The Research Of Evaluation Method And Application For Longitudinal Surrogate Endpoints Based On Joint Modeling

Background:When evaluating the efficacy of drugs in clinical trials,the endpoint with the best sensitivity to detect treatment effects and clinical relevance to goals of the trial will be called the true endpoint.However,true endpoint might be difficult to use in practice due to its weaknesses including requiring long follow-up time.To solve this contradiction,we need an endpoint,which is measured easier,earlier and more conveniently,to replace the true endpoint.Such replacement endpoint is termed surrogate endpoint.It could cut the follow-up time,reduce missing rate and improve the efficacy and reliability of the trial.Whereas,because of the misunderstanding of surrogate,some early applications have led to erroneous,or even harmful,conclusions.Therefore,before a candidate surrogate being selected for a new clinical trial,rigorous evaluation of the effectiveness and accuracy must be conducted.During the past 30 years,more and more studies have focused on surrogate evaluation method,while none of them has been selected as the standard evaluation method.The evaluation method of longitudinal surrogates and multivariate surrogates haven’t been thoroughly studied,let alone the evaluation method of multivariate longitudinal surrogates.So,it will be the main contents of this research.Objective:This study aims to find the best joint model with the simulation study,and build an evaluation system of longitudinal surrogates based on the combination of revised Prentice criteria,proportion of treatment explained（PTE）and causal chain.We also aim to present an application scheme of multivariate longitudinal surrogates based on dynamic prediction model,in order to promote its practice in clinical trials.We hope the whole system we suggest could actually cut the duration of trials and provide drugs with potential efficacy to patients as soon as possible.Methods:Firstly,we compared Joint Model,Random Effects Joint Model and Bayesian Joint Model by fitting to the simulation datasets generated by the PBC real data.Bias,standard error,mean-square error and coverage were calculated to select the best model and build a multivariate Joint model.Secondly,we assessed the balance of baseline covariates and evaluated the treatment effect.Then,univariate surrogate evaluation was conducted for 10 candidate surrogates by revised Prentice criteria and PTE.After that,all surrogate combinations were assessed by revised Prentice criteria,PTE and casual chain based on multivariate Joint model,so that the best combination of surrogates could be found.Finally,we built the dynamic prediction model based on the best combination to predict survival probability given the longitudinal outcomes.We also assessed the model by AUC and prediction error to present the best prediction scheme.Result:The simulation study showed that Bayesian Joint Model could estimate bothβ_s andβ_s accurately with the lowest MSE,so that we chose it as the best Joint Model.In the real data,variables other than age were found balanced between treatment groups,while we found no obviously improved efficacy of D-penicillamine on OS and TFS.log（bilirubin）,log（albumin）,log（alkaline）,hepatomegaly and edema passed the univariate evaluation.In all 26 combinations,the combination of log（bilirubin）and edema was the best with a high PTE as 0.986.By assessing the dynamic prediction model,we suggest to predict survival probability when 2￡（35）t￡4.And when the target survival is the end of 5^th year,we suggest to use the longitudinal data of 2 years,which could shorten 60%follow-up time of the trial.Conclusions:The combination of log（bilirubin）and edema is qualified surrogate for the overall survival of primary biliary cirrhosis.With the longitudinal data of the surrogate combination for 2 years,we could predict the survival probability of patient at the end of the 5^th year,so as to cut 60%follow-up time.The longitudinal surrogate evaluation system we built in this study worked well in real data,which verified its feasibility and precision.After the entire rigorous statistical evaluation,the surrogate combination not only could accurately replace the true endpoint,but also shorten the duration of the trial,which has shown the advantages of multiple surrogates and its broad prospects in application.