The inappropriateness of the sum of exponential terms for modelling plasma concentrations of bolus-injected, radiolabeled DTPA

Objectives Four statistical tests were applied to explore the problems in estimating plasma clearance (G ml/min) using Sums of (n) Exponential Terms (E_n SETs) fit to marker concentration of bolus-dilution of ¹⁶⁹Yb-DTPA (n=41, 8 samples, 10-240 min) and ^99mTc-DTPA (n=5, 9 samples, 5-180 min).

Methods Test 1 characterized E₂ SET’s parameter estimation error using bootstrap. Test 2 explored sample-subset selection effects on E₁ and E₂ SET parameters. Test 3 explored E₂ SET goodness-of-fit testing. Test 4 examined E₂ SET extrapolative errors.

Results Test 1 found that 19/46 E₂ elimination rate constants’ confidence intervals included 0, implying that the complexity of E_n>1 models was statistically unjustified. In Test 2, the standard deviation of residuals changed with sample-subset selection and was >3%, the maximum expected relative measurement error. Further, 8.1% of E₂ fit attempts yielded degenerate E₂ fits. Test 3 found the magnitude of the E₂ models’ mean residuals failed t-testing for 6 of the 8 sample times. For all samples, Chi-squared testing of fit quality suggested poor fits (P<0.039, n=46). Test 4, extrapolation, showed significant underestimation of concentration over time (31/46 times, Wilcoxon signed-rank sum P=0.0035) and overestimation of G.

Conclusions Consequently, SETs for modeling DTPA concentration are inappropriate and need replacement by better models