Neural Network Model of Pricing Health Care Insurance

Transcription

1 Neural Network Model of Pricing Health Care Insurance Abstract To pricing health insurance plan statisticians use atheatical odels to analysis custoer s future health condition. General Addictive Model (GAM) is a wide-accepted ethod for this proble however it have several liitations. To solve this proble a new ethod naed neural network odel is ipleented. Copare with GAM odel neural network provide a ore accurate predicting result. Keywords General Addictive Model; neural network odel; Health Care Insurance 1. Introduction 1.1 General inforation of health care insurance pricing proble Health care insurance is a financial structure that against the risk of future edical expenses of individuals. By predicting the health care expenses of a certain group of people an agency sets up a onthly payroll called preiu. The insurance copany will provide health care benefits to the individuals who pay the preiu regularly. Benefits are specified by a contract between the insurance agency and its custoer. Most Large copanies provide health care insurance to their eployee. And the governent also supplies Medicare (a special health insurance) to the disables aged people and people who have no incoe. [1] Pricing healthcare insurance is a coplex procedure. It is iportant for a copany to pricing each custoer s health insurance plan individually base on his/her life condition. Several factors including gender age health condition incoe job status and the living place would be considered [1]. The variability of price of health care insurance plan for different people is high. For people who had a severe disease the price of health care insurance will higher than average. Healthcare industries have several principles for pricing health insurance products []. Firstly preiu aount need to be adequate. The price ust low enough to attract consuers while providing a reasonable aount of profit to the copany itself. Secondly preiu aounts need to atch the coverage that the health insurance could provide and eet the requireent of custoer. Few costuers will pay for low price insurance without enough benefit. If the copany charges too uch oney for the coverage of the health care product it will lose its costuers. Thirdly the preiu of health insurance product need to copetitive copare with the aount charged by other health insurance copanies for siilar products. Few costuers wanted to spend a great deal of oney just for a special reasonable benefits policy. In ost cases a better price won ore costuers. Finally the health insurance of every custoer ust keep equality. Soe custoer placed uch ore clais than other costuers. As a result the price for each individual is expected to be different. Thus the health care insurance industries need to design distinct insurance plan focus on different target custoer group. For each plan health insurance copanies need to construct atheatical odels predicting the future health care expenditure base on custoer s health condition and other inforation. After consider future expenditure of custoers and operation cost of copany itself statistician could set up a reasonable price and coverage of a health insurance plan. Several statistical ethods were used to pricing health insurance plan [3]. 1. For History of atheatical odeling about pricing health care insurance Many researchers have developed statistical odels to estiate the future edical expenditure by analysis people s previous health status. In early 1990s ost health industries used General Linear Model (GLM) to predict future health condition for custoers. GLM is a flexible extension of linear regression for a single dependent variable. It contains several explanatory variables denoted as x1 x x and one responsive variable g( y ). For health insurance pricing proble statisticians choose gender age working status incoe and previous insurance clais of custoers as explanatory variables. And the response variable g( y ) could be future edical expenditure or price of health insurance of custoers. Then statisticians estiate by a dataset of previous paraeters 0 1 custoers inforation. The odel is shown as equation (1). g( y) x x x (1) After constructed the GLM odel health insurance copanies could predict the future edial expenditure of a new custoer and price his health insurance plan [3]. Recently GLM odel is still a wide-

