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Table 3 Linear mixed models for 1.5 T and 3 T multi-center temperature-adjusted T1 mapping data (normalized to 21 °C, considering the “Medium” native myocardium tubes “F” and “M” respectively). The best model is “A5” at 1.5 T and “A3” at 3 T

From: T1 mapping performance and measurement repeatability: results from the multi-national T1 mapping standardization phantom program (T1MES)

 Model fitting formulasAICBICLog likelihoodχ2P valueBest model
1.5 T modelA1: T1 ~ sequence + (1|ID)5850.35920.8− 2909.1“ref”“ref”“ref”
A2: T1 ~ sequence + (1|ID/age) [worse fit with age]5852.35927.2− 2909.10.01.000
A3: T1 ~ sequence × software + (1|ID)5725.45883.9− 2826.7164.9< 0.0001
A4: T1 ~ sequence × software + vendor + (1|ID) [vendor non-contributory to fit]5725.45883.9− 2826.70.01.000
A5: T1 ~ sequence × software + model + (1|ID)5723.45890.8− 2823.75.90.051A5
A6: T1 ~ sequence × software + vendor × model + (1|ID) [vendor non-contributory to fit]5723.45890.8− 2823.70.01.000
Final model (A5) parametersVarianceSDχ2Pvalue  
Random effectsID2547.250.47“ref”“ref”  
Fixed effectsSequence (β range  32.3 to 455.6a)//1101.0< 0.0001  
Software (β range 385.1 to 522.3a)//63.8< 0.0001  
Model (β range − 161.8 to 16.0a)//11.20.011  
Sequence: Software (β range − 161.8 to − 6.9a)//149.6< 0.0001  
3 T modelA1: T1 ~ sequence + (1|ID)4390.44447.0− 2181.2“ref”“ref”“ref”
A2: T1 ~ sequence + (1|ID/age) [worse fit with age]4392.44453.1− 2181.20.01.000
A3: T1 ~ sequence × software + (1|ID)4238.34339.4− 2094.2174.1< 0.0001A3
A4: T1 ~ sequence × software + vendor + (1|ID) [vendor non-contributory to fit]4238.34339.4− 2094.20.01.000
A5: T1 ~ sequence × software + model + (1|ID)4239.24348.4− 2092.63.10.212
A6: T1 ~ sequence × software + vendor × model + (1|ID) [vendor non-contributory to fit]4239.24348.4− 2092.60.01.000
Final model (A3) parametersVarianceSDχ2P-value  
Random effectsID372.419.3“ref”“ref”  
Fixed effectsSequence (β range − 114.5 to 38.5a)//732.8< 0.0001  
Software (β range − 203.0 to 32.7a)//46.0< 0.0001  
Sequence: Software (β range − 48.8 to 267.3a)//189.0< 0.0001  
  1. The symbol (1|ID) in the model formulas refers to the random effect of individual phantoms (by identity number). At 1.5 T models, A5 and A6 have equal AIC/BIC but given the lack of statistically significant χ2 improvement from A5 to A6 (P = 1.0); A5 is considered the most parsimonious model
  2. Age refers to phantom age at scanning since date of manufacture, AIC Akaike information criterion, BIC Bayesian information criterion, χ2 chi-square, ref reference, SD standard deviation
  3. aComplete list of β coefficients for model A5 at 1.5 T and A3 at 3 T are provided in Supplementary Tables 7 and 8 respectively