MM Algorithm For Estimating Proportional Odds Model

In the field of survival analysis,the proportional hazards model is probably the most popular model for analyzing survival data.However,when the mortality of individuals converges with time,the proportional odds model can often get better results when analyzing such survival data.With the continuous development of the data age,survival data has the characteristics of increasing sample size and increasing parameter dimension.Therefore,some current methods for analyzing proportional advantage models are computationally difficult to implement,and at the same time increase the computational cost.MM algorithm can separate multiple parameters to be estimated,and can realize the transformation of complex high-dimensional optimization problems to simple low-dimensional optimization problems,or even the sum of multiple one-dimensional optimization problems,and finally obtain an easy-to-implement and has numerical stability results.In this paper,MM algorithm is firstly introduced into the maximum likelihood estimation of the proportional odds model,and the estimation method of the proportional odds model for analyzing right-censored survival data is extended.Next,this paper applies MM algorithm to the variable selection problem of proportional odds model,and considers the proportional odds model with SCAD and MCP penalty for the first time.Then,parameter estimation of mixed proportional odds model is discussed using MM algorithm for heterogeneity analysis of survival data.The numerical simulation results show that the method proposed in this paper has the characteristics of small estimation error and stable estimation results.Even in the case of small sample size or high censoring ratio,the method proposed in this paper can show excellent performance in estimating regression coefficients and cumulative odds function.Finally,this paper applies the proposed method to a set of Veterans' Administration lung cancer study data for empirical analysis.