Variable Selection In Marginal Regression Mixture Cure Model For Clustered Failure Time Data With A Cure Fraction

Survival data with a sizable cure fraction is commonly encountered in cancer research.At the same time,the clustered failure time data has drawn more and more attention in the biomedical research.The marginal mixture cure model has been recently used to analyze such clustered failure data with a cure fraction.Existing methods for variable selection of clustered data are rarely in mixture cure models,and they generally assume that the data is independent and establish the corresponding likelihood function.The proposed method for penalized generalized estimating equations only needs to specify the first two marginal moments and a working correlation matrix,which avoids the calculation of complex joint likelihood functions and considers the correlation between data.And in the penalty term,we consider using the SCAD penalty function which satisfies the oracle feature and use the GIC criteria to select tuning parameters.Since the data is right censored,the estimation can be implemented by combining the penalized logistic regression and the penalized Cox proportional hazards models with the expectation–maximization algorithm.We use the Bootstrap method to estimate the variance of the estimated parameters.Numerical simulation shows that the proposed method is simple to use and more efficient than existing methods that ignore the within cluster correlation and the oracle model.Finally,we further apply the proposed method to a smoking cessation clustered data.