A data adaptive approach to the robust fitting of PET data: Application to group and test-retest analysis

Model fitting of PET time activity curves (TACs) is typically accomplished according to the least squares (LS) criterion, which is optimal for data with Gaussian distributed errors, but not robust in the presence of outliers (e.g., head motion). In contrast, quantile regression (QR) is an alternative for robust fitting that provides estimates not heavily influenced by outliers only losing a little efficiency, relative to LS, when no outliers are present. A data adaptive (DA) approach, relying on the rationale that QR should be used when outliers are present and LS otherwise, chooses LS or QR based solely on the observed TAC by measuring the influentiality of each TAC point and using QR when the maximum influentiality among the TAC points is higher than a given threshold. We first compare the results of applying DA to those using LS on a group of 24 healthy controls studied with [¹¹C]-DASB to investigate whether DA improves the accuracy of parameter estimates. We also studied the application of DA to a test-retest data set of 11 controls to determine whether DA improves test-retest reproducibility. DA decreases the standard deviation (SD) of the radioligand distribution volume (V_T) (relative improvement range: 0.12%-2.59%), while keeping the within-group average V _T values almost unchanged. This ∼2.5% decrease in SD would result in a ∼5% decrease in the number of subjects needed to maintain the same statistical power when doing group comparisons. For the test-retest data, DA reduces the V_T percent difference (PD) by 0.01%-4.39% in 63% of the regions for the majority of test-retest pairs. The practical import of this reduction in the SD and PD, achievable by simply implementing a different fitting approach, is smaller required sample size to detect differences between groups and enhanced test-retest experiments reproducibility (i.e. improved sensitivity in occupancy studies).