Prediction Model of Elderly Care Willingness Based on Machine Learning

Abstract

At present, the problem of an aging population in China is severe. The integration of existing healthcare services with elderly care services is inefficient and cannot meet the needs of the elderly. As such, China urgently needs the concerted efforts of various social forces to cope with the increasingly serious problem of aging. In accordance with Andersen’s behavioral model, a survey was conducted in Tangshan City among seniors 60 years of age and older. Using logistic regression models, decision tree models, and random forest models, we examined the factors impacting senior people’s desire to choose the integrated medical care and nursing care model. The results of the three models displayed that the elderly’s propensity to choose the combined medical care and nursing care model is significantly influenced by the amount of insurance, life care needs, and healthcare needs. Moreover, the study found that the willingness of the elderly in Tangshan to improve the combined medical and nursing care service system is low. The government should appeal to the community to participate in multiple developments to improve the integrated medical and nursing service system.

1. Introduction

The trend in population aging has been formed in developed countries and is either taking shape in developing countries or has yet to be formed. However, this trend is inevitable worldwide. At present, China is facing the dual pressure of deep aging and rapid urbanization [1]. According to the statistics of the seventh population census, in 2020 the number of people over 60 years of age in China reached 264 million, accounting for 18.7% of the total population, and the number of people aged 65 and over reached 190 million, accounting for 13.5% of the total population [2]. It is expected that China will become an aging society in 2022, and that by the 2060s the population of over 65-year-olds will be close to its peak, with roughly one in every three Chinese being over 65 years old, accounting for 33%. It will be a deeply aging society [3].

The first country to propose the concept of medical and elderly care was the United Kingdom. In the 1960s, the notion of integrating medical with elderly care in the UK appeared. With a view to “reducing costs, improving quality, and putting service first”, “integrated care” was regarded as an economic elderly care service model, ranging from the management of the elderly stage to the close management of different age stages, and from managing the patient himself to the family and social support systems [4]. With the increase in China’s elderly population, ensuring their health has become a challenge for families. The aging of the population is becoming more and more serious, and the demand for the elderly service industry is becoming more and more great. However, the development of China’s elderly care service industry started late and there are still many problems. With regards building a better elderly care service model, due to the current shortage of pension resources, the state has launched the pension model of institutional pensions, home care, pension real estate, and other aspects. However, the traditional pension services can no longer meet the growing needs of the elderly [5]. Majorly developing the integrated undertakings and industries of medical and elderly care is an inevitable choice to cope with the problems of an aging society [6]. The number of elderly people in China’s medical security system is increasing, which has a far-reaching impact on social and economic development. Therefore, from the perspective of the combination of medical care and nursing, we should give full attention to the function of family old-age security and improve the functions of community medical treatment, rehabilitation, and nursing [7].

Since 2013, China has promulgated a series of policies related to the integration of medical with elderly care, which has promoted the high-quality development of integrated medical and elderly care services [8]. Improving the overall health level is of great significance and can improve the health level of the elderly. The search found that as of 24 September 2020, a total of 180 “integrated medical and nursing care” documents have been issued [8]. When it comes to building an elderly care service system in China, there exists a contradiction between the need for healthy aging and the imbalance and insufficient supply of medical and elderly care resources [9]. The policy response to resolve this local contradiction in the present era is to integrate medical and health resources with elderly care service resources to provide high-quality integrated medical and elderly care services for all the elderly [10]. At present, from a policy perspective China has a home-based, community-based, and institution-supplemented nursing care system. Not only has the number of policies specifically aimed at integrating medical with nursing care gradually increased, but also the number of policies that mention the integration of medical with nursing care in terms of content has gradually increased [11]. The old service model and the community–home–medical–elderly care integrated service serve the elderly living in the community and at home by providing them with comprehensive, economical, and convenient, sustainable health and elderly care services. Their simple service supply and broad population coverage have become one of the mainstream forms of the medical and elderly care service model, which is theoretically more in line with the concept of healthy aging. Compared with professional elderly care service institutions, community homes allow the elderly’s families to take residence as the properties. For the elderly, staying in a suitable elderly care environment such as in the community or with family has positive significance for extending the lives and social relationships of the elderly and improving the overall health level [12]. The “combination of medical and nursing care” model is suitable for implementation in elderly care communities, elderly care institutions, nursing institutions, and medical and health institutions, and is a new type of old-age security service model that effectively combines medical service technology with the old-age insurance model to improve the utilization rate of medical resources and improve the quality of old-age services, thereby greatly improving the quality of life of the elderly and realizing “treatment with diseases and recuperation without diseases” [13].

