The Study Of Diagnosis And Prediction Of Cox's Proportional Hazards Regression Model

With improving of the world economy, developing of the public health work, changing of the disease chart and increasing of the life expectancy, there arc more and more clinical trails and follow-up studies on tumor, chronic disease and disease of aged people, which can be sorted as survival data. At present, the multivariate analysis for survival data is still Cox's proportional hazards regression model. The analysts often tend to neglect the requirements of the Cox model due to its wide scope of application. This may attribute to the instability of the model. The study explores and solves the following four problems in fitting and prediction of the Cox model.1. The power of graphical methods and formal tests for assessing the proportional hazards assumption is compared and validated by Monte-Carlo simulation study and real data. Smoothed plots of scaled Schoenfeld residual, score residual plots, cubic spline function methods and time-covariate tests, linear correlation tests, weighted residual score tests arc recommended. The methods dealing with non-proportionality in Cox model are discussed.2. The graphical methods investigating the assumption of linear relationship between covariates and log hazard ratio are compared. These plots can also provide best function form for a given continuous covariate to explore its effect3on survival in Cox model.3. By Monte-Carlo simulation, the power of six diagnostics to identify influential cases is presented. The result shows that weighted score residual, likelihood displacement, maximum influence curvature and their plots will detect influential cases from different view of model fitting. It is cmphasi/ed that influential cases should not be deleted casually and that data, model, andiprofessional knowledge should be combined to give reasonable explanation and to take proper measures such as weighted partial likelihood estimation.4. Concerning prediction of Cox model, proportion of explained variation to measure the prediction power of a given prognostic factor model is introduced. It is suggested that this measure being a part of standard output of Cox model, it should be put into the analysis of Cox model. The study also introduces shrinkage prediction. The examples show that shrinkage prediction can deal with over-fitting of the model and improve prediction effectively.The four parts above discuss the problems in construction and application of Cox model. The study aims at helping the analysts to judge correctly property of Cox model and to deal with these problems accordingly. So effective analysis is proposed for Cox model in medicine.