In the literature review, various studies are discussed regarding the prediction of health insurance premiums and healthcare costs using machine learning algorithms that are provided in this section.

In Vijayalakshmi, Selvakumar and Panimalar (2023), For insurance cost prediction, the dataset with 24 characteristics was used, which included all relevant attributes. It is implemented utilising R programming’s regression methods, including LR, DT, Lasso, Ridge, RF, Elastic Net, SVR, KNN, and Neural Network. Using an RS squared value of 0.9533, RFR demonstrated superior performance [15] .

In Marinova and Todorova, (2023) evaluate the model’s performance, we used R-Squared, RMSE, and training time as measurement measures. There is a 0.94 accuracy rate for the BMI feature model using the Bagged method, according to the testing data. Models built using the Bagged technique have a MSE of 0.06 for the attributes Smoker and Blood Pressure. It takes more time to train models that were constructed using the SVM compared to other methods [16] .

In Thejeshwar et al. (2023), seeks to educate the general people about insurance in order to facilitate their acquisition at an accurate and reasonable cost. The models’ predictions were enhanced by training on a dataset. By contrasting the estimated quantity with the actual data, the model was examined and verified. They evaluated the models’ levels of accuracy. This approach works well in RFR because, compared to competing methods, it finds the performance measure with the greatest accuracy rate (87%) with much less processing time [8] .

In Dutta et al. (2021), emphasizes the need of calculating the patient’s portion of the healthcare expenditure. The best prediction analysis is achieved by using a variety of data employing regression techniques, including DT, RF, polynomial regression, and linear regression. The best method for accurately predicting health insurance premiums was RFR, which achieved a r2 score of 0.862533 when utilised as intended [17] .

In Baro, Oliveira and De Souza Britto Junior (2022), investigate three data sets to extract characteristics, namely, medical specialty, the International Classification of Diseases and an account of the event. Also, a dataset with 34,930 patient records totalling 38,524 medical occurrences was provided. In order to evaluate and establish a standard for this fresh dataset, we have used two popular ensemble techniques: RF and GB. When the models from the three feature sets that were examined were combined using GB, the best outcomes (AUC = 0.82) were obtained [18] .

In Luo et al. (2021), information gathered between 2012 and 2014 from actual asthmatic patients in a large Chinese city was used to train prediction models, such as LR, RF, SVM, classification regression tree, and BPNN. According to the risk analysis of comorbidity on cost, the two main risks for asthmatic patients that impact treatment costs are respiratory diseases (36.38% in the adjusted odds ratio (95% Confidence Interval: 27.61%, 47.86%) and disorders of the circulatory system (23.83%; 95%CI: 15.95%, 35.22%) [19] .

Table 1 below summarizes prior research on predicting health insurance premiums using ML and DL methodologies.

Most studies depend on conventional algorithms; however, the research gap reveals a lack of investigation into advanced models of machine learning, such as ensemble approaches or deep learning. Many of these studies only look at small subsets of features or populations, which means their results are not relevant to the real world. Computational efficiency is still an issue, especially for complicated models like SVM, and there is an absence of real-time prediction systems that are responsive to changing data. There is a need for more study on the ethical implications and wider social effects of predictive models [20] - [22] , particularly in the area of insurance cost estimation, so that we may better understand how to reduce bias and ensure equality in these systems.

Personal datasets on medical costs are sourced from the KAGGLE repository. There is a grand total of 1388 items per column in the dataset, including seven characteristics with nonnull attributes.

Data pre-processing is the process of preparing unprocessed data for use in a more organised dataset. Stated differently, even while data is gathered from a variety of sources, it is not acquired in a format that has been processed and is ready for analysis. Preprocessing is any alteration done to the dataset before supplying it to the algorithm. The preprocessing techniques listed below are explained in:

Feature engineering in ML aims to increase the effectiveness of ML algorithms by using domain expertise to extract relevant features from unprocessed data. Factors like age, BMI, and smoking status are the most influential in the medical insurance cost dataset [23] .

Min-max scaling is a specific method within feature scaling that rescales all values of a particular feature to fit within a predefined minimum and maximum range, typically 0 and 1. This process helps maintain consistency and comparability among different features. The following Equation (1) scale the dataset.

