The Application Of Latent Variable Growth Model In The Medical Longitudinalresearch

Objective:Longitudinal data was often collected in many medical researches,the development trajectories may not come from the same population,that is,the trajectories is heterogeneous.Growth mixture model(GMM)has become a popular statistical method to identify population heterogeneity in longitudinal data.However,in correctly identifying heterogeneous development trajectories,the performance characteristics of GMM enumerated indicators(information criteria,entropy and entropy-penalty indexes,likelihood ratio test derivatives)are little known.Although a few simulation studies have been discussed this issue,they focused on linear GMM.The purpose of this study is to explore the performance of enumerated indexes to correctly identify potential trajectories in the quadratic GMM in homogeneous population(k = 1)and heterogeneous population(k = 3).In this study,the clinical trial about Danhong injection(DHI)in the treatment of coronary heart disease patients was used as an example,the development trajectories about syndrome of traditional Chinese medicine(TCM)were analyzd in two phases,intervention and follow-up periods,and the target population that is sensitive to DHI was eplored.Methods:Aiming at the performance of enumerated indicators in GMM,the simulation scenarios are as follows.For homogeneous population,only two design factors were examined: sample size and the number of timepoint.And for heterogeneous population,five design conditions were manipulated:(a)sample size,(b)degree of separation between latent class,(c)proportion of class members,(d)shape of growth trajectory,(e)the number of time points.Simulation data were generated and analyzed by Mplus 7.0 software.The longitudinal data were based on clinical trial about DHI,traditional Chinese medicine symptom score(TCMS)were collected 6 times(0,7,14,30,60,90 days)in 918 patients with chronic stain angina pectoris.Piecewise growth mixture models(PGMM)was used to explore the phase and heterogeneity of longitudinal data.Multinomial logistic regression was used to explore the predictive variables of latent class.Results:The results were as following:(1)GMM’s identification using enumerated indicatorsFor homogeneous population,the results showed that:(1)For all the information criteria and the sample-adjusted information criteria,when n=300 and time points was 4,all the information criteria could recover the population model in 100%;(2)Among the likelihood ratio test derivatives,BLRT could best identify the homogeneous population model,but its performance was not as good as that of CAIC,BIC,D-BIC and HQ.(3)Except for HT-AIC,sample-adjusted information criteria generally decreased population model recovery percentages.For heterogeneous populations,the results showed that:(1)When the degree of class separation is small,almost all enumeration indexes perform poorly in identifying the correct number of latent classes,and there is insufficient class extraction,which is shown in our research as a model of preference C=2.(2)The overall performance of HQ is the best,followed by aCAIC and aBIC,however,when the degree of separation of latent class is high,BIC and CAIC perform slightly better than aBIC and aCAIC.(3)On the whole,except for D-BIC and HQ,the sample-adjusted information criteria showd a higher model recovery rate than the unadjusted information criteria.(4)Some indicators that have not paid much attention to in the past are surprising,such as D-BIC and HQ,are not inferior to BIC and CAIC under the condition of high separation of class.(5)The entropy is not recommended under any conditions,but the performance of ICL＿BIC is excellent.(6)Among likelihood ratio test derivatives,BLRT performs best.(2)Heterogeneity and phase of the development trajectory of TCMSThe development trajectory of TCMS score in 918 patients with chronic stain angina pectoris could be classified into four latent categories: the Steady-Downward Group(C1,63.18%),the Moderate-Downward Group(C2,9.91%),the Rapid-Downward Group(C3,10.02%)and the SlowDownward Group(C4,16.89%).In general,the TCMS score of patients with chronic angina pectoris as a whole tended to get downward during the treatment period,and changed little during the followup period.The development trajectories of TCMS score in four groups showed significant time effect.During the treatment period(0-14 days),the TCMS scores of C1(slope:-0.594)and C2(slope:-0.526)showed a steady downward trend,C3(slope:-1.582)decreased rapidly,C4(slope:-0.237)decreased slowly.During the follow-up period(14-90 days),C1(slope:-0.025)and C3(slope:-0.025)showed a steady decline,C2(slope:-0.136)showed a rapid decline,and C4(slope:-0.014)showed a slow decline.However,the change rate of TCMS score in follow-up period was lower than that in treatment period.The treatment group( < 0.0001),the time of onset( = 0.0158)and the baseline SAQ score( < 0.0001)were important factors for predicting the trajectory classification.Conclusion:Simulation study showed that BIC,CAIC and aCAIC are proved to be highly reliable index in both heterogeneous and homogeneous populations.In addition,ICL＿BIC and D-BIC performs well in heterogeneous populations;in contrast,AIC,entropy and CLC are proved to be unreliable indicators to identify the true number of latent trajectory in data.Case analysis showed that linear-linear PGMM can effectively fit the heterogeneity and phase of TCMS scores’ development trajectory of patients with chronic angina pectoris,and 14 th day of intervention is node.Development trajectory was divided into four latent class.Most of subjects had mild disease at baseline,which was in slow remission during the treatment period and remained stable during the follow-up period.