with each pi representing characteristics such as layer size, filter size and learning rate. Each member $\mathrm{I}$ of the population is defined by a string of these parameters; $\mathrm{I}=\left(\mathrm{p}1,\mathrm{p}2,...,\mathrm{p}\mathrm{n}\right).$ The proposed GA for the optimization of CNN+BiLSTM model works as follows:

1. Representing chromosome: A single set of hyper-parameters for the CNN+BiLSTM model can be referred to as a chromosome. This chromosome can be depicted either as a string of characters or an array of numbers depending on the types of hyper-parameters selected.

2. Fitness function: The fitness function plays an important role in steering the algorithms search towards the best hyper-parameters. It assesses how well a CNN+BiLSTM model performs when trained with the hyper-parameter settings encoded in the chromosome. Let’s define a fitness function $\mathrm{F}\left(\mathrm{I}\right)$ that evaluates how well the model performs based on its parameters $\mathrm{I}$. Typical metrics used for this evaluation are accuracy and F1-score, depending on the nature of the problem at hand. We use this metric for predicting vitamin D level. In this scenario, $\mathrm{N}$ represents the data points, in the validation set, $\mathrm{y}\mathrm{\_}\mathrm{t}\mathrm{r}\mathrm{u}\mathrm{e}$ denotes the actual vitamin D level, $\mathrm{y}\mathrm{\_}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d}$ indicates the forecasted vitamin D level, by the CNN+BiLSTM model trained using chromosome x.

3. Selection: In this stage, we pick out individuals (chromosomes) for reproduction according to their fitness rating. We utilize the roulette wheel selection method to determine which individuals will contribute to the next generation. With roulette wheel selection, each individual is assigned a probability of being chosen based on its fitness score. Individuals, with high fitness scores are more likely to be picked. Let’s, denote the selection probability of individual $\mathrm{I}$ as $\mathrm{S}\left(\mathrm{I}\right)$ in proportion to $\mathrm{F}\left(\mathrm{I}\right).$ A pseudocode algorithm of roulette wheel selection is shown in Fig. 5.

4. Crossover: During crossover, individuals are paired together to create offspring for the next generation. When we choose two parent pairs: ${\mathrm{I}}_{\mathrm{a}}\mathrm{a}\mathrm{n}\mathrm{d}{\mathrm{I}}_{\mathrm{b}}$, crossover operation is performed to generate offspring ${\mathrm{I}}_{\mathrm{o}\mathrm{f}\mathrm{f}\mathrm{s}\mathrm{p}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g}}$. The crossover points are randomly selected along the string representation. Figure 5 shows algorithmic steps for single point crossover.

5. Mutation: Mutation introduces variations in offspring and helps explore solutions within the problem space. Using small probability $p_m$, segments of string representation of offspring, are alerted randomly, to generate mutated offspring $I_{muted}$. Figure 5 shows Bit Flip mutation & Gaussian mutation applied in the proposed model.

6. Replacement: During replacement step, population is updated with the new generation. Figure 5 shows the steps applied during steady-state replacement strategy.

7. Termination: In this step, GA iteration is continued until some termination condition is met. As shown in Fig. 5, process is repeated until max. no. of generations are reached or a predefined fitness threshold is achieved.

8. Solution extraction: In this step, individual(s) with best performance are identified as solution.

By following the above-mentioned steps, the GA can effectively explore the hyperparameter space of the CNN+BiLSTM model to discover a setup that improves the accuracy of predicting vitamin deficiency levels. A pseudocode algorithm is shown in Fig. 5.

Justification of proposed model

The choice of CNN and BiLSTM for this study is driven by their respective strengths in handling structured and sequential data, which aligns with the characteristics of the dataset utilized. CNNs are adept at capturing spatial features, while BiLSTMs excel at learning temporal patterns, such as seasonal variations in vitamin D levels. While Transformer architectures have demonstrated superior performance in certain domains, their application typically requires extensive datasets and significant computational resources. Considering the moderate size and structure of our dataset, CNN+BiLSTM offers a balanced approach, providing high predictive accuracy with computational efficiency. Additionally, the integration of GAs for hyperparameter optimization further enhances the model’s performance. This hybrid approach ensures robust predictions tailored to healthcare applications, as evidenced by the achieved state-of-the-art performance metrics.