Western developed countries have explored the needs of the elderly for old-age care and medical services since the 20th century. A relatively mature old-age medical service system has been established so far [14]. The integration of medical with elderly care is developed on the basis of long-term care, which refers to the healthy elderly care model of providing life care services, health management services, and medical care services for the elderly through the integration of medical treatment with old-age care [15]. An efficient integrated care system is a complete chain including care recipients, care providers, managers, care delivery sites, care content, coordination of various functional departments, etc., and is an organic whole in which all departments work together [16,17].

In the future, it is inevitable that China will become a deep aging population and that the country will face the severe challenge of aging. With the rapid development of today’s economy and the increasing improvement of people’s living standards, it is proposed that “the combination of medical health and elderly care services is a long-term plan to actively cope with the aging of the population, which is conducive to meeting the growing multi-level and diversified demand for health and elderly care services of the people” [4,18]. In the future, the use of new technologies to help elderly care institutions will be strengthened. The four major tasks of elderly care include healthy aging, active aging, successful aging, and productive aging. With the development of the times, intelligent elderly care has emerged; especially in the post-epidemic era, intelligent and intelligent elderly care services are particularly important. This is also the development trend of China’s medical and oxygen integration [19]. In this context, the combination of medical care and nursing care is emerging and will become increasingly important [20]. At present, some studies have been conducted on this issue, but they have only scratched the surface and have not explored in depth the reasons and factors that influence the willingness of elderly people to accept this model, nor have they provided good solutions to improve the implementation of this model. In order to better serve the elderly, we conducted a survey on the elderly aged 60 and above in Tangshan by means of questionnaires based on Andersen’s behavior model. We analyzed the factors that affected the attitude of the elderly to community healthcare and elderly care services through logical regression model, decision tree model, and random forest model. We hope that the results of this study can provide a basis for continuous improvement of community medical and nursing services and make them the best choice for the elderly.

2. Materials and Methods

2.1. Study Subjects

The respondents were the elderly aged 60 and above in Tangshan. In conformity with the data of the 7th National Population Census, the overall number of elderly people (aged 60 and above) in Tangshan City was 1,760,600, accounting for 22.81% of the resident population of Tangshan City [1]. The proportion of the population aged 60 and above in the total population in Tangshan is higher than the national average. Therefore, the study of the demand for and factors influencing the integration of healthcare for the elderly in Tangshan City has some significance for the development of integrated healthcare services.

2.2. Sampling Method

The survey design used the data from the Seventh National Census to obtain the distribution of elderly people in the administrative districts and counties of Tangshan in 2020, using a three-stage mixed sampling method with stratification and PPS (Probability Proportionate to Size Sampling) [21]. Among the 18 districts and counties in the Tangshan area, the primary sampling area was selected during the first stage using the PPS sampling method based on an estimated ratio of 2:1:1:1 for the number of districts, counties, cities, and functional areas. In the second stage, the streets in each district and county were stratified in the primary sampling area and then drawn. In the third stage, the number of randomly selected streets in the area where they were located was drawn and a questionnaire survey was conducted on the elderly. After adding the findings of the pre-survey, it was calculated that 510 individuals were used as the starting sample. Ultimately, 600 questionnaires were sent and 551 valid questionnaires were returned.

2.3. Andersen’s Behavioral Model Theory

The Andersen model has evolved into a model with three major categories of determinants of propensity characteristics, ability, and need, according to Wang Yisui, Wen Deliang, and Ren La [22], who used the literature research method to compile and analyze the pertinent literature for their 2017 publication, “The Andersen Model of Health Service Utilization Behavior and its Evolution”.

