Statistical Inference With Constraints Of Parameters Under Covariate Adjustment In Cox Model

In many scientific fields,such as medicine,reliability engineering,and demography,there is the problem of estimating and predicting the time of a given event.For example,the time when the disease occurred in medicine and the time when the disease recurred after treatment.In the real survival data,the covariates may be contaminated or interfered by non-random factors,which will cause great errors in the prediction and estimation,and the constraints on the parameters will have more reasonable practical interpretation significance.Therefore,this paper proposes The statistical inference of parameters with constraints under the adjustment of covariates in the Cox model is presented.First,use the kernel function to smoothly adjust the interfered covariates to remove the influence of interference factors,and secondly,the regression analysis of the parameters with constraints under the adjustment of the covariates,By applying the Lagrangian method based on Karush-Kuhn-Tucker(KKT)conditions to derive the asymptotic properties of the constrained parameter estimators,establish the asymptotic properties of the constrained parameters under the covariate adjustment,and develop a method for calculation Modified Mini-Max(MM)algorithm with constrained parameters under covariate adjustment,Finally,a numerical simulation study is performed to evaluate the performance of the proposed method on a limited sample.Numerical simulation shows:(1)For the unconstrained estimator,the parameters ? obtained by the Newton-Raphson algorithm and the MM algorithm have almost the same results,which means that the MM algorithm in practical applications is also a better algorithm compared with the Newton-Raphson algorithm.(2)The parameter estimates for the undisturbed covariate and the interfered-adjusted covariate is unbiased.The SMSE,SD,and SE are relatively close,and the CP values are all within a reasonable range.are all within a reasonable range.(3)When the covariate is disturbed,the estimated value of the parameter is biased.The difference between SMSE and SD is large,and the CP value is low.This also shows that if the covariate is disturbed,it will cause estimation errors.After adjustment,the estimated values of the parameters are more reasonable.(4)When the constraint condition is a box constraint,for the parameters,the correlation efficiency between the parameters of the CMM algorithm and the parameters of the NR algorithm is greater than 1.1.Similarly,when the constraint condition is a sequence constraint,for the parameters,the parameter estimation of the CMM algorithm The amount is also 80%greater than 1.1.This fact shows that considering parameter constraints in the modeling process and analysis will greatly increase benefit.