Statistical Simulation And Application Of Cross-lagged Path Analysis And Its Extended Model

Backgrounds:The temporality is one of the basic principles of causal inference in observational studies.Cross-lagged path model(CLPM)is a statistical method to explore the temporal relationship between two correlated variables.Nowadays,CLPM has been widely used in longitudinal studies to explore the temporal relationship of the risk factors of chronic diseases.However,it remains unclear how to perform the crosslagged panel design reasonably.Most of the studies using CLPM were based on the two-wave model.Researchers tended to combine the last follow-up records and baseline data in the two-wave CLPM,to get a larger sample size.This kind of strategy may confuse the results of models.Additionally,CLPM fails to discriminate betweenand within-person variation.Based on CLPM,researchers proposed random intercepts cross-lagged path model(RI-CLPM)to distinguish between-and within-person variation.The performance of CLPM and RI-CLPM is worth further discussion.With the change of modern lifestyle,the incidence of cognitive impairment in the elderly keeps increasing,more and more studies focused on the relationship between body mass index(BMI),grip strength and cognitive function,but the conclusions about the temporal relationship between them are still inconsistent.This study aims to explore the performance of the cross-lagged path model through statistical simulation,to give suggestions for cross-lagged panel design and modeling;and to compare the model performance of CLPM and RI-CLPM.Finally,we will explore the temporal relationship between BMI,grip strength(AGS)and cognitive function in the elderly by using CLPM and RI-CLPM in cohort data analysis.Methods:In this study,simulated dataset was firstly generated based on the twowave CLPM,and then a subset was sampled from the total dataset randomly for model estimation.By traversing different sample sizes and autocorrelation coefficients,we compare type I error,power,bias,standard error and mean square error of the estimated models.We further compared the model performance of CLPM and RI-CLPM in the scenario of three waves.Based on the Survey of Health,Ageing and Retirement in Europe(SHARE),twowave CLPM,three-wave CLPM and RI-CLPM were used to explore the temporal relationships between BMI and cognitive function,as well as hand grip strength and cognitive function in the elderly.Results:The statistical simulation showed that the sample size and the definition of the follow-up will impact the results of model:① In the case simulated in this study,when the sample size reached 1000,the model fitting tended to be stable;② When the follow-up intervals included were inconsistent,the type I error reached 0.11～0.16,and the type I error was still>0.10 after further adjustment for the follow-up time;③ When the follow-up intervals were consistent in two-wave CLPM,the autocorrelation coefficients had little effect on the standard error and mean square error of the model estimation,but the bias tended to increase when the autocorrelation coefficients were too large or too small;④ When the time stability of the variables was different,the estimation of the cross-lagged path model was basically unaffected;⑤ When there were random intercepts in the data,the type I error of CLPM was higher than that of RI-CLPM,and the bias of CLPM estimation was larger.By contrast,the estimation of RI-CLPM was relatively accurate.A total of 6682 participants(2828 males)in SHARE were included in this study,with a mean age of 61.2±8.23 years at baseline.There was a unidirectional relationship between BMI and cognitive function between 2004(T1)-2011(T2):the cross-lagged path coefficients of BMI→immediate memory(IM)and delayed memory(DM)were 0.049 and-0.046(P<0.001 for both),the cross-lagged path coefficients of IM and DM→BMI were 0.001(P=0.919)and-0.002(P=0.672),the change of BMI preceded the change of cognitive function.However,there was a bidirectional relationship between BMI and cognitive function during 2011(T2)-2017(T3):the path coefficients of BMI→IM and DM were-0.021 and-0.036(P<0.001 for both),the path coefficients of IM and DM→BMI were-0.008(P=0.029)and-0.011(P=0.003).Additionally,the extended model,RI-CLPM also showed that BMI was related with cognitive function bidirectionally among three waves:the path coefficients of BMI→IM at T1→T2 and T2→T3 were-0.140 and-0.263,the path coefficients of IM→BMI were0.023 and-0.112,which were all statistically significant;the path coefficients of BMI→DM at T1→T2 and T2→T3 were-0.139 and-0.268,the path coefficients of DM→BMI were-0.033 and-0.122,which are all statistically significant.The model fit of RI-CLPM was better.As for the relationship between grip strength and cognitive function,both CLPM and RI-CLPM suggested a bidirectional temporal relationship between them,but the model fit of RI-CLPM was better(results of RI-CLPM:the path coefficients of AGS→IM at T1→T2 and T2→T3 were 0.149 and 0.195,the path coefficients of IM→AGS were 0.088 and 0.097;the path coefficients of AGS→DM at T1→T2 and T2→T3 were 0.137 and 0.165,the path coefficients of DM→AGS were 0.099 and 0.131,the coefficients above were all statistically significant).Conclusions:In the process of modeling CLPM,sample sizes and the definition of follow-up will affect the results of the model.It is recommended to keep the followup waves consistent or the follow-up interval similar when the study population included.When there is heterogeneity in the population,RI-CLPM,which could discriminate between-and within-person variation,should be considered to explore the temporal relationship between variables.The findings from the cohort study provide evidence that BMI and grip strength are related with cognitive function bidirectionally.Improvements in both cognitive function and physical condition should be strengthened when implementing interventions for elders.