Application Of Joint Marginal Model With Frailties For Data Analysis Of Two Types Of Recurrent Events In The Presence Of A Terminal Event

Objective:Two types of recurrent events are common in longitudinal medical follow-up studies,and together with death constitute a bivariate recurrent event data with a terminal event?death?.The data structure is complex.The correlations between two types of recurrent events and a terminal event need to be considered in modeling.Analysis of the influence of each covariate on the mean effect of recurrent rates of both types of recurrent events and the impact on mortality risk is the main research objective.After introducing the frailties,the traditional marginal rate model no longer satisfies the proportional form and cannot directly reflect the average effect of the covariate.The joint marginal model with frailties,including the marginal proportional rates models of the recurrent event processes and the marginal proportional hazard model of the terminal event time.The frailties are used to consider the correlations between events.This paper mainly describes the principle,modeling process and software implementation of the joint marginal model with frailties,verifies the applicability of the model in the analysis of bivariate recurrent event data with a terminal event through simulation studies,and applies the model to the study of the influencing factors of local recurrence,distant metastasis and death in lung cancer patients.It provides a new method for analysis of this kind of data,and provides new ideas for the study of the disease progression and prognosis of lung cancer patients.Methods:Firstly,elaborating the modeling principle of joint marginal model with frailties,and throwing light on the two-stage parameter estimation method,estimation of the marginal parameters such as regression coefficient and the baseline hazard in the first stage,and estimation of the correlation parameters such as variances of three frailties in the second stage.Secondly,according to the principle of parameter estimation,considering the sample size,different end time of study?corresponding to different censoring rate?is to simulate the generation of bivariate recurrent event data with a terminal event,and seting several simulation scheme combinations is to test the simulation effect of the model?500 data sets for each scenario setting?.The evaluation of model parameter estimation is from the standard error estimation bias,the coverage ratio of 95% confidence intervals?CP%?,and the absolute relative bias for the variances of frailties.Finally,the joint marginal model with frailties is applied to the study of bivariate recurrent event data in the progression and prognosis of lung cancer patients.The influencing factors of multiple local recurrence,multiple distant metastasis and death in lung cancer patients are analyzed,and the correlations between two types of recurrent events and a terminal event are evaluated.Results and conclusion:1.The joint marginal model with frailties has unique advantages for the analysis of bivariate recurrent event data with a terminal event.The joint marginal model with frailties is a further extension of the traditional marginal model.Based on the marginal model,three frailties are introduced to link the two types of recurrent events rates with the hazard of a terminal event.Compared with the traditional marginal model,this model has the proportional rate and proportional hazard form after introducing frailties,which can explain the average effect of the influencing factors more directly.The joint marginal model with frailties considers the correlation between two types of recurrent events and a terminal event,also taking into account the correlation of inter-recurrence,and can assess the degree of correlation between recurrent events and a terminal event.Therefore,the model has unique advantages for data analysis of bivariate recurrent event with a terminal event.2.Simulation studies show that the parameter estimation results of the joint marginal model with frailties are reliable.Simulation studies have shown that the parameter estimation results of the joint marginal model with frailties are reliable for bivariate recurrent event data with a terminal event.When the bivariate recurrent event data with a terminal event is fitted by the model,the bias between the estimated values of the regression coefficients and the theoreticalvalues in the marginal parameters is small,and the coverage of the confidence interval is close to the normal level of 0.95,and the estimation of the standard error of the sample is also relatively reasonable,so on the whole,the simulation estimation of the marginal parameters performs well.For the estimation of correlation parameters,when the sample size is n=150 and the censoring rate is 34%,the correlation parameter,that is,the estimation of the variances of the frailties is not good,which may be because the sample size is small,The estimated value of the Gaussian quadrature technique produces a large deviation,and when the sample size is 350,the estimation effect of the variances of the three frailties is significantly improved;overall,as the sample size increases?from 150 to350?and the end time of follow-up study is extended?that is,the censoring rate decreases from 45% to 34%?,the standard error estimate is closer to the sample standard error,the absolute relative bias is less than 0.05,and the simulation effect is improved.3.Analysis of the results of multiple local recurrence,distant metastasis and death factors in patients with lung cancer.The results of case analysis showed that the factors influencing the local recurrence of prognosis in patients with lung cancer were family history,degree of differentiation,lymph node metastasis and treatment.The factors influencing the prognosis of distant metastasis of lung cancer patients were pathological types,the degree of differentiation and clinical stage;the influencing factors affecting the death of lung cancer patients are: age,clinical stage,degree of differentiation,maximum tumor size,lymph node metastasis and treatment.The variance of the frailties in the model indicates that there is a positive correlation between the two types of recurrence events and a terminal event.The higher the local recurrence rate,the higher the distant metastasis rate,the more likely the patient is to die;the average patient who experiences death experiences the recurrence event.The average number of times a patient with a death experienced a recurrent event,ie,the recurrence rate,was 2.738 times that of a patient who did not experience death.The variance of the frailty W₁????=1.565,P=0.028?indicates that there is a positive correlation within the multiple local recurrences,and the variance of the frailty W₂????=1.025,P?0.001?indicates that there are also positive correlations within the multiple distant metastasis.