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

Introduction: There is a growing need in clinical research domains for direct comparability between amyloid-beta (A beta) 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 A beta-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 A beta-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.