Using simultaneous equation modeling for defining complex phenotypes

Background

Interactions between multiple biological phenotypes are difficult to model. Simultaneous equation modelling (SEM), as used in econometric modelling, may prove an effective tool for this problem. Generalized linear models were used to derive the structural equations defining the interactions between cholesterol, glucose, triglycerides and high-density lipoprotein cholesterol (HDL-C). These structural equations were then applied, using SEM, to Cohort 2 data (replicates 1–100) to estimate the phenotypic structure underlying the simulation. The goal was to determine if this empiric method of deriving structural equations for use in SEM was able to recover the simulation model better than generalized linear models.

Results

First, the underlying structural equations were estimated using generalized linear model techniques, which found strong a relationship between glucose, triglycerides and HDL-C. Using these structural equations, I used SEM to evaluate these relationships jointly. I found that a combination of the empiric structural equations and the SEM method was better at recovering the underlying simulated relationship between biologic measures than generalized linear modelling.

Conclusion

The empiric SEM procedure presented here estimated different relationships between dependent variables than generalized linear modelling. The SEM procedure using empirically developed structural equations was able to recover the underlying simulation relationship partially and thus holds promise as a technique for complex phenotype analysis. Robust methods for determining the structural equations must be developed for application of SEM to population data.