Research on Covariate Adjustment Method Based on Proportional Hazards Model

In actual data, especially medical data, the covariates are contaminated or interfered by certain factors, while the real covariates cannot be observed. This paper discusses how to adjust the disturbed covariates in the proportional risk model. Covariate existed in the adjustment methods cannot be directly used for survival data, in order to solve this problem, we use kernel functions to construct the interference factors of the distribution function, the interference of covariate smoothly get the estimate of the real covariate, again to get the parameters in the model of regression estimate, and completed the estimate satisfying consistency and asymptotic normality. We also proposed the use of Minorization-Maximization (MM) algorithm to obtain parameter estimates. The first M is to construct a surrogate function by the convexity of the exponential function and the negative logarithm function, which the Hessian matrix is a diagonal matrix; The second M is to obtain the estimators by maximizing the surrogate function. Finally, we demonstrate the feasibility of our proposed method through numerical simulation and real data research.