2 accepted odel for approxiate estiate in soe health insurance copanies [4]. After 1995 General Additive Model (GAM) gradually entered people s vision. GAM odel is developed fro blending of the key characters of generalized linear odel and additive odel. [7] In a typical GAM odel the explanatory variables x1 x x and paraeters 0 1 in GLM is replaced by a series of ore coplex functions of explanatory variables denoted as f ( x1) f ( x) f ( x ). The function f( x ) provides a better fitting for dataset than paraeters in GLM odel. It naed sooth function. In the other hand we use link function g( E( y )) instead of g( y) as response variable of the odel. The odel is shown as equation (). g E y 0 f x1 f x f x ( ( )) ( ) ( ) ( ) () To construct a GAM odel we have several steps. Firstly assuing the data of custoers is selected fro a population with a specific distribution (usually noral distribution or binoial distribution). Then we use a link function g( E( y )) to relating the expectation value Ey ( ) of that distribution and several explanatory variables. Secondly we need to collect the custoer s inforation in database of healthcare insurance copany to construct the sooth function. This procedure called training. After training process the established GAM odel is well prepared for pricing the health insurance plan for a new custoer. Now GAM has becoe the ost popular ethod aong statistical odels in the field of pricing health care insurance [5] [6]. 1.3 Liitation of GAM odel GAM odel provides a good fitting of ost datasets. However it suffers fro four ajor liitations. Interaction of explanatory factors is the ost iportant proble. Interaction eans an effect of two or ore factors to a certain result is not siply added. For exaple regular soking will increase the probability of a people to suffer fro lung cancer. We denote the aount of increase as p 1. And drinking alcohol will also increase the probability of a person to have cancer. We denote the increase as p. Then for a person who is always drinking and soking his chance to suffer fro cancer is not only p 1 p but p1 p a p1 p where a is a constant index. In other words existence of an interaction effect iplies that the effect of one explanatory variable is a function of another explanatory variable. If variables x1 and x have interaction relationship the original GAM odel will be changed: g( E( y)) f ( x ) f ( x ) f ( x ) f ( x ) f( x ) (3) x x x For a set of explanatory variables 1 we need to exa the interaction effect of these variables ( 1) for ties. To acquire a ore accurate prediction of custoer s future health condition statisticians need to select ore than 0 explanatory variables to construct the GAM odel. If so reconstructing of GAM odel with interaction effect will ore than 00 ties. Statisticians need to exa whether each of the is significant. If we include high order interaction (the interaction effect of ore than variables) effect in the analysis the proble will be even ore coplex. In ost cases researchers spend a lot of tie on interactions of explanatory variables. They adjust the odel any ties to ake sure it is constructed correctly. To siplify this procedure researcher ight reduce the nuber of explanatory variables to iprove predictive ability of this odel. [6] The second disadvantage of GAM odel is collinear. Collinear is a ter describing two or ore variables have a correlation relationship. For exaple a soking custoer has a higher probability to have respiratory disease. It is unfair to charge this custoer for both reasons. To solve this proble analyst need to use factor analysis ethod to cobine the collinearly variables into one factor and then fitting the regression odel of several factors instead of explanatory variables. It will spend a lot of tie and lose the accuracy of the odel. [7]. Another liitation worth entioning is over fitting. Over fitting occurs when a statistical odel is excessively coplicated. A over fitting odel generally has a prefect fitting for its training data but has poor predicting result. It is not always good to pursue a better fitting result. Most statistical odels have a threshold. When training the odel if the fitting accuracy increase higher than this threshold the predicting accuracy will decrease while the training accuracy increase. For the GAM odel in health insurance pricing proble analysts used to control the fitting error of predicting expense not lower than 8% to avoid over fitting. As the nuber of sooth paraeters increase the over fitting proble will becoe ore obvious [4]. Besides GAM odel is restricted by paraetric assuption. To acquire an outcoe of custoer s health condition insurance copanies need to assue that data is selected fro a certain kind of distribution. However the assuption ight not exactly correct. The paraetric odel ight suffer fro the inaccurate assuption. It is difficult to estiate the paraeters of odel under this situation. [7]. Materials and ethods.1 Neural network odel Neural network odel (artificial neural network ANN) was designed base on the structure of brain and neural syste attepting to siulate the process of huan study and decision aking based on a certain data set. It is a newly developed coputational odel in artificial intelligence field.

3 3 Figure 1. Huan brain and nervous syste odeled by coputer syste. A neural network consists of several input variables one or ore output factors and a group of connected hidden points called inner neurons. Each input variable connects to all inner neuron in hidden layer. The value of an inner neuron is the su of each input value ultiple to a weight. The weight could be thought as the eory of huan s bran; it could be changed while training. And the output value of the odel denote as the su of each inner neuron value ultiple to other weight. The weights between each two points are different. The odel changes its weight when training inforation flowing through the network. After the odel was constructed it could be used to predict the future health care expense of a new custoer and deterine how uch insurance fee should be paid base on his current health condition [7]. propagation network (BP neural network). The structure of these two kinds of networks has slightly different. In the first step inner points of feed forward network could only accept inputting data. And points will output the data in next step. BP neural is a ore popular odel in recent years. In BP neural network each inner point could input inforation and output inforation at the sae tie. Neurons of BP neural network could accept feedback of next layer. This odel provides a ore accurate predicting result than FF neural network. Thus we use BP network to calculate the price of health care insurance in next paragraph.[14]. An exaple of pricing healthcare insurance by neural network odel To show how neural networks works on pricing healthcare insurance proble we run a neural network odel by a set of data of 00 custoer s personal inforation. This dataset is collected by Brockett in a research project at 009[8]. Table 1 the inforation of first 5 custoers in the training data of the exaple. (COPD is chronic obstructive pulonary disease). No. Gender Age Incoe Soke Previous Expenditure (per year) Clai 1 feale 58 0 Yes COPD 1050$ ale $ No None 0 3 ale $ Yes Lung $ Cancer 4 feale $ No None 100$ 5 feale $ No Diabetes 500$ Figure. Structure plot of neural network odel. Copare with GAM odel neural network odel have several advantages [16]. First of all ANN is a nonparaetric ethod. In other word this odel adapted saple dataset selected fro population of all kinds of distributions. Therefore statisticians could use ANN odel directly without analysis the probability distribution of dataset. Secondly because of its coplex inner structure the statisticians need not to consider interaction effect during analysis. Finally in the training process the changing of weight structure will autoatically cobine the collinear factors. In a word by using ANN odel statisticians avoid spending tie on interaction effect collinear analysis and assuption of population distribution. Thus the process of constructing an artificial neural network is uch sipler than GAM odel and other regression odel. ANN odel has better perforance than traditional statistical approaches on predicting of people s health condition. [9] Neural network have two different classifications: feed forward network (FF neural network) and back We use neural network Toolbox of Matlab software to deal with this proble. We construct a BP neural network odel with 6 input points 8 inner points (1 layer) and 1 output point. And we use half of data as training saple and other half data to exa the predicting accuracy of this odel.[13] 3. Result and Discussion 3.1 Coparison of the results of neural network odel and GAM odel Table the suary of accuracy of neural network odel and GAM odel Accuracy Interaction Collinear analysis analysis ANN 94%~107% None None GAM 90%~110% Soke Soke & Clai Fro table we could see that ANN has a better predicting accuracy than GAM odel.

