The Application And Bayesian Estimation Method Of Additive Interaction And Its Attributable Indices In Cox Proportion Risk Model

In epidemiological studies,the biological and public health implications of the interactions between influencing factors are often more important than their statistical significance.Compared with multiplicative interaction,additive interaction can better reflect the biological significance of interaction.Cox proportional risk model is one of the most common multiplicative models to estimate the effect of influencing factors on survival outcome.However,the multiplicative model cannot directly obtain the additive interaction between factors,and when the output parameters of the multiplicative model are used to calculate the additive interaction index,it is often difficult to calculate the standard error of the parameter effect value of the additive interaction index.As a sampling solution method of numerical simulation,Bayesian method can easily get the estimation and confidence interval of these effect values without complicated mathematical derivation.this study aims to use Bayesian method to estimate the parameters of additive interactions between influencing factors and their attibutable indices in Cox proportional risk regression model and use confidence interval to test hypotheses,so as to solve the statistical inference problem of additive interactions in traditional model.Firstly,based on the inconsistent test results between multiplicative interaction and additive interaction,five different simulation experiment scenarios were designed to analyze Bayesian Cox proportional hazards model to estimate additive interactions between factors determine index SI and its relative excess risk attribution(RERI,API,p API).The feasibility and availability of the three indicators in statistical inference of additive interactions,The advantages and disadvantages of these indicators(SI,RERI,API and p API)on the accuracy of Bayesian point estimation and variation indicators were compared by using the accuracy,coefficient of variation,95% confidence interval(CIK)and the coverage of confidence interval to the true value of indicators under K repeated experiments(CICP).Secondly,an example of survival analysis in epidemiology is used to further verify the feasibility of the Bayesian approach in statistical inference of additive interactions.The results of the simulation experiment results show that the five simulation scenario,SI although in some situations between point estimates and the real value of absolute error is small,but the CIK SI are contains 1,and its standard error is far more than other indicators,Bayesian Cox regression model in the estimation of risk SI lack of additive interactions determine statistical inference ability.In the simulation scenario where there is additive interaction between the two factors,the CIK of each attribution indicator(RERI,API,p API)does not contain 0.In the simulation scenario where there is no additive interaction between the two factors,the CIK of each attribution indicator(RERI,API,p API)contains 0.In terms of CICP,p API was closest to 0.95,followed by API and RERI.In terms of the absolute error between the point estimate value and the real value,p API has the highest accuracy,followed by API,and RERI is the worst.In terms of the standard error of each attribution indicator,the standard error of each attribution indicator is very small compared with SI.In most simulated scenarios,the standard error gradually decreases with the increase of experiment times and sample size,and the statistical significance of each attribution indicator is completely consistent with the simulated scenario.It is suggested that the three attibutable indices can well predict the existence of additional interaction.From the comprehensive evaluation indicators,p API has the best comprehensive estimation effect.In addition,the inference results of Bayesian Cox risk regression model are similar to those of simulated scenario when estimating additive interaction indicators,which further verifies the usability of the proposed method.In the Bayesian Cox proportional risk regression model implemented in this paper,the index SI of additive interaction between two factors lacks the ability of inferences of no additive interaction,but the attibutable indices(RERI,API,p API)have better inferences of additive interaction.Therefore,when need to infer whether additive interaction is established,Bayesian Cox proportional risk regression model can be used to estimate any attribution index of additive interaction to infer that there is no additive interaction and p API comprehensive estimation has the best effect.