This study further develops the Andersen behavior model and applies it to an analysis of the factors that affect healthcare integration, adapting it to China’s elderly healthcare integration system and providing a valuable foundation for China’s healthcare integration reform based on an understanding of the evolution of Andersen’s health service behavior model.

2.4. Model Introduction

2.4.1. Principle of Binary Logical Regression Model

Logistic regression is a mathematical model which can be applied to estimate the probability of belonging to a certain class. In fact, binary logic regression is the study of the influence of X on Y, which is binary data. When analyzing the influence of X on Y, the mathematical model can be constructed as follows:

$$\ln \left(\frac{P}{1-P}\right)={\beta }_0+{\beta }_1{X}_1+{\beta }_2{X}_2+\cdots +{\beta }_m{X}_m$$

(1)

Binary logistic regression is one of the most commonly used statistical methods for binary results [23]. It predicts the likelihood of a binary event from a set of variables. As can be seen from the above formula, $\ln \left(\frac{P}{1 - P}\right)$ obeys the binary logical distribution, where P represents the probability of the occurrence of an event, 1 − P represents the probability that the event did not occur, and the value of the dependent variable Y under study will be only 1 and 0. Therefore, when building logistic regression using this model, we hope that the original data is 1, and then the predicted value fitted by the model will also be close to 1. Moreover, the original value of the model is 0; thus, the fitting value predicted by the model is also as close to 0 as possible. $X_1$ and $X_2$ are the influencing factors of the study and the coefficient in front is the regression coefficient. The model applies the principle of maximum likelihood method. The mathematical formula of this principle is as follows:

$$L={\displaystyle \prod }_{i=1}^n{P}_i^{Y_i}{\left(1-P_i\right)}^{1-Y_i}$$

(2)

Y can have a value of 0 or 1. It goes without saying that if Y is 1, then P, and if Y is 0, then 1 − P. As stated earlier, our goal is to have the P calculated by model fitting be as near to 1 as possible when Y is 1, and as close to 0 as possible when Y is 0. Therefore, the model fitting effect is good if the value of the above formula L is the maximum. The aforementioned formula’s logarithm is as follows:

$$\ln L={\displaystyle \sum }_{i=1}^n\left[Y_i\ln P_i+\left(1-Y_i\right)\ln \left(1-P_i\right)\right]$$

(3)

At this time, the problem is converted into the maximum value of$\ln L$, where Y is known data (original data) and P is the data to be fitted by the model. The calculation formula of p value can be converted in combination with the previous formula. After conversion, the formula is as follows:

$$P=\frac{1}{1+\exp \left[-\left({\beta }_0+{\beta }_1{X}_1+{\beta }_2{X}_2+\cdots +{\beta }_m{X}_m\right)\right]}$$

(4)

The value of $\beta$ is the estimated parameter; the regression coefficient obtained when $\ln L$ is the maximum is the regression coefficient of the final model. Generally, the Newton iteration method is adopted when solving regression coefficients. The common formula of the Newton iteration method is as follows [24]:

$$x_{n+1}=x_n-\frac{f\left(x_n\right)}{f^{\prime }\left(x_n\right)}$$

(5)

Select $x_0$ as the starting point of iteration and continue to iterate through the above equation until the specified accuracy is reached. The selection of this starting point is critical because the Newton iteration method obtains a local optimal solution. If there is only one zero point in the function, the selection of $x_0$is not important. If there are multiple local optimal solutions, it is generally the goal to find the zero-point specified near a$x_0$ point [25].

2.4.2. Principle of the Decision Tree Model

Decision trees can perform regression and classification problems. The model has a traditional tree structure that is quite interpretable and consistent with how people think. A tree structure that describes the classification of instances is the classification decision number model. Nodes and divided edges make up the decision tree [26]. There are numerous internal nodes, several leaf nodes, and a root node among the nodes. Leaf nodes indicate a category, whereas internal nodes represent a characteristic or trait. The decision tree has many nodes and a set number of nodes reflect the testing of particular attributes [27]. The basic flow chart of the decision tree is attached in Figure 1.

