Modeling delayed drug effect using discrete-time nonlinear autoregressive models: a connection with indirect response models

Indirect response (IDR) models have been widely applied to pharmacodynamic (PD) modeling, particularly when delayed response (hysteresis) is present. This paper proposes a class of nonlinear discrete-time autoregressive (AR) models with drug concentrations acting as a time-varying covariate on the asymptote parameter or the autocorrelation parameter of the AR models as an alternative modeling approach for delayed response data. The mathematical derivations revealed the inherent connection between IDR models and nonlinear AR models, and showed that the nonlinear AR models approximate the IDR models when the time interval between response data is small. Simulations demonstrate that the IDR models and the corresponding AR models produce similar temporal response profiles, and as the time interval decreased (i.e., more intensive sampling designs), the AR model based parameter estimates were more comparable to those estimated from the IDR models. In conjunction with mixed-effects modeling, the nonlinear AR models have been shown to well describe a set of simulated longitudinal PK/PD data for a clinical study. Further extensions of the proposed nonlinear AR models are warranted to model irregular and sparse PK/PD data.