Application Research Of Bayesian Competing Risk Model

Objective and methodsThe Competing Risk Model is an analysis method for dealing with multiple potential outcome data?including competing risk events?.These data include the endpoint event that caused the failure ending and the time of failure.There may be multiple endpoint events.These potential end-point events are called competing risk events.In the study of competing risk events,if the existence of competing risks are ignored,the correlation between research factors and diseases will be exaggerated or overshadowed.In such cases,competing risk models need to be used for analysis.At present,the research on the classical competing risk model mainly focuses on the use of the cause-specific competing risk model or subdistribution competing risk model to estimate the evaluation of cumulative incidence and how to use statistical analysis software to analyze the competing risk model.The bayesian statistical method has been increasingly favored by researchers because of its effective use of prior information,sample information and.overall information.The bayesian competing risk model used in this study was to fit the likelihood function of the Weibull distribution under the framework of the cause-specific competing risk model,and used Gibbs sampling for a posteriori estimation.This study explored the practical application of the bayesian competing risk model and the classical competing risk model?the method of cause-specific competing risk and subdistribution competing risk?.In this study,follow-up study data of recurrence of cardiovascular events after discharged from patients with coronary artery disease was taken as an example.And based on simulation samples,the statistical performance of the bayesian cause-specific competing risk model and the classic cause-specific competing risk model under different competing risk ratios was evaluated.Results:?1?Example data analysis resultsa.The results of the classical method and the bayesian method showed that age and diabetes were the factors affecting the recurrence of cardiovascular disease in patients with coronary artery disease.The older the patients were,the greater the risk of recurrent cardiovascular disease in patients with coronary artery disease.Diabetic patients had a higher risk of recurrent cardiovascular disease than patients without diabetesb.After three-and-a-half months of follow-up,the change in the cumulative incidence rate curve of recurrent cardiovascular disease?target outcome events?had a tendency to increase steadily and then increase.The cumulative incidence curve of non-recurring cardiovascular disease?competing events?had a small increase with follow-up time.c.The parameter estimates of bayesian competing risk model were very close to the results of the classical competing risk analysis,but the standard errors and confidence intervals were smaller than the results of the two classical methods.The diagnostic indicators of the model?Monte-Carlo standard error,trace plots,kernel density plots?showed that the model had good convergence.?2?Simulation data analysis resultsa.In the case where the parameter?had a fixed true value and the competing risk ratio is different,the absolute value of the bias,the standard deviation?SD?and the standard error?SE?of the regression coefficient?₁,?₂ increased with the proportion of competing risks.The width of 95%confidence interval of regression coefficient gradually widened with increasing proportion of competing risk.The 95%coverage rate?cp95?of the regression coefficient decreases with increasing proportion of competition risk.b.When the proportion of competing risk was fixed and the value of parameter?was changed,the model evaluation indexes?absolute values of Bias,SD,SE,and Width?of the regression coefficient?₁ estimated by?₁ true value equalled 0 were all smaller than the corresponding index values of?₁ estimated by?₁ true value equalled 1.At the same time,the model evaluation indexes?SD,SE,and Width?of the regression coefficient?₂ estimated by the?₂ true value equalled 0 were all smaller than the corresponding index values of the?₂estimated by the?₂ truth value equalled 1.c.Compared with the classical method,the bayesian method calculated the absolute values of Bias,SD,SE,and Width of?₁ and?₂ were smaller than those of the classical method.The bayesian method could obtain a lower bias absolute value regardless of whether the true value of the regression coefficient was zero.d.The classical method had a faster computational speed,and the bayesian method had a longer computation time,about 95 times than that of classical method's calculation time.The two methods had no obvious effect on computing time under different parameters'true values and different competing risk ratios.Conclusions:?1?In epidemiological follow-up studies,competing risk models should be used when competing outcomes exist.There are simple and convenient statistical softwares for model fitting currently.?2?The greater the proportion of competing outcomes,the greater the impact on the target outcome and the worse the accuracy of the parameter estimates of the target outcome.?3?Comparing the classical competing risk model with the bayesian competing risk model,the results showed that the bayesian method had higher stability than the classical method when the accuracy of the estimation was guaranteed.Therefore,bayesian competing risk model is recommended for parameter estimation when the sample size and computation time of the study object are allowed.