$\tilde{x}=\frac{x-\text{min}\left(x\right)}{\max \left(x\right)-\text{min}\left(x\right)}$ (1)

In machine learning modeling, dataset splitting is an essential step that aids in various stages, from training to evaluating the model. There are two separate subsets of the dataset: a testing set and a training set. 30% of the data is used for testing and 70% of the data is used for training throughout the experimental phase.

Choose various regression models, such as the KNN, Ridge, Lasso, and XGB models that are described below, to estimate health insurance costs:

1) K-nearest neighbor

The KNN approach finds the K data items or training patterns that are nearest to an input pattern, and then it chooses the model class with the highest number of models. The number of nearest neighbours that will be taken into account for predicting class labels in test data is known as the K value. K was selected by neighbouring K’s class vote. Utilise the Euclidean Distance formula (2) to determine distances between neighbours [24] :

$dxy=\sqrt{{\displaystyle {\sum }_{i=1}^n{\left(x_i-y_i\right)}^2}}$ (2)

The prediction ${\hat{y}}_i$ for a new point x is given by formula (3):

${\hat{y}}_i=\frac{1}{k}\underset{i=1}{\overset{k}{{\displaystyle \sum }}}{y}_i$ (3)

where $y_i$ are the target values of the k nearest neighbors.

2) Ridge regression

Ridge regression is used when dealing with data that exhibit multi-collinearity. It is a method for fine-tuning the analysis of multi-collinear data. If the independent variables have a strong correlation, we may approximate the regression model’s coefficient in this scenario. In order to avoid overfitting, ridge regression is a kind of linear regression that incorporates a 𝐿 2 regularisation term. The formula defines the cost function for Ridge regression (4):

$j\left(\theta \right)=\underset{i=1}{\overset{m}{{\displaystyle \sum }}}{\left(y_i-{\hat{y}}_i\right)}^2+\lambda \underset{j=1}{\overset{n}{{\displaystyle \sum }}}{\theta }_j^2$ (4)

where:

$y_i$ = is the true value.

${\hat{y}}_i$ = is the predicted value.

$\lambda$ = is the regularization parameter.

${\theta }_j$ = are the coefficients of the model.

3) Lasso regression

Ridge regression is extremely similar to Lasso, also referred to as the Selection Operator and Least Absolute Shrinkage. In ML, Lasso regression is used to pick a significant subset of variables. In general, Lasso regression prediction Lasso regression is similar to Ridge regression but employs 𝐿 1 regularization, promoting sparsity in the model coefficients. s are more accurate than those made by other models formulate as Equation (5).

$j\left(\theta \right)=\underset{i=1}{\overset{m}{{\displaystyle \sum }}}{\left(y_i-{\hat{y}}_i\right)}^2+\lambda \underset{j=1}{\overset{n}{{\displaystyle \sum }}}\left|{\theta }_j\right|$ (5)

where $\left|{\theta }_j\right|$ represents the absolute value of the coefficients, encouraging some coefficients to be exactly zero.

4) XGBoost regressor

The XGBoost model [25] is an integrated model based on gradient boosting and tree-based. The fundamental structure is composed of numerous CARTs, which calculate the final prediction result by adding the desired value as well as each decision tree’s predicted values from the past. Once each decision tree has finished training, a consensus is obtained. Pruning decision trees created during XGBoost model training is necessary to avoid overfitting, which occurs when each new tree is learnt using the previously trained tree. For the purpose of minimizing error, the XGBoost model uses the error that each tree produces as an input to train subsequent trees. By gradually reducing prediction error, this procedure forces the model’s predicted outcome to be closer to the actual value. Assume the sample used for training is ( $x_i$, $y_i$). XGB prediction model may thus be written as (63) [26] :

${\hat{y}}_i=\underset{k=1}{\overset{k}{{\displaystyle \sum }}}{f}_k\left(x_i\right),f_k\in F$ (6)

where $x\in R^m$, $y\in R$, x is the eigenvector, y is the sample label, and kth decision tree is represented by $f_k\left(x_i\right)$.