Information purity is taken into consideration when building decision trees. When building decision trees, information purity is frequently measured using terms such as information gain, information gain rate, Gini impurity, etc. Information entropy serves as the foundation of the ID3 algorithm. The node division standard chooses the attribute with the largest information gain as the division attribute in order to determine the information gain (X, Y) of each attribute. Only discrete attributes can be handled by the ID3 algorithm and input variables with more category values are more likely to become the current optimal division point. The following formulas are available:

$$\mathrm{Gains}\left(X,Y\right)=\mathrm{Ent}\left(X\right)-\mathrm{Ent}\left(X\mid Y\right)=\mathrm{Ent}\left(X\right)-{\displaystyle \sum }_{i=0}^v\frac{\left|D^v\right|}{\left|D\right|}\mathrm{Ent}\left(D^v\right)$$

(6)

$$\mathrm{Ent}\left(X\right)=-{\displaystyle \sum }_{i=0}^v{p}_i{\log }_2{p}_i$$

(7)

In the formula, v is the number of attribute values and p_i is the probability of the occurrence of type I labels [28,29]. In the process of decision making, the decision tree may have the problem of over fitting. Common solutions include the minimum leaf node limit, the maximum decision tree depth limit, or pruning the tree.

2.4.3. Principle of the Random Forest Model

Random forest is a set of decision trees based on the concepts of bagging and random subspace. As Breiman suggested, the power of unstable learners and the diversity among them are the core advantages of the integrated model. A random forest is one that was created randomly [30]. The forest is full of decision trees. In the random forest, there is no correlation between any of the decision trees. Following the creation of the random forest, each decision tree in the forest is tasked with deciding which category the new input sample belongs to. The most often chosen category is then counted and the predicted category is determined using that data. Each decision tree should be created with consideration for sampling and complete splitting [31]. First, there are two methods for random sampling. The input data are sampled at random from rows and columns. The putting back approach is used for row sampling, meaning that duplicate samples may exist in the sampled sample set. Let us assume that there are N input samples and N samples. By not using all of each tree’s input samples during training, it is relatively impossible to appear overfitted. After that, choose m features (mM) from the M features using column sampling [32]. The sampled data are then completely divided, either to prevent a leaf node of the decision tree from further splitting or to ensure that all of the samples in the tree point to the same classification. Below is a flow chart which is attached in Figure 2.

Many CART trees make up a random forest. The training set that each tree uses is sampled from the overall training set, which means that some samples from the total training set may appear in a tree’s training set numerous times or never at all. The features used to train the nodes of each tree are randomly picked from all the features according to a predetermined proportion [33]. Assume that there are M characteristics total, and this proportion can be sqrt (M), 1/2 sqrt (M), or 2sqrt. In each round of sampling, the probability of sample x being sampled is 1/m. Therefore, the probability of the sample not being sampled after m round of sampling is:

$$\underset{m\to \infty }{\lim }{\left(1-\frac{1}{m}\right)}^m\approx \frac{1}{e}\approx 0.368$$

(8)

Therefore, about 36.8% of the samples in the original dataset have not been sampled, and these samples can be used for the external estimation of learners trained by the new dataset D′ [14]. When the dataset is so small that the training and test sets cannot be separated well, this method is applicable and provides a lot of help for integrated learning. However, since the new dataset obtained changes the sample distribution of the original dataset, the self-service sampling method may introduce some errors. Therefore, when the original dataset is large enough, reserve and cross validation methods should be used as far as possible [30].

2.5. Data Processing

The data on demographic characteristics were analyzed using SPSS 26.0 software and R software for frequency analysis; χ² analysis was conducted on the data on the elderly’s willingness to select the combined medical care and nursing care model under different propensity characteristics, ability, and need factors. The factors with statistically significant differences in the χ² analysis were used as independent variables for multivariate logistic regression with the elderly’s willingness to select the combined medical care and nursing care model as the dependent variable. The factors with statistically significant differences in the χ² analysis were used as independent variables for a decision tree with the elderly’s willingness to select the combined medical care and nursing care model as the dependent variable. The factors with statistically significant differences in the χ² analysis were used as independent variables for a random forest with the elderly’s willingness to select the combined medical care and nursing care model as the dependent variable. The difference was considered statistically significant at p < 0.05.

