Analysis Of Longitudinal And Survival Data Based On Joint Model

Objectives:Longitudinal data and survival data are collected at same time in many medical researches.In general,the mixed effect model is used to analyze the change of longitudinal trajectory,and Cox proportional hazard model or parameter regression model is applied to analyze survival data.However,there is often a correlation between longitudinal data and survival data,and separate analysis may lead to the deviation of model regression coefficient or standard error.TheⅡ&Ⅲstage gastric cancer patients were collected radiotherapy and/or chemotherapy,the primary endpoint was the recurrence or death,considering quality of life at different times,and joint modeling was used to analyze two types of data at the same time.Methods:483Ⅱ/Ⅲstage gastric cancer patients were collected from 9 hospitals,control group is radiotherapy and/or chemotherapy,experimental group is radiotherapy and/or chemotherapy combined with traditional Chinese medicine.The primary outcome was disease-free survival(DFS).The longest follow-up time was 9.39 years,and the median follow-up time was 4.64years.The European Organization for Research and Treatment scale was measured at 0,3,6,9,12,15 and 18 weeks.First,the mixed effect model was used to analyze the change of total health status score over time,and Cox regression and parametric regression were used to analyze the factors of progression-free survival.Finally,a jointed model was constructed according to the in factors of the mixed model and factors of survival analysis.In this study,SAS 9.4 software and R 3.5.2 statistical software were used to analyze.Results:The main results are as follows:(1)Results of mixed effect model:The covariance matrix of level 1 and level 2 is defined as unstructured covariance matrix according to the maximum values of BIC,which were got from mixed effect models with different covariance matrix.The interaction between groups and time was not statistically significant(P=0.9995).In the final model,the random effects were intercept and follow-up time,the fixed effects were age,group,time,time*time and gastric cancer stage,and the corresponding regression coefficients were:-0.084,-5.716,0.513,-0.009and-1.982(IIIa Vs II),-2.038(IIIb Vs II),respectively.The correlation coefficient matrix of the random effect on level 1 showed that most coefficients were greater than 0.3.The correlation coefficient between the intercept of level 2 and the time is-0.6573.(2)Survival analysis results:Stepwise Cox regression results showed:compared with the control group,the hazard ratio and 95%CI of tumor recurrence were 0.678(0.517,0.888),Cancer stage IIIa Vs II were 2.001(1.342,2.982),and stage IIIb vs II were 1.541(0.898,2.646),The status of Lymph node metastasis N1 vs N0 were 1.208(0.761,1.917),and stage N2 vs N0were 2.062(1.121,3.792).The curves of Kaplan-meier and log[-logs(t)]showed that the PH assumptions of the Cox proportional hazard model were satisfied for the variables of group,the status of Lymph node metastasis and cancer stage.The three parametric regression(exponential model,weibull model and lognormal model)were similar,but the BIC statistic in lognormal was the smallest.Its regression coefficients were similar from Cox regression model.(3)Joint model results:Age,group,time,time*time,gastric cancer stage were considered as factors in longitudinal data,and group,cancer stage and the status of Lymph node metastasis were considered as factors of PFS in survival data.After four joint models were analyzed,Cox proportional hazards model which had the minimum BIC was selected as submodel of survival model.In longitudinal submodel,the coefficients of age,group,time,time*time and gastric cancer stage were-0.118,-3.594,0.499,-0.010,-1.294(IIIa Vs II)、-1.124(IIIb Vs II).In survival submodel,the hazard ratio and 95%CI of group were 0.674(0.524,0.867).Cancer stage IIIa and II were 1.921(1.312,2.814),and stage IIIb and II were 1.508(0.892,2.549).The status of Lymph node metastasis N1 and N0 were 1.182(0.815,1.716),and stage N2 and N0 were2.014(1.161,3.495).the coefficient between M_i(t)and risk events was-0.0016(P<0.05),with hazard ratio 0.998(0.997,1.000).Conclusions:For the longitudinal data,the mixed model can deals missing values well,and explans the changes in the longitudinal trajectory.In this study,the overall health score showed a non-linear change over time and a negative correlation between the baseline scores and the trend of change,the results of Cox regression model was similar to the parametric regression models.The association between longitudinal measurement and hazard is well dealt with by using joint model,which can effectively analyze,and full information can be used.