| ObjectivesMedical expenses grow radiaily in China.Reducing medical expenses and optimizing the allocation of resources is one of the key problems of government health care reform.Reducing medical expenses and optimizing the allocation of resources is one of the key problems of government health care reform.Therefore,it is an important prerequisite to formulate medical reform plan and strategy by accurately evaluating and forecasting medical expenses.The distribution of medical expenses was skewed,heavy-tailed.The special distribution of medical costs suggests a serious heterogeneity of the patient population.The assumption that the distribution of medical expenses from multiple distributions can provide a new idea for accurate estimation of medical costs.Based on the theory of regression analysis and clustering analysis,FMM assumed that the initial distribution could be a mixture of different distributions to identify heterogeneity among populations.This research introduces the principle of finite mixture model,simulates the distribution of real medical data,evaluates the predictive performance of FMM,and applies it to the case analysis and validates the influencing factors of FMM recognition performance by full sample and external sample verification.MethodsIn the first part,the Quasi-Monte Carlo experiment was performed based on the total cost of 104646 chronic hepatitis B outpatients outpatients in Eighth People's Hospital of Guangzhou in 2012.The simple random sampling method was used to extract the sample sizes of 500,1000,2000,5000,8000,10000,20000.Each sample size repeated 50 times the experiment.The generalized linear model,the two components of finite mixture model and the three components of finite mixture model with Lognormal,Gamma and Weibull distribution were perfomed respectively in the samples.The accuracy,bias and goodness of each model were evaluated.And the optimal model was applied in 2 chronic hepatitis B patients outpatient cost of the whole sample in Eighth People's Hospital in 2012,and and used hepatitis B outpatient cost of 2015 as external sample verification.In the second part,based on the above results and the case study,the Gamma distribution and Weibull distribution were selected as the theoretical distribution.The Monte Carlo simulation method was used to extract that the two components or 3components were mixed by adjusting the composition parameters and mixing probability.We seted the sample size to a total of 1000,5000,10000.Each model experiments 50 times per sample size.The finite mixture models and generalized linear models of the theoretical distributions are fitted to the simulation experiments.The number of components,the correct classification rate and the absolute prediction error of each model under various parameters are evaluated.ResultsQuasi-Monte Carlo experiment showed that the three-component finite mixture model of Weibull distribution was dominant in terms of accuracy and goodness-fit for the medicalexpenses data of the chronic hepatitis B outpatients in the Eighth People's Hospital of Guangzhou in 2012.From the mean prediction,the generalized linear model dominates.Full sample validation showed the same result.The sample of the external sample showed that the 2-component finite mixture model of the Weibull distribution was the optimal model,and the effect of goodness-fit and the individual prediction are higher than the generalized linear model.Monte Carlo simulation experiments showed that the two components of the specified Weibull distribution of finite mixed model performed well.In the simulation experiment the three components of the specified Weibull distribution,when the high cost component and the other components were different,the FMM recognition ability was strong.When the difference between high cost components and other components was reduced,FMM tends to be identified as two components.When the medium component cost and the high cost component were heacy-tailed,the FMM tended to be identified as two components.When the three components showed three distinct unimodal distributions,FMM tended to be identified as three components.FMM behaved similarly in both proportions.In the simulation experiment,when the ratio of component 1 and component 2 overlap,the FMM tends to be identified as three components when the mixing ratio of high cost components was high,and the mixing ratio of high cost components was higher than that of the two components.FMM tended to identify two components.When the difference between the two components was significant(the expected value and the variance difference was large),FMM tended to be identified as two components at various ratios.In the simulation experiment,when the ratio of component 3 to component 2 increases,FMM tended to be identified as two components in the case of low mixing ratio of high cost components,and the two components of the Gamma distribution,When the mixing ratio was the same,FMM tends to identify three components.When the components 2 and 3 were simultaneouslyshifted to the right,the difference between the three components increases,and the 3components were crossed away from the 3 single-peak distribution.When the high cost ratio was small,the FMM tended to be identified as three components.When the mixing ratio was the same,FMM tended to identify the number of components greater than 3.The larger the sample size,the better the model performance.The accuracy of FMM was higher than that of generalized linear model.ConclusionsThe finite mixture model can identify the heterogeneity of medical expenses by recognizing the population as different components.The model provides a model choice for solving the medical expenses data with skewed,heavy tail distribution characteristics.The difference between the size of the data and the mixing probability affect the recognition performance of the model,and the sample size has little effect,and the Weibull distribution can better fit the heavy tail distribution data.FMM has an advantage in individual prediction.FMM model can further explore the characteristics of sub-groups of the influencing factors,in order provide suggest to develop a specific medical insurance strategy,high-cost patient monitoring and intervention. |
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