Model Comparison Metrics Require Adaptive Correction if Parameters Are Discretized: Proof-of-Concept Applied to Transient Signals in Dynamic PET.

Linear parametric neurotransmitter PET (lp-ntPET) is a novel kinetic model that estimates the temporal characteristics of a transient neurotransmitter component in PET data. To preserve computational simplicity in estimation, the parameters of the nonlinear term that describe this transient signal are discretized, and only a limited set of values for each parameter are allowed. Thus, linear estimation can be performed. Linear estimation is implemented using predefined basis functions that incorporate the discretized parameters. The implementation of the model using discretized parameters poses unique challenges for significance testing. Significance testing employs model comparison metrics to determine the significance of the improvement of the fit accomplished by including a basis function, i.e. it determines the presence of a transient signal in the PET data. A false positive occurs when the bases overfit data that do not contain a transient component. The number of parameters in a model, p, is necessary to determine the degrees of freedom in the model. In turn, p is crucial for the calculation of model selection metrics and controlling the false positive rate (FPR). In this work, we first explore the effect of parameter discretization on FPR by fitting simulated null data with varying numbers of bases. We demonstrate the dependence of FPR on number of bases. Then, we propose a correction to the number of parameters in the model, peff , which adapts to the number of bases used. Implementing model selection with peff maintains a stable FPR independent of number of bases.