Research Of Establishing Hospitalization Charge Fitting Model By Using BP Neural Network

During recent a few years, the charge of medical care has increased rapidly. The large medical care charge, especially the hospitalization charge, bring heavy economical burden to people. How to control the hospitalization charge so that it can not increase so rapidly is what researchers concerned most. An effective way to control it is to research about its influence factors. To fit the relationship between hospitalization charge and its influence factors, and establish effective hospitalization fitting model is the key topic in the research.One method which is used frequently for analyzing hospitalization charge is multiple linear regression , but it has some limitations, such as independent, normal distribution, equal variance, linear and so on. In fact, the relationship between hospitalization charge and its influence factors is very complex, it is perhaps not linear, or there may be multicollinearity in influesce factors.So we need to develop another useful model which is suitable for hospitalization charge to express the relationship.Artificial neural network, also known as neural network, is a mathematical model which was developed according to the work of biological neuron. Neural network is widely used forpattern recognition, prediction, and value approach and so on. BP (Backpropagation) neural network is a kind of multilayer perceptron. It is named because the weight of network is adjusted by error backpropagation arithmetic, and is the most mature and widely used method of all kinds of neural network. It is proved that for any continual function, the input variables with n dimensionality can predict output variables with m dimensionality in any accuracy by a BP neural network with one hidden layer. But standard BP arithmetic has some disadvantages, such as the rate to convergence is low, and it is easy to get into lowest local point, and it can't generalize well. Since 90th, a lot of arithmetic was developed to optimize standard BP arithmetic, to make BP network have better performance in fitting and generalization.As BP neural network has no limitation to the type and distribution of data, and has the ability to tolerance error, also it can fit complex relationship between input variables and output variables by learning and adjusting itself. So we consider establishing model to fit hospitalization charge and influence factors by using BP neural network.ObjectivesDiscuss about how to optimize the setting of model parameter during process of establishing BP neural network model, and finally get a suitable BP neural network to fit hospitalization charge. Then use sensitivity analysis to analyze how these influence factor affect hospitalization charge. We expect that the establishing process and results of our research can provide some references to methodology of how to establish BP neural network model, and can help health care managers and medical insurance workers to make right decision and analysis.Data and MethodsData came from information of inpatient records of digestive system malignancy offered by 2 hospitals in Zhejiang Province. There are 4853 cases collected in all. After eliminating imperfect cases, illogical cases and the cases that are not cured, we got 3893 effective casesfinally, which were 80.22%of the total cases.We used BP neural network to fit function between influence factors and hospitalization charge which is not visual.During process of establishing model, ANOVA, / test and nonparametric test were all used to compare different training arithmetics and different numbers of neurons in hidden layer. Sensitivity analysis was used to analyze those influence factors based on the model. ANOVA, / test and nonparametric test were all completed by using SAS 8.2, and establishing of BP neural network model and sensitivity analysis were both completed by using MATLAB.Results(1) Results of comparing parameters of model establishingFour types of BP neural network wered established, 5, 10, 30 and 60 were used as the number of neurons in hidden layer separately, and each type of network used LM arithmetic and SCG arithmetic separately. So, eight types of neural network were established, and all neural networks were trained 500 times. The result was that no matter how many neurons the hidden layer has, LM arithmetic is better than SCG arithmetic in both fitting and generalization.By comparing the performance of LM arithmetic in the network each has S, 10, 30 and 60 neurons in hidden layer, we found that when the number of neurons in neural network is 5 and 10, generalization ability of neural network has no difference, others has difference between each other. When the number of neurons in hidden layer is 30 or 60, generalization ability of neural network decreased. When the number of neuron in hidden layer if 5, 10 or 30, if the number increased, R1 of train set increased, fitting performance of network is better, when the number is 30 or 60, there is no difference between each network. The result showed that if LM arithmetic was chosen, the number of neurons in hidden layer should be around 10, so that the network can get better performance.Another three types of BP neural network were established, 5, 7 and 10 were used as thenumber of neuron in hidden layer separately, and each type of network used Bayesian regulanzation BP arithmetic, and all neural networks were trained 500 times. By comparing the performance of Bayesian regularization'BP arithmetic in each network, we found that when the number of neurons in neural network increased, generalization ability decreased, but fitting ability increased. The result showed that if Bayesian regulanzation BP arithmetic was chosen, as we consider generalization ability of network first, the number of neurons in hidden layer should be around 5, so that the network can get better performance.(2) LM arithmetic was chosen to train the network based on the results above. And the number of neurons in hidden layer is near 10. And Bayesian regulanzation BP arithmetic was also chosen to train the network, and the number of neurons in hidden layer is near 5. We used different numbers of neurons in hidden layer and different values of weights and bias when initialization. Finally a BP neural network model was established to fit relationship between influence factors and hospitalization charge for patients of digestive system malignancy. The residual scatter graph showed that residual is varied around zero, it indicated that the model fits well. The parameter of established BP neural network is: one hidden layer, 9 neurons in hidden layer, 12 neurons in input layer, and 1 neuron in output layer. The parameter used for training is: using LM arithmetic and early stopping method, the learn rate is 0.01, the performance function of error is set as SSE, 24 epochs was got when the neural network stopped training. The fittingresult of train set: ^=0.85744, ^=0.73521, ^ =0.7201, SSE= 1.0146 e+012, MSE= 4.5929e+008, RMSE= 21431. The test result of test set is: tf=0.82695, /?2=0.68385, R^ =0.62275,55ï¿¡=5.2225e+011, MSE=8.01e+008, RMSE=2%W2.(3) Result of sensitivity analysisThe result of sensitivity analysis showed that, the order of sensitivity value of all influence factors is: length of stay(0.92113), operation(0.84083), times of salvage(0.83802), second diagnoses(0.60272), age(0.40353), disease(0.35043), hospital(0.34762), the condition when getout of hospital(0.32585), fee type(0.30425), the condition when get into hospital(0.25735), occupation(0.25312), sex(0.075872). It is obvious that the factor influence hospitalization charge most is length of stay, and least is sex.ConclusionsFrom our research, some conclusions were got: BP neural network is usable for eatablishing hospital charge fitting model, different parameters were set to optimize the model;the fitting ability and generalization ability can't be both very good. If the network fitted output variable very well, the generalization ability can't be good. So during process of establishing BP neural network, we should consider how to balance the fitting ability and generalization ability. A good neural network should first have good generalization ability, otherwise the model is meaningless although the model may fit train test very well. Sensitivity analysis can be used for analyzing the influence of input variables.As the information of inpatient records we chose for establishing BP neural network is limited, and both fitting and generalization ability of the model were considered, so the model we established finally for predicting the hospitalization charge has limited accuracy, but the model can provide some reference in theory. It is reliable to do sensitivity analysis based on established neural network model to test the influence of input variables. The performance of neural network can be affected by different parameters, such as different number of neurons in hidden layers, different values of weights and bias when initialization. There are still no definite theory of how to set these values, and we need to research more.