A kind of data analysis known as exploratory data analysis (EDA) seeks to discover broad patterns from the collected information. Notable data features and outliers are all part of these patterns. EDA is a critical initial stage in any data analysis. Histograms and boxplots are graphical methods for analysing the data’s distribution. Some visualization graphs are given in below:

The heat map Dependencies of Medical Charges in Figure 2 demonstrates sex, age, correlation between BMI, area, number of children, smoking status, and medical costs. Purple suggests strong positive connections, green suggests strong negative correlations, and beige suggests weak or no relationships. Smokers incur greater medical bills; therefore, dark purple indicates that.

The red bar in Figure 3 indicates that typical insurance charges for Sex Category “0” are just over 12,000, while the blue bar for Sex Category “1” are just below 12,000; the error lines indicate small differences between the two groups.

Figure 4 shows the plot for age, where the horizontal axis represents age, with intervals of 10 years from 20 to 60 vertical axis represents the count, ranging from 0 to 200. The graph displays variable distribution across age groups, with the highest count around age 20 and subsequent counts below 200. It aids in demographic analysis and pattern understanding.

Figure 5 shows the distribution of BMI values as a histogram superimposed on top of a line graph. The x-axis ranges from 15 to 50, and the y-axis ranges from 0 to 140. The tallest bar around a BMI value of 25 shows that this value has the highest frequency in the dataset. This visualization aids in understanding the spread of BMI values across the population.

To evaluate the quality of ML models, use the evaluation error matrix. Metrics like as R²-square, and Root Mean Squared Error need to be measured for us to be able to compare different algorithms.

1) RMSE

The RMSE is computed by calculating the MSE’s square root. The RMSE formula is (7):

$\text{RMSE}=\sqrt{\frac{1}{n}\underset{t=1}{\overset{n}{{\displaystyle \sum }}}{\left({y^{\prime }}_t-y_t\right)}^2}$. (7)

where

${y^{\prime }}_t$ is a forecasted value,

$y_t$ is an original value, and,

n is the sum of all the test set values.

2) R²-score

T constant of purpose is also referred to as R-squared (R²). It is a statistical metric. It determines the degree to which the data are in close proximity to the regression line that has been fitted. R² is calculated using formula (8).

${\text{R}}^2=1-\frac{\text{Unexplained Variation}}{\text{Total Variation}}$ (8)

where,

The R² metric, also referred to as the coefficient of determination, measures the percentage of the dependent variable’s volatility that can be anticipated based on the independent variables in a regression model. It has a range of 0 to 1, where a model that predicts the dependent variable perfectly has an R² of 1 and a model that does not explain any variability in the data has an R² of 0.

This section displays the machine learning model experiment outcomes. The following Table 2 shows the XGB model achieves 86.81% R-score.

Figure 6 XGBoost Regression’s scatter plot shows actual and forecasted costs related to one another. The red dots demonstrate that actual costs tend to increase with expected prices, suggesting that the XGBoost regression model accurately uses actual values to make cost predictions.

In this section, present the outcomes of a machine learning method, including KNN [7] , Ridge [27] , Lasso [28] , and XGB on the dataset. In this step, evaluate how well the model could predict. It presents the result in the procedure of bar graphs, Table 3 , and figures.

Figure 7 shows the results of comparing the R²-scores of the different models.

XGB fits the data the best, with a R²-score of 86.81. In a regression model, the R²-score, also known as the coefficient of determination, quantifies the percentage of the dependent variable’s variation that is accounted for by the independent variables. Lasso follows closely with an R²-score of 79.78, slightly outperforming Ridge at 78.38. KNN has the lowest R²-score at 55.21, reflecting the lowest accuracy among the models in predicting the target variable. The overall XGB model outperforms other models.

Figure 8 RMSE comparison reveals that KNN has an RMSE of 4431.1, slightly better than XGB with an RMSE of 4450.4, indicating better accuracy in predictions. Ridge Regression follows with an RMSE of 4652.06, and Lasso has the highest RMSE at 5671.6, suggesting it has the greatest prediction error among the models.