A novel gamma GLM approach to MRI relaxometry comparisons

Abstract

Purpose:To demonstrate that constant coefficient of variation (CV), but nonconstant absolute variance in MRI relaxometry (T 1 , T 2 , R 1 , R 2 ) 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). Methods: 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 R 1 repeatability and LIC data sets. Results: 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 R 1 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. Conclusions: 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. K E Y W O R D S coefficient of variation, gamma GLM, MRI relaxometry, relaxivity, repeatability | 1593 KAPRE Et Al.

Relaxivity‐iron calibration in hepatic iron overload: Reproducibility and extension of a Monte Carlo model

“…Our finding is consistent with those of a previous simulation study conducted by Ghugre et al 16 and patient studies, 17,25–28 in which the increase in of 1.5–3.0 T is reported to be a factor of 2. For LIC‐R 2 calibration at 1.5 T, the systematic bias observed between Monte Carlo predictions and the St. Pierre calibration (Figure 1 and Table 1) may be related to limitations in the Ferriscan calibration due to an insufficient number of patients with severe iron overload and data heteroscedasticity 5,29–31 . For SSE R 2 , a strong linear relationship with a slope of 1.51 is observed at 3.0 relative to 1.5 T, similar to previously estimated slopes of 1.47 from simulation, 16 and 1.55 from in vivo liver data 32 .…”

“…For LIC-R 2 calibration at 1.5 T, the systematic bias observed between Monte Carlo predictions and the St. Pierre calibration (Figure 1 and Table 1) may be related to limitations in the Ferriscan calibration due to an insufficient number of patients with severe iron overload and data heteroscedasticity. 5,[29][30][31] For SSE R 2 , a strong linear relationship with a slope of 1.51 is observed at 3.0 relative to 1.5 T, similar to previously estimated slopes of 1.47 from simulation, 16 and 1.55 from in vivo liver data. 32 Thus, we conclude that the Monte Carlo model developed by our group has successfully reproduced the results of Ghurge et al for R 2 and R Ã 2 relaxometry of liver iron overload at both 1.5 and 3.0 T. MSE R 2 -iron calibrations at 1.5 T or higher field strengths were limited, in part due to the dependence on the interecho time.…”

Magnetic resonance imaging of tumor-associated-macrophages (TAMs) with a nanoparticle contrast agent

“…The Gamma GLM accounts for a constant coefficient of variation in MRI relaxometry data as previously shown by our group. 57 Cell (M0/M1L/M1H/M2), NP (none, DIO/SDIO 1 : 1/SDIO 10 : 1), and 3 trials were each included up to all 2-factor interactions. A total of 42 Bonferroni–Holm corrected pairwise comparisons were performed within each cell between NPs and between cells given SDIO 1 : 1 or SDIO 10 : 1.…”

“…The pairwise comparisons were done in emmeans using Kenward–Roger T -tests (within the log LMM) on the back-transformed and bias-corrected R2 scale, since R2 (and not log R2) is linearly related to concentration of uptake. 57 …”