3. Results

3.1. Basic Information regarding Older People

Among the 551 cases of elderly people, 298 (54.1%) were male and 253 (45.9%) were female; 220 (39.9%) were aged 70 or below; 312 (56.6%) were living in urban areas; 271 (49.2%) had 2 or fewer children; 320 (58.1%) lived alone; 287 (52.1%) had a junior high school education or below; 258 (46.8%) had their own financial resources; 291 (52.8%) had a monthly income of RMB 3000 or less; 299 (54.3%) had 3 or less insurance policies; 103 (18.7%) were in poor health; 518 (94.0%) were able to take care of themselves; and 75 (13.6%) had a desire to select the combined medical care and nursing care model. See

Table 1. Analysis of the willingness of the elderly to select the combined medical care and nursing care model with different characteristics.

Features	Number of Examples	Percentage of People Who Would Like to Select a Combined Healthcare Model	χ2	p
Gender			0.734	0.455
Male	298	44(14.8%)
Female	253	31(12.3%)
Age			0.058	0.899
≤70	220	29(13.2%)
>70	331	46(13.9%)
Residence			0.403	0.616
City	312	45(14.4%)
Country	239	30(12.6%)
Number of children			1.614	0.216
≤2	271	42(15.5%)
>2	280	33(11.8%)
Residence conditions			0.020	0.900
Solitary	320	43(13.4%)
Non solitary	231	32(13.9%)
Education level			6.266	0.013
Junior high school and below	287	29(10.1%)
Above junior high school	264	46(17.4%)

and

Table 2. Analysis of the willingness of the elderly to select the combined medical care and nursing care model with different abilities.

Features	Number of Examples	Percentage of People Who Would Like to Select a Combined Healthcare Model	χ2	p
Economic sources			0.048	0.901
Own	258	36(14.0%)
Others	293	39(13.3%)
Monthly income			0.807	0.386
≤3000	291	36(12.4%)
>3000	260	39(15.0%)
Insurance quantity			19.480	<0.001
≤3	299	23(8.1%)
>3	252	52(20.6%)
Health			2.559	0.150
Good	448	66(14.7%)
Poor	103	9(8.7%)
Self-care ability			0.071	0.793
Able	518	70(13.5%)
Unable	33	5(15.2%)

for detailed basic information.

3.2. A Comparison of the Willingness of the Elderly with Different Characteristics to Select the Combined Medical Care and Nursing Care Model

The percentage of elderly people in Tangshan who have a willingness to age in a combined medical and nursing care model is 13.6%. A comparison was made of the elderly’s willingness to choose the combined medical care and nursing care model under three major categories of determinants: propensity characteristics, ability, and need. As a grouping variable, whether or not the elderly are willing to choose the model of care that combines medical and nursing care was utilized. A single-factor analysis was conducted on the influencing factors under each of the three major dimensions.

In terms of propensity characteristics, the willingness of elderly people with different levels of education to select the combined medical care and nursing care model differed, with all differences being statistically significant (p < 0.05), while in other aspects the willingness of elderly people to select the combined medical care and nursing care model was comparable, with no statistically significant differences (p > 0.05), see Table 1.

In terms of capacity, the willingness of elderly people to select the combined medical care and nursing care model differed by the number of insurance policies, and the differences were all statistically significant (p < 0.05). In other aspects of the willingness of elderly people to select the combined medical care and nursing care model, the differences were not statistically significant (p < 0.05). See Table 2.

In terms of needs, the willingness of elderly people to select the combined medical care and nursing care model differed between those with different needs for life care, healthcare, day care services, and emergency care, and the differences were statistically significant (p < 0.05), while in other aspects the willingness of elderly people to select the combined medical care and nursing care model was not statistically significant (p < 0.05). See

Table 3. Analysis of the willingness of the elderly to select the combined medical care and nursing care model with different needs.