4 4 Table 3 the suary of over fitting of neural network odel and GAM odel Distribution assuption Error of Over fitting threshold ANN None 6% GAM Noral 8% 3. Liitation of neural network odel The neural network odel has an excellent predicting result on pricing health care insurance proble. However it have not solved the over fitting proble entirely. It just reduce the over fitting threshold of the odel. In a GAM odel analyst needs to control the error of predicting result close to 8%. And statisticians could reduce the over fitting threshold to 6% in ANN odel [9]. 3.3 Analysis iproveent and developent of neural network odel of healthcare insurance proble To iprove the accuracy of predicting without over fitting analyst could try to collect ore custoers inforation as training data. The over fitting threshold will decrease while training saple is large. [1011] References [1]. Richard G. Frank Karine Lairaud Choice price copetition and coplexity in arkets for health insurance Journal of Econoic Behavior ≈ Organization Volue 71 Issue August 009 Pages 55 []. Does health insurance reduce illness-related worker absenteeis? Xiao Xu Gail A Jensen. Applied Econoics. London:01. Vol. 44 Iss. 35 p [3]. More health care utilization with ore insurance coverage? Evidence fro a latent class odel with Geran data Hendrik Schitz. Applied Econoics. London: 01. Vol. 44 Iss. 34 p [4]. Does patient trust proote better care? Debra Dwyer Hong Liu John A Rizzo. Applied Econoics. London: 01. Vol. 44 Iss. 18 p. 83 [5]. The ipact of clinical trial insurance coverage andates on racial inorities and low incoe individuals Natalie Chun Minjung Park. Applied Econoics. London:01. Vol. 44 Iss. 15 p [6]. Does inequality in China affect health differently in high- versus low-incoe households? Hai Fang John A Rizzo. Applied Econoics. London:01. Vol. 44 Iss. 9 p [7]. A coparison of neural network statistical ethods and variable. Brockett Patrick L; Golden Linda L; Jang Jaeho; Yang Chuanhou Journal of Risk and Insurance; Sep 006; p.397 [8]. Fuzzy clustering and neural network applications in activity duration odeling Cao Ling. Proquest Dissertations And Theses 009. Section 0148 Part pages; [M.A.Sc. dissertation].canada: The University of Regina (Canada); 009. Publication Nuber: AAT MR [9]. Neural network for identification and control of stochastic systes Wang Zhennong. Proquest Dissertations And Theses Section 0099 Part pages; [Ph.D. dissertation].united States -- Kansas: University of Kansas; Publication Nuber: AAT [10]Qixin Wang Yang Liu Xiaochuan Pan (008) Atosphere pollutants and ortality rate of respiratory diseases in Beijing Science of the Total Environent Vol.391 No.1 pp [11]Does health insurance reduce illness-related worker absenteeis? Xiao Xu Gail A Jensen. Applied Econoics. London:01. Vol. 44 Iss. 35 p [1] Qixin Wang Menghui Li Hualong Zu Mingyi Gao Chenghua Cao Li Charlie Xia(013) A Quantitative Evaluation of Health Care Syste in US China and Sweden HealthMED Vol.7 No.4 PP [13]Qixin Wang Menghui Li Li Charlie Xia Ge Wen Hualong Zu Mingyi Gao (013) Genetic Analysis of Differentiation of T-helper lyphocytes Genetics and Molecular Research Vol.1 No. PP [14]Qixin Wang Chenghua Cao Menghui Li Hualong Zu (013) A New Model Based on Grey Theory and Neural Network Algorith for Evaluation of AIDS Clinical Trial Advances in Coputational Matheatics and its Applications Vol. No.3 PP [15]Qixin Wang Menghui Li (013) Syste Dynaic Modeling for Spread of AIDS in representative Countries Advances in Coputational Matheatics and its Applications Vol. No.3 PP [16] Qixin Wang Yang Liu Lihong Mo (007) The evaluation and prediction of the effect of AIDS therapy Proceeding of IEEE International Conference on Coplex Medical Engineering pp [17] Y. Han and A. T. Chronopoulos. Distributed Loop Scheduling Schees for Cloud Systes. IEEE High- Perforance Grid and Cloud Coputing Workshop(HPGC'13) in conjunction with IPDPS 013 Boston MA May 013. [18] Y. Han and A. T. Chronopoulos. Scalable Loop Self- Scheduling Schees Ipleented on Large-Scale Clusters IEEE Workshop on Large-Scale Parallel Processing(LSPP'13) in conjunction with IPDPS 013 Boston MA May 013.

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