摘要
目的构建一种处理混合相依删失数据的非参数比例风险(PH)模型,探讨心脏移植手术风险与风险因子直接的关系并预测心脏移植手术风险。方法基于混合相依区间删失数据的复杂性,考虑失效时间过程与观测时间过程的相依关系,假设风险因子与心脏移植手术风险存在非线性函数关系,建立具有非参数结构的比例风险模型,并给出两步Sieve估计极大似然算法。根据观测过程模型建立估计方程,获得脆弱变量的估计;再分别利用I-样条和B-样条去近似基准风险函数和非参数结构函数,获得Sieve空间中的工作似然函数,对于模型参数求偏导获得得分方程;最后通过求解方程获得参数的极大似然估计,绘制风险因子影响心脏移植手术风险的函数曲线。结果模拟研究揭示了各种设置下所提方法获得的估计量是相合的且渐近有效的,同时获得很好的参数拟合曲线。心脏移植手术数据分析结果显示,心脏供体的年龄对患者手术风险影响呈现正向线性关系,患者(受体)发病年龄影响先增大后平稳,最后有缓慢增大,供体与受体的年龄差对患者手术风险影响呈现正向线性关系。结论本研究建立了一个可分析复杂相依删数据的非参数PH模型,该模型应用于分析预测心脏移植手术风险,通过模型可探索出心脏移植手术风险与风险因子之间的函数关系。
Objective To construct a nonparametric proportional hazards(PH)model for mixed informative interval-censored failure time data for predicting the risks in heart transplantation surgeries.Methods Based on the complexity of mixed informative interval-censored failure time data,we considered the interdependent relationship between failure time process and observation time process,constructed a nonparametric proportional hazards(PH)model to describe the nonlinear relationship between the risk factors and heart transplant surgery risks and proposed a two-step sieve estimation maximum likelihood algorithm.An estimation equation was established to estimate frailty variables using the observation process model.I-spline and B-spline were used to approximate the unknown baseline hazard function and nonparametric function,respectively,to obtain the working likelihood function in the sieve space.The partial derivative of the model parameters was used to obtain the scoring equation.The maximum likelihood estimation of the parameters was obtained by solving the scoring equation,and a function curve of the impact of risk factors on the risk of heart transplantation surgery was drawn.Results Simulation experiment suggested that the estimated values obtained by the proposed method were consistent and asymptotically effective under various settings with good fitting effects.Analysis of heart transplant surgery data showed that the donor's age had a positive linear relationship with the surgical risk.The impact of the recipient's age at disease onset increased at first and then stabilized,but increased against at an older age.The donor-recipient age difference had a positive linear relationship with the surgical risk of heart transplantation.Conclusion The nonparametric PH model established in this study can be used for predicting the risks in heart transplantation surgery and exploring the functional relationship between the surgery risks and the risk factors.
作者
王淑影
姜馨竹
赵波
董贺
WANG Shuying;JIANG Xinzhu;ZHAO Bo;DONG He(School of Mathematics and Statistics,Changchun University of Technology,Changchun 130000,China)
出处
《南方医科大学学报》
CAS
CSCD
北大核心
2024年第4期689-696,共8页
Journal of Southern Medical University
基金
吉林省自然科学基金优秀青年项目(20230101371JC)。
关键词
心脏移植手术
相依区间删失
非参数比例风险模型
两步估计方法
Sieve极大似然估计
heart transplantation surgery
informative interval-censored
nonparametric proportional hazards model
two step estimation method
sieve likelihood estimation
