Simultaneous Confidence Band Of Extra Risk Of Dose Based On Log-Logistic Regression

In clinical trials,we usually study the relationship between the level of drugs and medicated effects to evaluate the potential risks of drugs.In animal experiments,the exposure level of drugs is generally set at relatively high values to obtain a dose-response relationship to evaluate the risk of low dose levels.Crump(1984)first proposed the benchmark dose method as a method for determining reference doses to describe the uncertainty of the risks.On the basis of introducing the structures of linear regression models,logistic regressio n models,and log-logistic regression models,as well as the basic theory of constructing confidence bands,this article provides detailed derivation steps for the Abbott-adjusted log-logistic regression model using the benchmark dose method and six methods to construct the upper limit of confidence bands and corresponding maximum likelihood estimates of benchmark dose.Different experimental scenarios were designed for six methods,and eight models and continuously increasing large sample sizes were selected for simulation calculations.The simulation results show that all methods perform well under large sample sizes.When the number M of inference is small,Wald,LR,and bootstrap methods perform better than Scheff é method,hyperbolic band,and three segment band;As M increases,the hyperbolic band performs better than the Scheffé method and the three segment band,and simultaneous hyperbolic band can be used to estimate at selected dose levels or the upper limit of BMDL at a given BMR.