| BACKGROUND Disease outcomes are often influenced directly by early exposure and indirectly by changes in exposure via biomarkers.Mediation methods are often used to identify and quantify these two types of effects and to further explain the mechanisms underlying the causal association between exposure and outcome.However,in many complex diseases,the transition from a healthy to a diseased state does not occur abruptly,but is a dynamic process of change.Biomarkers often change over time during this process,potentially leading to a time-varying relationship between mediators and exposure and outcome.Longitudinal mediator models extend the mediator analysis models of single cross-sections,usually containing variable measurements from multiple cross-sections,and are commonly used to examine the mediating effects between early exposure,time-varying mediators,and disease outcome.Current longitudinal mediation analyses are often implemented with latent growth curve(LGC)-based model mediators,latent difference score(LDS)models,cross-lagged panel models(CLPM)and G-formula methods.However,structural equation modeling(SEM)based methods are based on artificially set explicit equations(e.g.,primary versus quadratic term equations),model misspecification introduces nonnegligible estimation bias,and the burden of model fitting increases with the number of observed cross-sections.None of the above methods consider the possible timevarying relationship between mediators and exposure and outcome.In addition,the current methods are still focused on the case of data with few observations and the same interval,and the limitations of model fitting make them inapplicable to dense regular and sparse non-regular data commonly found in real-world studies.Functional mediation analysis(FMA)is a longitudinal mediator analysis method based on basis function fitting,whose unique method of effect estimation makes it applicable in principle to all observed types of repeated measures of mediators and can demonstrate the dynamic components of mediator effects over time.FMA is able to describe trends in mediator variables over time and differences between individuals,and to quantify mediator effects over complete time intervals.The principle of FMA is to project the variable measurements of individuals at different time points onto the basis function space by means of basis function expansion,and to reduce the underlying complete smoothing curve of individual mediating variables with the help of basis functions and basis function coefficients,thus completing the infinite to finite dimensional dimensionality reduction.The parameter estimates of the mediating effect are obtained by fitting the time-varying coefficient model of the mediator and exposure after smoothing,and the function-scalar regression model with the ending in the form of the summation of the dot product of the coefficients in the stepwise model.According to the chosen basis functions as B spline or functional principal components(FPC),FMAs can be classified into two categories:dense and sparse.However,the applicable scenarios and methodological efficacy of FMA in different data situations have not been fully discussed previously.METHODS This study evaluates the accuracy and precision of FMA with different sample sizes(500,1000,2000,3000),average number of observations(dense:20,40,60,80,100;sparse:5,6,7,8,9,10),and different forms of variable coefficients(linear and nonlinear)based on two data scenarios:dense regular and sparse irregular,using Monte Carlo simulation.The precision and accuracy of FMA were evaluated in terms of absolute bias,proportion of bias,standard error(SE)and root mean square error(RMSE).For each scenario,the analysis data set was randomly selected from the overall population of 100,000 people and 100 replicate simulations were performed.The Blood pressure and clinical Outcome in Stroke Survivors study(BOSS)database was selected,and patients had their heart rate and blood pressure measured at 15-minute intervals during the day and 30-minute intervals during the night,consistent with dense,regular data.Therefore,in the example study,we investigated the mediating effect of heart rate on high WBC and short-term neurological deficits in post-stroke patients throughout the day based on the FMA method.The Medical Information Mart for Intensive Care(MIMIC)database was selected,and patients had irregular laboratory biochemical measurements during their ICU stay,which is consistent with sparse and irregular data.Therefore,in the example study Ⅱ,the mediating effect of lactate within 48 hours on the risk of admission hypoglycemia and 90-day death in ICU sepsis patients was investigated based on the FMA method.RESULTS(1)Under the dense rule scenario,as the sample size n increases,the mediating effect estimates of the FMA method gradually approach the true value and the RMSE gradually decreases,and when the sample size reaches 2000,the volatility of the indicators diminishes and tends to be stable.As the average number of observations rises from 20 to 40,the absolute bias proportion of the mediating effect decreases by about 20%and approaches a stable trend above 40.In the case where the coefficients are nearly linear with quadratic term functions,the accuracy and precision of the estimation of the mediation effect do not differ much.(2)In the sparse non-regular scenario,the sample size has little effect on the estimation accuracy of the mediation effect,and the SE and RMSE tend to decrease gradually with the increase of the sample size,but the change is not obvious.As the average number of observations increases from 4 to 8,the absolute proportion of bias of the mediation effect decreases by about 20%,while the difference is smaller at 9 and 10.When the coefficients are nearly linear and quadratic term functions,the precision of the estimation of the mediation effect does not differ significantly from the accuracy.(3)The BOSS cohort used for the final analysis contained 2085 patients with a mean number of heart rate measurements of 63.6.The results of case study 1 found a significant mediating effect of ambulatory heart rate throughout the day.Patients in the lower WBC group had a "w" shaped heart rate throughout the day.Patients in the high WBC group had an all-day heart rate approximately 1.5 units higher than those in the low WBC group,and high heart rates between 0-4 am and midday naps increased the risk of short-term neurological deficits.Further results of single-point mediation showed that the proportion of mediating effects for nighttime mean heart rate was 15.2%,whereas the proportion of mediating effects for daytime mean heart rate was not significant.(4)The MIMIC cohort used for the final analysis included 1051 patients with sepsis and the mean number of lactate measurements over 48 hours was 7.93.The results of Instance Study Ⅱ found a significant mediating effect of 48-hour lactate.Baseline lactate levels were higher and increased sharply in septic patients admitted with hypoglycemia compared to the normoglycemic group,and were approximately 2 mmol/L higher in patients admitted with hypoglycemia by 24 hours,with a gradual decrease in serum lactate levels in the second 24 hours.Lactate levels in the first 24 hours of ICU admission were not associated with 90-day mortality outcome,whereas lactate levels in the second 24 hours significantly affected 90-day mortality in septic patients.Further results of single-point mediation showed that the proportion of mediated effects of admission lactate versus mean 48-hour lactate was 10.1%versus 46.2%,respectively.CONCLUSIONS(1)The B-spline based FMA method is applicable to dense data with an average number of observations of 40 or more and a sample size of more than 2000,and the effect estimate is not reduced due to the complex coefficient of variation.(2)The FPCA-based FMA method is applicable to sparse irregular data with an average number of observations of 8 or more,and it requires a lower sample size,and is recommended to be used when the sample size is 500 or more.Its effect estimate is not reduced due to the complex coefficient of variation.(3)For patients admitted with hypoglycemia,lactate changes in the previous 24 hours should be strictly monitored and effective means of lactate removal should be performed.(4)For post-stroke patients with in-hospital monitoring of high WBC,care should be taken to monitor ambulatory heart rate from 0-4 am versus midday nap. |
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