Features	Number of Examples	Percentage of People Who Would Like to Select a Combined Healthcare Model	χ2	p
Life care needs			93.038	<0.001
Unwanted	457	33(7.2%)
Wanted	94	42(44.7%)
Healthcare needs			158.876	<0.001
Unwanted	476	30(6.3%)
Wanted	75	45(60%)
Day care service needs			72.014	<0.001
Unwanted	482	43(8.9%)
Wanted	69	32(46.4%)
Emergency rescue needs			27.938	<0.001
Unwanted	497	55(11.1%)
Wanted	54	20(37%)
Demand for sports and recreation			2.403	0.133
Unwanted	526	69(13.1%)
Wanted	25	6(24%)
Learning and training needs			2.567	0.119
Unwanted	504	65(12.9%)
Wanted	47	10(21.3%)
Psychological nursing needs			0.555	0.471
Unwanted	511	68(13.3%)
Wanted	40	7(17.5%)

.

3.3. Multivariate Logistic Regression Analysis of Factors Influencing the Willingness of the Elderly to Select the Combined Medical Care and Nursing Care Model

A multivariate logistic regression analysis was carried out with the willingness to select the combined medical care and nursing care model as the dependent variable and the factors with statistically significant differences in the univariate analysis as the independent variables (see

Table 4. Multivariate logistic regression analysis of factors influencing the elderly’s willingness to select the combined medical care and nursing care model.

Dimension	Indicators	Assignment
Dependent variable	Willingness to choose a combined care model for aging	No = 0; Yes = 1
Dispositional characteristics	Education level	Junior high school and below = 1; Above junior high school = 2
	Insurance quantity	≤3 = 1; >3 = 2
Capabilities	Life care needs	Unwanted = 0; Wanted = 1
needs	Healthcare needs	Unwanted = 0; Wanted = 1
	Day care service needs	Unwanted = 0; Wanted = 1
	Emergency rescue needs	Unwanted = 0; Wanted = 1

for the assignment of variables). The results showed that insurance quantity had a significant effect on the elderly’s willingness to select the combined medical care and nursing care model (p < 0.05), and that the greater the insurance quantity, the stronger the willingness to select the combined medical care and nursing care model (OR = 3.433). Healthcare needs had a significant effect (p < 0.05) on the elderly’s willingness to select the combined medical care and nursing care model; those with healthcare needs were more likely to choose the combined medical care and nursing care model (OR = 11.32). 0.05), and those with day care service demands were more likely to choose the combined medical care and nursing care model (OR = 3.524). See

Table 5. Multivariate logistic regression analysis of the factors influencing the elderly’s willingness to select the combined medical care and nursing care model.

Independent Variable	B	SE	p	OR
Education level	−0.073	0.338	0.828	0.929
Insurance quantity	1.234	0.349	0.000	3.433
Life care needs	1.312	0.362	0.000	3.713
Healthcare needs	2.427	0.343	0.000	11.32
Day care service needs	1.260	0.392	0.001	3.524
Emergency rescue needs	0.720	0.421	0.087	2.055
Constant	−5.111	0.812	0.000

.

The logistic prediction model had a specificity of 83.82%, a sensitivity of 88%, and an AUC of 0.891, p < 0.05, indicating that the logistic model was significant in predicting the willingness of the elderly to choose integrated healthcare. See

Table 6. Prediction accuracy of the logistic model.

	Specificity	Sensitivity	AUC	p
Logistic model	83.82%	88%	0.891	<0.001

and Figure 3.

3.4. Decision Tree Model Analysis of Factors Influencing the Elderly’s Willingness to Select the Combined Medical Care and Nursing Care Model

A decision tree analysis was carried out with the willingness to select the combined medical care and nursing care model as the dependent variable and the factors with statistically significant differences in the univariate analysis as the independent variables (see Table 4 for the assignment of variables). The decision tree model is shown in Figure 4. The root node of the tree is divided according to the willingness to select the combined medical care and nursing care model, while other nodes in the tree include gender, learning and training needs, and healthcare needs.

The probability of having healthcare needs and choosing the combined medical care and nursing care model was 60% (45 cases). The probability of not having healthcare needs but having life care needs and choosing the combined medical care and nursing care model was 21.8% (12 cases). The probability of having no healthcare needs and no life care needs but having an insurance quantity >3 and being willing to choose the combined medical care and nursing care model was 6.7% (12 cases).

