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. 2019 Feb 1:186:446-454.
doi: 10.1016/j.neuroimage.2018.11.019. Epub 2018 Nov 17.

Nonlinear Distributional Mapping (NoDiM) for harmonization across amyloid-PET radiotracers

Michael J Properzi  1 , Rachel F Buckley  2 , Jasmeer P Chhatwal  3 , Michael C Donohue  4 , Cristina Lois  5 , Elizabeth C Mormino  6 , Keith A Johnson  7 , Reisa A Sperling  3 , Aaron P Schultz  8
Affiliations
Free PMC article

Nonlinear Distributional Mapping (NoDiM) for harmonization across amyloid-PET radiotracers

Michael J Properzi et al. Neuroimage. .
Free PMC article

Abstract

Introduction: There is a growing need in clinical research domains for direct comparability between amyloid-beta (Aβ) Positron Emission Tomography (PET) measures obtained via different radiotracers and processing methodologies. Previous efforts to provide a common measurement scale fail to account for non-linearities between measurement scales that can arise from these differences. We introduce a new application of distribution mapping, based on well established statistical orthodoxy, that we call Nonlinear Distribution Mapping (NoDiM). NoDiM uses cumulative distribution functions to derive mappings between Aβ-PET measurements from different tracers and processing streams that align data based on their location in their respective distributions.

Methods: Utilizing large datasets of Florbetapir (FBP) from the Alzheimer's Disease Neuroimaging Initiative (n = 349 female (%) = 53) and Pittsburgh Compound B (PiB) from the Harvard Aging Brain Study (n = 305 female (%) = 59.3) and the Australian Imaging, Biomarker & Lifestyle Flagship Study of Ageing (n = 184 female (%) = 53.3), we fit explicit mathematical models of a mixture of two normal distributions, with parameter estimates from Gaussian Mixture Models, to each tracer's empirical data. We demonstrate the accuracy of these fits, and then show the ability of NoDiM to transform FBP measurements into PiB-like units.

Results: A mixture of two normal distributions fit both the FBP and PiB empirical data and provides a strong basis for derivation of a transfer function. Transforming Aβ-PET data with NoDiM results in FBP and PiB distributions that are closely aligned throughout their entire range, while a linear transformation does not. Additionally the NoDiM transform better matches true positive and false positive profiles across tracers.

Discussion: The NoDiM transformation provides a useful alternative to the linear mapping advocated in the Centiloid project, and provides improved correspondence between measurements from different tracers across the range of observed values. This improved alignment enables disparate measures to be merged on to continuous scale, and better enables the use of uniform thresholds across tracers.

Keywords: Alzheimer's disease; Amyloid; Centiloid; Harmonization; Positron emission tomography.

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Figures

FIGURE 1
FIGURE 1
Synthetic CDF testing: The explicit CDFs (Panel A) constructed from GMM parameter estimates provide distributional approximations that mirror the empirical data from which they’re modelled. KS-test p values in panels (Panel B) and (Panel C) from 10,000 bootstraps provide confidence that synthetic and empirical data approach parity.
FIGURE 2
FIGURE 2
Distributional Transformation: Panel A shows the uncertainty in transforming Aβ-PET data with unknown distributional proportions. With low/high burden proportions creating an uncertainty envelope in the mid range. (Panel B) Raw Aβ-PET values from PiB and FBP show significant differences in their distributions. (Panel C) After linear scaling distributional differences remain. (Panel D) After NoDiM transformation Aβ-PET distributions can be aligned closely, maximizing the probability of transformed burdens aligning.
FIGURE 3
FIGURE 3
Proportion Harmonization: NoDiM transformed FBP values show sensitivity (panel B) and specificity (panel A) profiles that are more parsimonious with PiB than is possible with linearly transformed data. The resulting Receiver Operator Characteristic curve (panel C) demonstrates the inescapable reality of pairing radiotracers with different SNRs, no transformation can change the measurement characteristics.
FIGURE 4
FIGURE 4
Empirical Histogram Harmonization: Empirical PiB and raw (Panel A), linearly transformed (Panel B), and NoDiM transformed (Panel C) FBP histograms highlight the distributional differences pre and post transformation.
FIGURE 5
FIGURE 5
Threshold Proportional Matching: The percentage of true positives (true positives / (true+false positives)) for a given threshold more closely mirrors PiB when transforming values using NoDiM as opposed to a linear mapping.
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