Survival Analysis Based On Proportional Hazards Model

The Cox proportional hazards model can analyse the dependence of survival time on co-variates.It has been one of the most popular model in survival analysis,since it can analyse the survival data containing censored samples,which alleviates the problem of insufficient samples to some extent,and does not require estimation of survival distribution of the data.Selection of prognostic genes associated with survival phenotypes is an important subject of survival analysis.In order to solve high dimensionality and collinearity of gene expression profiles,?₁-norm estimation is the common method,so the Lasso-Cox model,an improved al-gorithm of the Cox model,is an effective solution.Based on the sparse regression algorithm,the regularization parameter must be carefully tuned by cross-validation to optimize performance,which usually consumes massive computation resource.We propose a data-driven sparse re-gression algorithm,in which the regularization parameter is determined adaptively from data by Bayesian method,and the regression coefficients are solved by alternate iteration process.Simulation results show that the Bayesian-Lasso is highly competitive in terms of predictive performance with a more stable model and less computing time.In real dataset experiments,the prognostic genes selected have close relationship with phenotypes,and the algorithm can be used to establish a prognosis predictive model of high-dimensional gene expression profiling.There may be intrinsic links between different diseases,so the related survival predictive models are common in practical applications,which involves multi-task survival analysis prob-lems.In addition,obtaining sufficient labeled training instances for learning a robust prediction model can be extremely difficult in practice.In order to solve above problems,a multi-task learning method based on Cox model has been proposed,using the?_2,1-norm penalty to encour-age multiple predictors sharing similar sparsity patterns.It considers the correlation between different tasks,increases the training information of each task,and improves the model perfor-mance.Bayesian method and alternate iteration process are also used to be more stable and faster.We demonstrate the performance of the proposed method using TCGA dataset,and the results show that it can significantly improve the predictive performance.