The CNN BiLTSM model improved with GAs is well suited for predicting vitamin D deficiency because it can make use of both temporal data effectively. CNNs are good at identifying features in images that are important for bone health and tissue density. At the same time, BiLTSM can capture the relationships between health data and current vitamin D levels efficiently. Incorporating GAs into the model optimization process and feature selection ensures performance and easy interpretation. This dual method improves the accuracy of predictions and offers insights essential for making clinical decisions when dealing with vitamin D deficiency.

Discussion on selection method

The way the CNN+BiLSTM model selects its information to predict vitamin D deficiency plays a role in ensuring the accuracy and dependability of the forecasts it makes. When incorporating a mix of sampling and cross validation techniques in the selection process, it allows the model to effectively address class imbalances which are often present in medical data sets where vitamin D deficiency cases might be scarce. Stratified sampling guarantees that each category is appropriately represented in both the training and test data sets resultantly giving a truer portrayal of how the model performs across groups. Cross validation boosts the models strength by splitting the data into parts, for repeated training and validation rounds to prevent overfitting and ensure its effectiveness on data sets. This method guarantees an assessment of the CNN+BiLSTM models accuracy in predicting vitamin D deficiency and aids in making more informed clinical decisions at the end of the day.

Experiment #1

We conducted a comparative evaluation of the GA against a conventional grid search for optimizing the hyperparameters of the CNN+BiLSTM model. Both methods were applied to tune critical parameters such as the learning rate, dropout rates, number of filters, and BiLSTM units, which significantly impact model performance. Grid search exhaustively explored predefined parameter combinations, systematically evaluating each possible setting within a fixed range. In contrast, GA employed evolutionary strategies to iteratively refine the hyperparameter configuration, leveraging selection, crossover, and mutation operators to navigate the search space more efficiently. The configurations for GA were based on parameters described in Table 4, while grid search was conducted with an equivalent range and granularity of parameter values to ensure a fair comparison. This approach allowed us to assess the relative effectiveness of GA in terms of model performance and computational efficiency. Table 5 presents the performance metrics achieved by the two optimization method

As shown in Table 5, the GA consistently outperformed grid search across all performance metrics, achieving a higher accuracy (96.2% vs. 92.3%) and F1-score (94.6% vs. 91.4%). Furthermore, GA required only 6 h for optimization compared to 15 h for grid search, highlighting its computational efficiency. These improvements can be attributed to GA’s ability to navigate high-dimensional hyperparameter spaces effectively, leveraging evolutionary strategies to converge on optimal solutions without exhaustively evaluating all combinations.

Implications of results: These findings underscore the utility of GA as an efficient and robust optimization method for deep learning tasks, particularly when dealing with complex architectures and large datasets. The reduced optimization time and improved performance metrics demonstrate that GA is a superior alternative to conventional methods such as grid search in this context.

Experiment #2

The performance of the CNN+BiLSTM model was evaluated using dataset processed with label encoding, OHE, and LOOE. Table 6 summarizes the comparative results.

As shown in Table 6, LOOE outperformed label encoding and OHE across all performance metrics. This improvement is attributed to its ability to capture target-dependent categorical information, which provides additional predictive power for the CNN+BiLSTM model. In contrast, while OHE avoids ordinality bias, it does not leverage inter-category variance, which may explain its slightly lower performance. These results highlight the importance of selecting encoding techniques that align with the data characteristics and the model’s requirements. The superior performance of LOOE suggests its potential as a preprocessing strategy for categorical data in healthcare prediction tasks.

Experiment #3

To assess how well the proposed model compares to existing machine learning and deep learning models, we tested the CNN+BiLSTM+GA models’ ability to predict VDD levels, against other machine learning and deep learning approaches. The findings of this comparison are presented in Table 7, concentrating on measures like accuracy, precision, recall, and F1-score.

