A Quadratic Upper Bound Algorithm In Proportional Hazards Regression With Case-Cohort Data

A case-cohort design is a cost-effective biased-sampling scheme in studies on survival data.We study the regression analysis of credit risk by fitting the proportional hazards model to data collected via the case-cohort design.Based on a pseudo-likelihood statistical inference method,two new quadratic upper bound algorithms are proposed to realize the numerical calculation of pseudo-likelihood estimation,and the monotonicity and convergence of the algorithms are studied.The proposed algorithm involves the inversion of the derived upper-bound matrix only one time in the whole process and the upper-bound matrix is independent of parameters.These features make the proposed algorithm have simple update and low per-iterative cost,especially to large-dimensional problems.Furthermore,we used the quasi-Newton algorithm to accelerate the proposed quadratic upper bound algorithm.Rcpp is an R package which enables users to write R extensions with C++.In this paper,we write the program of the proposed algorithm via Rcpp and improve the efficiency of R program execution and realize the fast computing.We conduct simulation studies to illustrate the performance of the proposed algorithms.The proposed algorithms are applied to analyze a real data example from the mortgage dataset and realize the survival regression analysis of credit risk and evaluate the credit risk.