基于Bernstein多项式的半变系数组合诊断方法研究  

Research on Semi-varying Coefficients Combination Diagnosis Method based on Bernstein Polynomial

作　　者：张中文 许晴晴 王玖 韩春蕾 孙红卫 Zhang Zhongwen;Xu Qingqing;Wang Jiu(School of Public Health and Management,Binzhou Medical University(264003),Yantai)

机构地区：[1]滨州医学院公共卫生与管理学院,264003

出　　处：《中国卫生统计》2023年第3期377-381,共5页Chinese Journal of Health Statistics

基　　金：全国统计科学研究项目(2018LY57);2022年滨州医学院青年骨干教师培养计划项目。

摘　　要：目的探讨基于Bernstein多项式的半变系数logistic回归模型的估计,从而描述协变量与二分类结果变量间更为复杂的关系,并探索该模型在多变量组合诊断试验中的应用。方法利用Bernstein多项式将半变系数logistic回归模型近似转化为普通logistic回归模型,随后采用极大似然法估计回归参数。利用蒙特卡罗模拟评价模型的估计效果。在实例研究中,采用随机抽样法将数据集分割为训练集与测试集,并分别将其用于训练建模及验证评估。不同组合诊断方法的比较采用ROC曲线,检验采用Bootstrap配对法。结果在不同的样本量条件下,常数系数和变系数的估计偏差均较小,常数系数的估计标准误和经验标准误的偏差也不大,变系数函数估计的95%置信带基本平行。随着样本量的不断增加,常数系数的估计偏差逐渐变小,变系数函数的95%置信带也逐渐变窄。在本文的模拟假设下,半变系数logistic回归模型的诊断效果优于普通logistic回归模型,差别具有统计学意义。在实例研究中,应用半变系数logistic回归模型进行多变量组合诊断的AUC值大于普通的logistic回归模型,且差别具有统计学意义(P=0.003)。结论本研究提出的基于Bernstein多项式的估计方法具有良好的估计效果,估计方法稳定,计算速度较快,而且对样本量的要求也不高。同时,半变系数logistic回归模型可显著提高多变量组合诊断的效果,对于提高疾病诊断的准确性具有一定的应用价值。Objective To evaluate the estimated effect of the semi-varying coefficients logistic regression model based on Bernstein polynomial,so as to describe the more complex relationship between the covariates and the binomial result variables,and analyze the application of this model in the multivariate diagnostic test.Methods The semi-varying coefficients logistic regression model was approximated by Bernstein polynomial and the regression parameters were estimated by maximum likelihood method.Monte Carlo simulation was used to evaluate the estimated effect of the model.In application study,the data set is divided into training set and validation set by random sampling method,and used for training modeling and validation to evaluate respectively.ROC and Bootstrap method were used for the comparison of different diagnostic methods.Results The estimation deviations of constant coefficients and varying coefficients are small under different sample sizes,the estimation deviation of the estimated standard error and empirical standard error for constant coefficients are also small,and the 95% confidence bands of varying coefficients function estimation are almost parallel.With the increasing the sample size,the estimation deviation of constant coefficients become smaller and the 95% confidence bands of varying coefficients function become narrower.Under the simulation hypothesis in this paper,the diagnostic effect of semi-variable coefficient logistic regression model is better than that of ordinary logistic regression model,and the difference is statistically significant.In application study,the AUC of the multivariate diagnosis using the semi-varying coefficients logistic regression model was higher than that of the normal logistic regression model,and the difference was statistically significant(P=0.003).Conclusion The estimated method based on Bernstein polynomials proposed in this study has good performance,and it is stable to estimate with fast calculation speed,and low requirement on sample size.At the same time,the

关 键 词：BERNSTEIN多项式 半变系数logistic回归模型 多变量诊断 极大似然估计 

分 类 号：R195.1[医药卫生—卫生统计学]