Population cell life span models for effects of drugs following indirect mechanisms of action

Pharmacokinetic/pharmacodynamic (PK/PD) models for hematological drug effects exist that assume that cells are produced by a zero- or first-order process, survive for a specific duration (cell lifespan), and then are lost. Due to the fact that delay differential equations (DDE) are needed for cell lifespan models, their software implementation is not straightforward. Our objective is to demonstrate methods to implement three different cell lifespan models for dealing with hematological drug effects and to evaluate the performance of NONMEM to estimate the model parameters. For the basic lifespan indirect response (LIDR) model, cells are produced by a zero-order process and removed due to senescence. The modified LIDR model adds a precursor pool. The LIDR model of cytotoxicity assumes a three-pool indirect model to account for the cell proliferation with capacity-limited cytotoxicity followed by maturation, and removal from the circulation. A numerical method (method of steps) implementing DDE in NONMEM was introduced. Simulation followed by estimation was used to evaluate NONMEM performance and the impact of the minimization algorithm (first-order method vs. first-order conditional estimation method) and the model for residual variability on the estimates of the population parameters. The FOCE method combined with log-transformation of data was found to be superior. This report provides methodology that will assist in application of population methods for assessing hematological responses to various types of drugs.