The decision tree prediction model had a specificity of 84.66%, a sensitivity of 76%, and an AUC of 0.851, p < 0.05, indicating that the decision tree model was significant in predicting older people’s intention to choose the combined medical care and nursing care model. See

Table 7. Prediction accuracy of the decision tree model.

	Specificity	Sensitivity	AUC	p
Decision tree model	84.66%	76%	0.851	<0.001

and Figure 5.

3.5. Random Forest Model Analysis of Factors Influencing the Elderly’s Willingness to Select the Combined Medical Care and Nursing Care Model

A random forest analysis was carried out with the willingness to select the combined medical care and nursing care model as the dependent variable and the factors with statistically significant differences in the univariate analysis as the independent variables (see Table 4 for the assignment of variables). The random forest model is shown in Figure 6. The root nodes of the tree are divided according to whether or not the elderly people were willing to select the combined medical care and nursing care model.

It can be seen from Figure 7 that the model error values level off as the survival tree approaches 500. The random forest model indicators are ranked in order of importance: healthcare needs, day care service needs, life care needs, emergency rescue needs, insurance quantity, and education level. It can be seen that in the random forest model, healthcare needs have a strong influence on whether the elderly are willing to select the combined medical care and nursing care model.

The random forest prediction model had a specificity of 86.67%, a sensitivity of 84.24%, and an AUC of 0.877, p < 0.05, indicating that the random forest model was significant in predicting the willingness of older people to select the combined medical care and nursing care model. See

Table 8. Prediction accuracy of the random forest model.

	Specificity	Sensitivity	AUC	p
Random forest model	86.67%	84.24%	0.877	<0.001

and Figure 8.

3.6. Comparison of Predictive Model Results

The results of the DeLong test displayed that the AUC of the logistic model was significantly higher than that of the decision tree model (p < 0.05); moreover, the prediction accuracy of the logistic model was significantly higher than that of the decision tree model. The AUC of the logistic model was not significantly different to that of the random forest model (p > 0.05) and the AUC of the decision tree model was not significantly different to that of the random forest model (p > 0.05). See

Table 9. Model prediction accuracy comparison.

Models	C-Statistic Difference	SE	Z	p (DeLong’s Test)
Logistic and decision tree models	0.040	0.014	2.961	0.003
Decision tree model and random forest model	0.026	0.018	1.416	0.157
Logistic model and random forest model	0.014	0.014	0.994	0.320

and Figure 9.

4. Discussion

4.1. Low Willingness to Select the Combined Medical Care and Nursing Care Model

The study found that the willingness of the elderly in Tangshan city to select the combined medical care and nursing care model was low, being only 13.6% (75 cases), which is higher than the findings of scholars such as Huang Sufen [34] (61.1%) and Wang Wen [35] (64.7%), showing that the willingness of the elderly in Tangshan city to select the combined medical care and nursing care model is very low. This indicates that the Party committee and the municipal government of Tangshan City should attach great importance to the aging of the population and speed up the construction of the combined medical and nursing care system by increasing financial investment, formulating perfect plans, and introducing policy measures.

4.2. Factors Influencing the Elderly’s Willingness to Select the Combined Medical Care and Nursing Care Model

The factors impacting the elderly’s inclination to choose the combined medical care and nursing care model were screened using a multi-factor logistic regression model, a decision tree model, and a random forest model. The study discovered that the elderly’s propensity to choose the combined medical care and nursing care model was significantly influenced by the amount of insurance, life care needs, and healthcare needs. The ability and need-based variables had a higher impact on the elderly’s propensity to choose the combined medical care and nursing care model, according to the Andersen behavioral model, when taken together.

4.2.1. Insurance Quantity

Under the dimension of ability characteristics, insurance quantity had a significant impact on the willingness of older people to select the combined medical care and nursing care model. The study found that older people with more insurance had a stronger willingness to select the combined medical care and nursing care model. Compared to those with a small amount of insurance, those with a large amount of insurance invested more in insurance funds for medical care and pensions, had a deeper knowledge of the integration of healthcare with pensions, and were more widely involved in society. As a result, older people with a higher quantity of insurance were more accepting of the combined medical and healthcare model.

