Comparison And Application Of Parallel Multiple Mediation Analysis Methods Based On Binary Outcome Data

Objective: Since the mediation effect of the binary outcome data cannot be analyzed by the traditional mediation analysis methods,this paper will introduce the fundamental theory of three methods which are available to analyze the multiple mediation effect based on binary outcome data.And the performance of three methods in estimating total indirect effect and specific path effect under different simulated scenarios are explored.Methods: Based on the counterfactual framework,this paper systematically introduces the mediation formula method,probit SEM method(probit structural equation modeling)and one by one analysis method which are the multi-mediation analysis methods for the binary outcome data.The influence of different types of mediators,different correlations between mediators,different decomposition of total effects and different decomposition of indirect effects on the performance of each method respectively were simulated based on binary outcome data.During the simulation study,we considered two kinds of sample size n =(200,500);three combinations of two mediators were two binary mediators,one binary and one continuous mediators,two continuous mediators;the correlation coefficient of two mediators were ρ=(-0.5,0,0.5,0.9);three decomposition of total effects were dominant direct effect,dominant indirect,and similar magnitude of indirect effect and direct effect;three decomposition of total indirect effects were indirect effect exclusively through one mediator,similar mediation effect through each mediator,and substantial mediation effects through each mediator but with different directions.Simulation one: To study the empirical bias of three methods in the above scenarios.Simulation two: The percentile bootstrap method was used to test the effect estimates of the three methods,and the coverage probability and the power were calculated.A cross-sectional survey data of the health status of workers in Datong Coal Mine was used.A parallel multiple mediation model was established for the status of snoring,body mass index,sleep quality and the prevalence ofhypertension.And three methods were used to analyze the multiple mediation effects.SAS,R and Mplus software were used to evaluate the mediation effect in both simulation and the real data.Results: The simulation results show that,in general,the average percent error of the mediation formula method is lower than that of the other two methods in different scenarios,and the mediation formula method has lower average percent error than the probit SEM method and the one by one analysis method when the mediators are two binary variables,but the standard deviations of the estimated effects are slightly higher.The probit SEM method is more suitable for the case that two mediators are continuous variables.When the mediators are two binary or binary-continuous combinations,the probit SEM method tends to underestimate the total indirect effect.When the indirect effect is equal to or greater than the direct effect and the direction of the mediation effect is opposite through two continuous mediators,probit SEM may underestimate the total indirect effect and the specific path effect.In the most scenarios,the average percent error of the one by one analysis method is positive when two mediators are binary variables.While in the most scenarios,the average percent error of this method is negative for binary-continuous combination and two continuous variable combination.But overall,the empirical bias is high and the efficiency of non-zero power is low.Either method,the smaller sample size,the stronger correlations between the mediators or the opposite direction of the mediating effects of the two mediators will lead to the greater the empirical bias of the estimated effects.The real data analysis results show that the mediation formula method,the probit SEM method and the one by one analysis method all found that snoring had negative effects on hypertension through body mass index.And this specific path effect were 0.026,0.012,0.111 respectively and 95%CI(confidence interval)were(0.020,0.030),(0.010,0.029),(0.078,0.135)respectively.It can be seen that the mediation effect estimates of the one by one analysis method was higher while that of the probit SEM was lower.It was not found that snoring had effects on hypertension through sleep quality.Conclusion: Given the sample size,correlation coefficient,total effect decomposition and total indirect effect decomposition,when the mediators’ combination is a combination of binaryor binary-continuous variables,in most scenarios,the empirical bias of the total indirect effect and specific path effect obtained by the mediation formula method is low,so the mediation formula method is recommended in this case.When the mediators are two continuous variables,the empirical bias of the total indirect effect and the specific path effect obtained by the probit SEM method is low.Therefore,the probit SEM method is recommended in this case.The average percent error of the total indirect effect obtained by the one by one analysis method is lower than that of other scenarios when the mediators are independent and the indirect effect is only through one mediator.But overall,the empirical bias of this method is high,so this method is not recommended when we analyze the multiple mediation models.In addition,the reliability of the three methods’ results should be noted when the sample size is small,the correlation between the mediation variables is high,and the direction of specific path effect is opposite.