| In survival analysis,hazard function plays an important role in the study of various diseases.Researchers also pay more attention to the change of hazard rate with covariate during long-term follow-up,so as to provide more scientific and reasonable prognosis plan for patients.However,the follow-up data of actual observation is often incomplete,and "censor" often occurs.It is also difficult to process "censor" data.Artificial Neural Networks(ANN)is a distributed parallel information processing algorithm model that simulates human brain tissue structure.The algorithm model is highly adaptive and can be used to solve multi-factor and nonlinear problems,so it is widely used in many research fields.In recent years,it has become a hot model in medical diagnosis and prediction,providing new analytical ideas for the diagnosis and prediction of various diseases.Therefore,this paper considers the application of neural network method in the modeling of the hazard rate of censored data,and carries out two parts of the study.In the first part of this paper,a piecewise exponential neural network algorithm based on interval I censored data is proposed.According to the idea of piecewise index model,the follow-up time was divided into multiple non-adjacent intervals,and the survival time of the research object was assumed to obey the exponential distribution with possibly different parameters in each interval.The interval into which the object fell was defined,and the model likelihood function was written.Secondly,a three-layer artificial neural network model was established based on Keras,and the negative logarithm of the defined likelihood function was selected as the loss function of the network.The network was optimized by gradient descent method and the hazard function was predicted.In this paper,a large number of simulation studies on the piecewise exponential neural network model are carried out,and the results show that the proposed method is better than the maximum likelihood estimation.Finally,the model algorithm was applied to the tumor test data of mice to analyze the change of tumor hazard function in mice.In the second part of this paper,the piecewise index neural network algorithm is applied to interval II censored data.Based on the piecewise index idea,the interval II censored data is divided to make the number of fallen individuals in each interval as close as possible.It is assumed that the individual obeies the exponential distribution with possibly different parameters in each interval,and the likelihood function is written according to the interval in which the individual falls.Based on the established neural network,batch gradient descent training model was selected for small sample size,and mini-batch gradient descent method was selected for large sample size.The effectiveness of the proposed method is verified in simulation and compared with maximum likelihood estimation.The results show that the proposed method is more accurate than the maximum likelihood estimation.Finally,the model algorithm is applied to decompression sickness data of air force to estimate the hazard change of decompression sickness patients in low-pressure environment. |
