Regression estimation of the marginal models with general relative risk form for multivariate failure time data

Abstract

We develop the quadratic inference function method to the parameter estimation of the marginal models with general relative risk form and common baseline hazard function for multivariate failure time data. The usual exponential relative risk form is relaxed to an non-negative twice differentiable form. The proposed estimator, under some regularity conditions, is shown to be consistent and asymptotically normal with a covariance matrix that can be consistently estimated. In addition, a test statistic based on the quadratic inference function for the parameter inference has been provided. The simulation results show that the proposed method taking the correlation between the failure times into the estimation procedure gains more efficiency than the method using the independent structure when the correlation cannot be ignored, and can easily deal with the situation when the cluster size is large. The proposed method is illustrated by analysis of a real data from the Diabetic Retinopathy Study.

Keywords:

• Chi-squared test
• Generalized estimating equations
• Proportional hazards
• Quadratic inference function
• Semiparametric regression

Acknowledgements

The authors are very grateful for the constructive and insightful comments and suggestions from the referees.

Additional information

Funding

This work was supported by National Natural Science Foundation of China under Grant 41766001.