Comparison Of Longitudinal Incomplete Data Imputation Methods And Application In Critical Illness Score Trajectory Analysis Of Sepsis

Backgrounds:Sepsis is an inflammatory and immune disorder caused by infection.Severe cases can lead to multiple organ failure or even death.Early identification and treatment of sepsis have improved in recent years,but its mortality rate remains above 20%.Strengthening the treatment and management of sepsis patients and accurately evaluate their condition and prognosis are quite important.The sequential organ failure assessment(SOFA)can assess the number and severity of organ dysfunction in sepsis patients,comprehensively reflect the condition of sepsis patients and have good prognostic prediction.Most studies of critical illness score systems focused on baseline scores,the worst-case scores during hospitalization,or deltas to predict patient outcomes that ignored dynamic changes in patient’s physiological status and organ function during treatment.Based on the longitudinal SOFA score of patients with sepsis,it is of great clinical significance to explore the dynamic trajectory pattern of SOFA score and identify the poorprognostic and high-risk trajectory subgroups.SOFA score includes six sub-score indexes.Each sub-score index would be missed due to measurement difficulties,recording errors,instrument failure and other reasons.The miss rate in the calculation of comprehensive score is further increased,which brings challenges to the longitudinal trajectory analysis of SOFA score.The last observation coming forward(LOCF)method is often used to deal with missing SOFA scores,which is simple and direct but ignores the variability of data.Joint multivariate linear mixed effects model(JM-MLMM)and fully conditional specification linear mixed effects model(FCS-LMM)are commonly used multiple imputation methods,which consider the uncertainty of missing data and has been widely used in the processing of longitudinal missing data.However,the comparative study of imputing performance within the above three methods in longitudinal missing data has not been sufficient.The study aimed to compare the imputing performance of LOCF,JM-MLMM and FCSLMM in longitudinal missing data through simulation,in order to provide valuable reference for the imputation of longitudinal missing data.Using the better and appropriate imputation method to impute SOFA sub-scores,identify SOFA score trajectory groups in sepsis patients,and explore the relationship between trajectory groups and clinical outcomes.Methods:Firstly,longitudinal survival data was generated by simulation.In the missing completely at random(MCAR)and the missing at random(MAR)mechanism,generating missing data with different miss rates(5%,10%,15%,20%,30%,40%and 50%),and each simulation situation was repeated 100 times.Using LOCF,JM-MLMM and FCS-LMM to impute the above missing data sets.The imputation times of JM-MLMM and FCS-LMM were set as 1,3 and 5 times,respectively.After obtaining the "complete data set",the linear mixed effect model was constructed for parameter estimation.The imputation accuracy of the above three methods were comprehensively evaluated from two aspects including model parameter(bias,relative bias,standard error,root mean square error and coverage rate)and imputed missing value(root mean square error).The better imputation method was selected for the trajectory analysis of SOFA score.Based on the medical information mart for intensive care Ⅳ(MIMIC-Ⅳ),sepsis patients aged 18-90 years who stayed in intensive care unit(ICU)for 2 days or more were included.The day admitted to ICU was recorded as the first day,and then the daily SOFA score was calculated on a 24-hour period.Before calculating SOFA score,the optimal imputation method obtained by the simulation experiment was used to impute each SOFA sub-score.Using the latent class growth mixed model(LCGMM)to identify SOFA score trajectory groups in ICU sepsis patients and Cox proportional hazard regression model was used to evaluate the association between the trajectory groups and discharge outcome.Logistic regression model was used to explore the relationship between SOFA score area under the growth curve(AUC)and discharge outcome.Results:Simulation experiment results show that ① With the increase of the overall data miss rate,the estimates of the real parameters of the three imputation methods including LOCF,JM-MLMM and FCS-LMM,gradually deviated from the true values,and the accuracy and precision of the model estimation parameters decreased.② With the increase of imputation times,the accuracy of fixed effect parameter estimation increased when imputed by JMMLMM and FCS-LMM.③For the parameter estimation of fixed time effect term,JMMLMM and FCS-LMM were more accurate,and FCS-LMM had the best performance,while LOCF had the worst performance.Even when the missing rate was only 5%,the estimation of fixed time effect term was obviously deviated from the true value when imputed by LOCF.④For the parameter estimation of intercept and continuous covariable,when the miss rate was greater than 20%,the estimated parameter values of LOCF and JM-MLMM were apparently deviated from the true value,and the accuracy and precision of model estimation parameters descended rapidly.FCS-LMM had the best performance among the three methods.⑤Compared with other fixed effect parameters,LOCF was more accurate in the estimation of binary covariable parameter,but in terms of accuracy and precision of estimation,FCS-LMM was still the best,followed by JM-MLMM.⑥ From the evaluation of imputing missing values,JM-MLMM was more accurate,FCS-LMM followed,and LOCF had the worst imputing performance.A total of 2734 sepsis patients in ICU in MIMIC-Ⅳ database were included in the study,including 1572 males(57.5%).The discharge outcome was 1131 cases(41.4%)of death.The comprehensive SOFA score was calculated after imputing SOFA sub-score with FCS-LMM.Three SOFA score trajectory groups were identified based on LCGMM,including high increasing group(n=337,12.3%),moderate increasing group(n=1531,56.0%)and decline group(n=866,31.7%).In the high increasing group,baseline of SOFA scores was low,but increased rapidly in the first four days after ICU admission and exceeded the other two groups after day two.In the moderate increasing group,SOFA scores increased slightly in the first two days,and then showed a descending trend,but SOFA scores were always above the decline group.In the decline group,SOFA score baseline was the highest among the three groups,but in the first four days,SOFA scores decreased rapidly.Compared with the decline group,the moderate increasing and high increasing group had higher risks of discharge to death with the hazard ratios(HR)and 95%confidence intervals(CI)for death were 1.62(1.37～1.92)and 3.11(2.55～3.79),respectively.There was a dose-response relationship between the AUC of SOFA score trajectory and hospital discharge outcome.Compared with the first quartile of increasing SOFA score AUC,the odds ratios(OR)and 95%CIs of the second,third and fourth quartile were 2.90(2.25～3.76),3.90(3.02～5.07)and 16.22(12.13～21.85),respectively.Conclusions:From the imputation accuracy and precision of analysis model parameter estimation and missing value,FCS-LMM has the best imputation performance and remains stable,which is better than JM-MLMM and LOCF.With the assumption of longitudinal missing data with the longitudinal indicator changing over time and under the condition of different miss rates,FCS-LMM is the most recommended choice among the three imputation methods.Three different trajectory groups identified in SOFA score of ICU sepsis patients,and the risks of death were different among these trajectory groups.The dynamic changes of longitudinal SOFA trajectory contain more information about the condition of sepsis patient,which is of great significance in monitoring the prognosis of patients with sepsis.More attention should be paid to sepsis patients with an upward trend in SOFA score during hospitalization.