Sufficiently high observation density justifies a sequential modeling approach of PKPD and dropout data
Paul Matthias Diderichsen (1), Sandeep Dutta (2)
(1) Abbott Laboratories A/S, Emdrupvej 28C, DK-2100 København Ø, Denmark, (2) Abbott Laboratories, Abbott Park, Illinois, USA
Objectives: A common approach to modeling the exposure-dependent efficacy or safety outcome of a clinical trial is to first develop a model describing the pharmacokinetics (PK) of the drug, and subsequently explaining the observed efficacy using the mean or individually predicted PK as an independent variable in a pharmacodynamic (PD) model. A similar sequential approach may be used in the construction of hazard models for describing observed dropout, where the predicted PKPD is used to drive the hazard model. Unless the hazard is described using observed data only, the sequential approach to modeling the hazard is theoretically less preferable to a simultaneous approach where PKPD and hazard model parameters are estimated jointly. In this work, we investigate if sequential and simultaneous approaches result in similar parameter estimates for six simulated study scenarios with varying density of PKPD data.
Methods: The data for this study was simulated using a one-compartment PK model and an inhibitory PD model describing the effect (EFF) using parameter IC50. Dropout was simulated using a hazard proportional to the efficacy: HAZ=A*EFF. Six scenarios with increasing number of PD observations (from 2 to 24) were simulated. The hazard of dropping out was modeled using a random dropout model (RD [2]) based on observed data only, and an informed dropout model (ID [2]), that used the PD model to explain the hazard. The ID model was fit sequentially (SEQ-ID) and simultaneously (SIM-ID) with the PD data. PD and hazard model parameters were estimated for the 3 models using NONMEM.
The joint likelihood for observing the pain intensity data (YO) and dropout data (T) is given by [2]:
P(Y0,T)=∫P(T|Y0,η) P(Y0, η) P(η)dη
The conditional likelihood for the dropout data depends on the random effect, η, only in the ID models, which should therefore be estimated simultaneously with the PD data.
Results: The deviation from the true parameter value was estimated for A, IC50, the CV on IC50, and the error on EFF. The deviation in IC50, CV(IC50) and A decreased when the density of observed data was increased. While the hazard proportionality factor, A, was well estimated for both the SEQ-ID and SIM-ID methods in all six scenarios, IC50 was accurately estimated in sparse data scenarios only when the SIM-ID model was used.
Conclusions: The hazard model parameter was well described in all six scenarios with either of the SIM-ID and SEQ-ID approaches. The benefit of the joint analysis was a reduction in deviation of PD model parameter in sparse scenarios where the true effect had considerable fluctuations between observations. The benefit of a sequential analysis was a simplification of models and datasets and decreased model runtime. While the conclusion that sufficient density in the observed PD data allows for a sequential analysis holds for the present simulated dataset, other datasets require individual consideration as to whether sequential or joint analysis should be used.
References:
[1] Diderichsen et al.: Modeling “Pain Memory” is Central to Characterizing the Hazard of Dropping Out in Acute Pain Studies, ACOP 2009 (poster)
[2] Hu and Sale: A Joint Model for Nonlinear Longitudinal Data with Informative Dropout, J Pharmacokinetics and Pharmacodynamics, 30, 2003
