A novel gamma GLM approach to MRI relaxometry comparisons

To demonstrate that constant coefficient of variation (CV), but nonconstant absolute variance in MRI relaxometry (T₁ , T₂ , R₁ , R₂ ) data leads to erroneous conclusions based on standard linear models such as ordinary least squares (OLS). We propose a gamma generalized linear model identity link (GGLM-ID) framework that factors the inherent CV into parameter estimates. We first examined the effects on calculations of contrast agent relaxivity before broadening to other applications such as analysis of variance (ANOVA) and liver iron content (LIC).

Eight models including OLS and GGLM-ID were initially fit to data obtained on sulfated dextran iron oxide (SDIO) nanoparticles. Both a resampling simulation on the data as well as two separate Monte Carlo simulations (with and without concentration error) were performed to determine mean square error (MSE) and type I error rate. We then evaluated the performance of OLS/GGLM-ID on R₁ repeatability and LIC data sets.

OLS had an MSE of 4-5× that of GGLM-ID as well as a type I error rate of 20-30%, whereas GGLM-ID was near the nominal 5% level in the relaxivity study. Only OLS found statistically significant effects of MRI facility on relaxivity in an R₁ repeatability study, but no significant differences were found in a resampling, whereas GGLM was more consistent. GGLM-ID was also superior to OLS for modeling LIC.

OLS leads to erroneous conclusions when analyzing MRI relaxometry data. GGLM-ID factors in the inherent CV of an MRI experiment, leading to more reproducible conclusions.