Statistical Analysis Of Marginal Proportional Hazards Model Based On Quadratic Inference Function

Clustered failure time data is commonly encountered in biology and medicine studies and marginal regression modeling is usually used to determine the potential factors of failure risk.Based on the potentially correlation right-censored clustered failure time data,the generalized estimating equation of the marginal proportional hazards model introduces a working correlation matrix to consider the correlation structure within the data cluster.Firstly,based on the generalized moment method and quadratic inference function,the inverse of working correlation matrix is replaced by a linear combination of some basis matrices.The extended score vector is constructed and a new parameter estimating function and an iterative algorithm are given.Secondly,the parameter estimators obtained by the proposed method are proved to satisfy the consistency and asymptotic normality and a joint variance estimation formula of the estimators and baseline cumulative hazard function is proposed.Thirdly,the properties of the parameter estimation method are verified by simulation study based on the previous work.Finally,the proposed method is applied to an infection data of patients with kidney disease and a data of diabetic retinopathy for illustration.