4.2.2. Life Care Needs

The study discovered that the elderly’s propensity to choose the combined medical care and nursing care model was significantly influenced by the amount of insurance, life care needs, and healthcare needs. The ability and need-based variables had a higher im-pact on the elderly’s propensity to choose the combined medical care and nursing care model, according to the Andersen behavioral model, when taken together.

4.2.3. Healthcare Needs

The desire of older individuals to choose the combined medical care and nursing care model was significantly impacted by the need for healthcare, according to the demand dimension. The demand for healthcare reflected the different needs of older people with different health conditions for integrated healthcare services. Studies have found that older people with healthcare needs have a stronger willingness to age in a combined healthcare model [36]. As older people age, the risk of illness increases, their frailty deepens, and they suffer from multiple illnesses, making it difficult for families to take on the burden of aging alone. The combined medical and nursing model can offer the practical and essential services to lessen family stress. As a result, older people with healthcare needs are more likely to be interested in this model.

4.3. Recommendations

4.3.1. Calling on the Community to Participate in the Development and Improvement of the Integrated Healthcare Service System

We should promote health management for the elderly, elderly health and medical and healthcare integration services, and family doctor contracting services. Moreover, we should encourage social forces to establish institutions for the provision of integrated healthcare and support social forces in their participation in integrated healthcare through a variety of models, such as public construction, private ownership, or private management and assistance.

4.3.2. Relying on the Construction of a Medical Association and Medical Community to Improve the Level of Integrated Medical and Healthcare Services

Building medical communities and associations is a good way to put the “people-centered” idea into practice, integrate medical resources, encourage resource sharing across urban and rural regions, raise the standard of medical care, and better serve the public. Likewise important is accelerating the development of close-knit medical association communities to strengthen the capacity and standard of grassroots medical and health institutions’ services and to encourage the sinking of high-quality resources. It is also crucial to strengthen the introduction and training of talents and create a system for the medical staff of combined medical and health institutions to continue their education.

4.3.3. Improve Pricing Policies and Promote Long-Term Care Insurance Systems

The pricing policy for combined medical and nursing services should be improved, which should be based on the actual cost of services and be approved based on factors such as market supply and demand and the affordability of the elderly, so as to prevent the elderly from giving up their choice of combined medical and nursing services for financial reasons, and to provide protection for the development of home care services. To encourage the long-term growth of integrated medical with nursing services, the government should also strengthen its oversight of health insurance and define the difference between “medical” and “nursing” payments. At the same time, the long-term care insurance system should be promoted as a means of reducing costs, alleviating the care and financial burdens on the families of the elderly, and maintaining the quality of life and dignity of the elderly.

5. Conclusions

The study found that the willingness of the elderly in Tangshan city to select the combined medical care and nursing care model was low. The results of the logistic regression model displayed that insurance quantity, life care needs, healthcare needs, and day care service needs were the factors which influenced the elderly’s willingness to select the combined healthcare model (p < 0.05). The results of the decision tree model showed that healthcare needs, life care needs and insurance quantity were the factors influencing the elderly’s willingness to select the combined healthcare model (p < 0.05). The results of the random forest model revealed that healthcare needs, day care service needs, and life care needs were the top three influencing factors for the elderly’s willingness to select the combined healthcare model (p < 0.05). The area under the ROC curve of the logistic model was 0.891 (0.845–0.936); the decision tree model’s area under the ROC curve was 0.851 (0.800–0.902); and the area under the ROC curve of the random forest model was 0.877 (0.819–0.934). The AUC of the logistic model was significantly higher than that of the decision tree model (p < 0.05) and there was no statistical difference in prediction model accuracy between the two groups for the remaining methods (p > 0.05). The use of the logistic regression model, decision tree model, and random forest model were of high value in the study of the main influencing factors on the willingness of elderly people to select the combined medical care and nursing care model. Due to the lack of funds, only Tangshan City was selected for this research. This will lead to the deviation of the research results from the national situation.