Application Of Zero Inflated And Its Extended Model In The Research Of School Absenteeism Due To Illness/Injury

Objective: This paper systematically organizes the theoretical knowledge of various discrete models including Poisson regression model,Zero-inflated Poisson regression model and Zero-K inflated Poisson regression model.By introducing the Zero-K inflated Poisson regression model to explore and solve the problem of fitting zero and K value inflated characteristic data in actual medical research,and uses the constructed zero-K inflated Poisson regression model to analyze the data of school absenteeism due to illness/injury.At the same time,several discrete models are compared and evaluated to determine the best fitting model,so as to explore the relationship and effect between various influencing factors and school absenteeism behavior due to illness/injury.In addition,this research can provide methodological help and support for the fitting problems of discrete quantitative variable data with excessive zero and K values encountered by scholars engaged in epidemiological survey work.Materials and methods: The 2018 National Health Interview Survey(NHIS)child sample data was obtained from the official website of the US Centers for Disease Control and Prevention(CDC),and the data of school absenteeism due to illness/injury and various possible influencing factors in the same period were collected.The characteristics of over-dispersion and zero inflation of school absenteeism due to illness/injury were tested.According to the principle of model simplicity,Spearman correlation analysis was used to conduct univariate correlation analysis on the relationship between multiple possible influencing factors and school absenteeism due to illness/injury,and then combined with single factor Poisson regression analysis to screen out statistically significant influencing factors.Further constructed zero-inflated discrete models including Zero-K inflated Poisson regression model(ZKIP),and compared with the traditional discrete models including Poisson regression model,the best fitting model was determined according to the goodness of fit evaluation index of each discrete model,so as to explore the relationship between the influencing factors and the school absenteeism behavior due to illness/injury in the data,and estimated the effect of each possible influencing factor on the days of school absenteeism due to illness/injury.Results: 1.The O test results of the data over-discrete test show that the data of the number of days of school absenteeism due to illness/injury in the past 12 months has over-discretization characteristics.According to the histogram results of school absenteeism days due to illness/injury,it can be seen that the data on the number of days of school absenteeism due to illness/injury has 0 and 2 inflation phenomena.2.The discrete models used to fit the number of days of school absenteeism due to illness/injury were compared respectively,and the constructed models were compared and evaluated according to the goodness of fit evaluation and other indicators.The zero-inflated Poisson regression model was superior to the traditional Poisson regression model.and the Zero-K inflated Poisson regression model with K=2 was the best fitting model.The variables revealed by the Zero-2 inflated Poisson regression model which had significant effects on the zero inflation characteristics of the data were completely consistent with the Zero-inflated Poisson regression model.Compared with the zero-inflated Poisson regression model,the OR value of the parameter estimates of the same variables were similar,but the 95% confidence interval(CI)width of the OR value of the zero-2 inflated Poisson regression model was narrower,and the standard error(SE)of the parameter estimation was smaller.The zero-K inflated Poisson regression model was suitable for school absenteeism data with zero-2 inflation characteristics,which may have higher value in practical applications.3.The regression results of the zero-2 inflated Poisson regression model with zero-inflated parameters showed that in the past 12 months,delayed care(Delayed care),history of surgery(Surgery),asthma attacks(Cashyr),allergies(Allergies),physical discomfort(Physically sick)and taking prescription drugs for 3 months or more(Probrx)had statistically significant effects on the zero-inflated part of the data on the number of days of school absenteeism due to illness/injury,and negatively correlated with school absenteeism days.The OR values of these variables were all less than 1,indicating that when the above events occurred,the number of zero absenteeism days decreased and the risk of school absenteeism due to illness/injury increased.At the same time,compared with adolescent students aged 12-17,children aged 5-11 had fewer zero absenteeism days and more absenteeism days due to illness/injury.Race and region variables also had statistically significant effects on the zero-inflated part of the data.Compared with white only(White only)children and adolescent students,Black/African American only(Black/African American only),Asian only(Asian only)and multiple race(Multiple race)students had decreased the risk of school absenteeism(all P<0.05).In terms of Region variables,students in the South had more 0-day absenteeism than those in the Northeast and had a lower risk of absenteeism.The Gender variable had no significant effect on the zero inflation part of the absenteeism data.The zero-2 inflated Poisson regression model found that in the past 12 months,Allergies(β=0.25,OR = 1.29)had a significant effect on the inflation parameter η of K = 2,and the occurrence of student allergies would increase the risk of 2 days absenteeism.According to the variables which had statistical significance on the parameters of the Poisson distribution(that is,non-inflated part),compared with White only students,students who were AIAN only were more likely to report absenteeism(β=0.16,OR = 1.17),while students whose race was Black/African-American had lower risk of absenteeism(β=-0.17,OR = 0.84).At the same time,Delayed care,Can’t afford care,and Surgery in the past 12 months increased the risk of school absenteeism for children and adolescents students(all OR>1),while having a regular preventive health care places(Chcplrou)decreased the occurrence of school absenteeism(β=-0.14,OR=0.87).Having vision problems(Cvision),bad disease condition(Disease condition),taking prescription drugs for 3 months or more(Probrx),asthma attack(Cashyr)in the past 12 months,Allergies,Physically sick,and flu vaccination(Cshflu12)also had a significant impact on the Poisson distribution of the data on days of absenteeism due to illness/injury(all OR>1).Boys had a higher risk of absenteeism than girls(β=0.06,OR=1.07).Compared with students in the northeast,students in the western region had a higher risk of absenteeism(β=0.08,OR=1.08).Conclusion: Although in many cases,Poisson regression is the first choice for discrete data modeling,in specific problems,because the data is over-discretized with zero inflation,it is possible to obtain better goodness of fit by selecting a variety of zero inflation and extended models including Zero-K inflated Poisson regression(ZKIP)model according to data characteristics.The Zero-K Inflated Poisson Regression(ZKIP)Model is suitable for fitting the data of the number of days of school absenteeism due to illness/injury.Like most parametric models,ZKIP model is very sensitive to the deviation of hypothesis distribution,and it has an incomparable advantage in discussing and estimating the relationship and effects between various influencing factors in the data and school absenteeism behavior due to illness/injury.Therefore,the zero-K inflated Poisson regression(ZKIP)model has research significance and practical application value,and is a powerful extension model of the zero inflation model.