Variable Selection For Interval-Censored Data With Varying-Coefficient Cox Models

The problem of variable selection skillfully uses the methods in statistics to select a few suitable variables from many characteristic variables to explain and predict the model.It has gradually become a hot topic in statistics.Nowadays,the problem of variable selection involves many aspects,and the related models are also diverse.For survival analysis related models,many literature studies so far are based on right-censored data,and there are not many literatures on interval-censored data.More in-depth research is necessary.In this paper,the varying-coefficient Cox model is used to study the variable selection problem under the type-I interval-censored data.Due to the special form of this type of model,its likelihood function contains two unknown parameters:the cumulative baseline hazard function（？）₀（t）and the varying-coefficient function β（t）.this paper uses Bernstein polynomials to fit the cumulative baseline hazard function（？）₀（t）.For the varying-coefficient function β（t）,The article uses the B-splines approximate expansion method for fitting,combined with the classic adaptive group Lasso variable selection method,penalizes the log-likelihood function,and turns the maximum log-likelihood function into a minimum negative penalty log-likelihood function.In order to achieve the purpose of simplifying the formula,the article uses Cholesky decomposition to process the log-likelihood function,transforming it into the form of least squares,and proposes a new iterative process to solve the model,and complete the whole variable selection procedures.In order to test the feasibility and effectiveness of the method,and further discuss the variable selection problem of the varying-coefficient Cox model with type-I interval-censored data,the article gives specific data generation schemes and evaluation indicators for numerical simulation.The results show that the method in the article is effective in selecting the main variables of the varying-coefficient Cox model with type-I interval-censored data.In addition,the fitting effect of the unsegmented function is better than that of the piecewise function.When the number of observed individuals is larger or the censoring rate is lower,the accuracy of variable selection is higher.In addition,the article also combined actual examples of Alzheimer’s disease,established a model to explore its influencing factors,and found that five factors have an impact on the disease,namely:clinical dementia rating scale score,auditory language instant retelling learning test score,caregiver level,chronic disease score and patient self-care ability.According to the experimental results,the function images of these factors changing over time are drawn,and reasonable suggestions are given accordingly.