Likelihood estimation of drug occupancy for brain PET studies

Neuroimaging with PET is unique in its capability to measure in vivo the occupancy of a drug. The occupancy is typically obtained by conducting PET measurements before and after administration of the drug. For radioligands for which no reference region exists, however, the only established procedure to estimate the occupancy from these data is via linear regression analysis, forming the basis for the so-called Lassen plot. There are several reasons why simple linear regression analysis is not ideal for analyzing these data, including regression attenuation and correlated errors. Here, we propose the use of Likelihood Estimation of Occupancy (LEO) in such a situation. Similar to the Lassen plot, LEO uses the total distribution volume estimates at baseline and at block condition as input, but estimates the non-displaceable distribution volume (V_ND) and fractional occupancy (Δ) via direct maximum likelihood estimation (MLE). This study outlines the rationale for using MLE to estimate Δ and V_ND from PET data, and evaluates its performance in relation to the Lassen Plot via two separate simulation experiments. Finally, LEO and Lassen plot are applied to a PET dataset acquired with [¹¹C]WAY-100635. LEO can exploit the covariance structure of the data to improve the accuracy and precision of the estimates of Δ and V_ND. Theoretically, the covariance matrix can be extracted from a test-retest dataset for the radioligand at hand. Several procedures to estimate the covariance matrix were considered as part of the simulation experiments, and the effect of the test-retest sample size was also assessed. The results are conclusive in that MLE can be used to estimate Δ and V_ND from PET data, avoiding the limitations associated with linear regression. The performance of LEO was, naturally, dependent on the procedure used to estimate the covariance matrix, and the test-retest sample size. Given a test-retest sample size of at least 5, but preferably 10 individuals, LEO provides higher accuracy and precision than Lassen plot in the estimation of Δ and V_ND. We conclude that LEO is valuable in drug occupancy studies.