# Prediction of Health Care Costs by Dental Health Care Costs and Periodontal Status
## 3 Results  
The study population was 46 individuals (29 men and 17 women; mean age pf 44.6 \(\pm\) 1.7 years). A descriptive analysis of the data used in this study is shown in Table 1. The standard deviation values were high, and their distributions were skewed. In the Kolmogorov-Smirnov test, none of these values were normally distributed. Figure 1 shows a scatter plot of health care costs (2017) against health care costs (2016), dental health care costs (2016), and salivary levels of lactate dehydrogenase (LD) (2016). The coefficient of determination was not sufficient to create a regression model for predicting health care costs. A nonlinear prediction model based on a neural network model was applied. For the prediction of health care costs (2017), we first constructed models with a single independent variable of health care costs from the previous year (2016), dental health care costs from the previous year (2016), or salivary levels of LD from the previous year (2016) (Figure 2A-C). Health care costs from the previous year were a strong predictor for health care costs, and the inclusion of dental health care costs and salivary levels of LD for health care costs improved the prediction accuracy. Predictive values were calculated by the models shown in Figure 2A-D.  
Next, we used all three independent variables to build a health care cost prediction model (Figure 2D). Predictive accuracy was improved by including dental health care costs and salivary levels of LD in addition to health care costs from the previous year (Figure 3, solid circle and empty circle). \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Mean \(\pm\) SD** & **Median (25 th–75 th Percentile)** \\ \hline
**2016** & & & \\ Health care costs (USD) & 1035.00 & \(\pm\)1300.27 & 572.45 (220.36–1255.09) \\ Medical health care costs (USD) & 877.27 & \(\pm\)248.55 & 482.36 (126.91–1161.73) \\ Dental health care costs (USD) & 157.73 & \(\pm\)2.39 & 84.55 (0–279.55) \\ Salivary levels of LD (IU/mL) & 4.09 & \(\pm\)2.39 & 3.70 (1.73–5.94) \\
**2017** & & & \\ Health care costs (USD) & 994.00 & \(\pm\)1172.27 & 550.45 (122–1577.27) \\ Medical health care costs (USD) & 775.55 & \(\pm\)975.55 & 42.65 (105.45–1165.73) \\ Dental health care costs (USD) & 218.36 & \(\pm\)402.64 & 0 (0–455.91) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Descriptive analysis of the health care costs and salivary levels of lactate dehydrogenase (LD). Figure 1: Scatter plot and linear regression line of health care costs against total health care costs, dental health care costs, and salivary levels of lactate dehydrogenase (LD). The coefficient of determination (R\({}^{2}\)) was not high. Health care costs were not easy to predict by linear regression analyses. Figure 2: Models by a single independent variable. (**A**) health care costs from the previous year; (**B**) dental health care costs from the previous year; (**C**) salivary levels of LD from the previous year (2016); (**D**) Models by multiple these three independent variable. The predicted values are shown in the scatter plot of the prediction values against the observed values (Figure 3). Among the three independent variables, health care costs from the previous year were the most important predictor of health care costs. Then, by using the model in Figure 2D, we simulated the health care costs by health care costs, dental health care costs, and salivary levels of LD from the previous year. Since the vector space was four-dimensional, the results are displayed conditionally with the fixed healthcare cost data at 0, 100,000, 200,000, 500,000, and 1 million Japanese yen. The results of the response surfaces are illustrated in Figure 4.  
In the case of healthcare costs of 0 yen, if the LD levels in saliva are 0, then the medical expenses will be 0 yen, and the health care costs the following year will be predicted near the flat surface. As LD levels or dental health care costs increased, health care costs increased, but the gradient was moderate.