Experiment #4

In this experiment, we evaluated our proposed CNN-BiLSTM-GA model for predicting VDD, against existing research. Specifically, we assessed its effectiveness compared to established methods and a standard baseline (refer to Table 8). Our proposed model outperformed the studies. To contextualize our contribution, Table 8 presents a comparative analysis of precision, recall, F1-score, and accuracy across existing methods and the proposed CNN+BiLSTM model with GA. While prior approaches achieved moderate performance, with F1-scores and accuracy between 81% and 86%, our model demonstrates superior results (F1-score: 96%, accuracy: 97%). This improvement is attributed to the combined strengths of CNNs for spatial feature extraction, BiLSTMs for temporal dependencies, and GA for optimizing model parameters, enabling significant advancements in predictive performance and generalizability.

Ablation study

The ablation study is carried out to assess the effectiveness of each part by eliminating the components and observing how the model works under various conditions. The following conclusions are reached from the dataset results (see Table 9):

When comparing Model 1 and Model 2, the CNN combined with the GA model demonstrated better performance than the BiLSTM, achieving superior results in predicting Vitamin D deficiency. Additionally, as illustrated in Model 3, incorporating Data Balancing enhanced the performance of both the CNN+BILSTM and GA modules.

Algorithmic complexity

To analyze the algorithmic complexity of the CNN+BILSTM with GA for your research on enhancing the prediction of vitamin D deficiency levels, we need to consider the complexity of each component involved: the BiLSTM network, the CNN network, and the GA.

• 1)

  CNN+BiLSTM component: The complexity of a CNN component is proportional to $O(n.k^2.C_{in}$. $C_{out}$), where $n$ is the input size, $k$ is the kernel size, $C_{in}$ is the number of input channels, and $C_{out}$ is the number of output channels. The pooling operation adds $O\left(n\right)$ complexity. The BiLSTM adds $O(n.d^2$), where $n$ is the sequence length and $d$ is the hidden state size. The overall complexity of the model is $O(n.k^2\text{·}$ $C_{in}$. $C_{out}$+ $n.d^2,$which falls within the polynomial range.

• 2)

  Computational complexity of GA: The complexity of GA is primarily determined by the population size ( $\mathrm{P}$), the number of generations ( $\mathrm{G}$), and the evaluation cost of each individual ( $\mathrm{C}$), which is determined by training the CNN+BiLSTM model. The total complexity of GA is $O\left(P\cdot G\cdot C\right)=O(\mathrm{P}\cdot \mathrm{G}.(n.k^2.C_{in}$. $C_{out}+n.d^2)$. This highlights that GA’s computational cost scales with the complexity of the evaluated model.

This polynomial complexity ensures scalability for medium to large datasets, with GA enabling efficient hyperparameter search and improved performance.

For deployment, techniques such as model pruning and quantization reduce inference latency and memory usage, while frameworks like TensorRT or ONNX Runtime optimize real-time performance. Batch processing can further minimize computation in non-real-time scenarios. Simulated deployment tests on resource-constrained systems confirmed the model’s feasibility, achieving a balance between accuracy and efficiency, making it suitable for real-world applications.

Computational efficiency

The integrated approach of CNN+BILSTM and GA offers a potent combination for predicting vitamin D deficiency levels, but it also introduces computational challenges. CNN and BILSTM, as deep learning models, are known for their computational complexity, especially when dealing with large datasets and intricate architectures. The GA, while a powerful optimization technique, is also be computationally demanding due to its iterative nature and the need to evaluate numerous potential solutions. However, the benefits of this approach, such as improved accuracy and interpretability, may outweigh the computational costs, especially when implemented efficiently using optimized hardware and software. Techniques such as early stopping, pruning, and quantization can help mitigate the computational burden without sacrificing performance. Additionally, careful consideration of hyperparameter tuning and the choice of optimization algorithms can significantly impact the overall computational efficiency of the model.