Bernard Sebastien
Sanofi Aventis R&D
Objectives: In connection with the development of specific statistical methods for the analysis of thorough QT studies, growing attention has been recently paid on the PKPD models to consider for Concentration-QT analyses. For this purpose, PKPD models considered, generally assume direct concentration-QT increase relationships: assumption mostly assessed using graphical diagnostic methods. The purpose of this work is to quantitatively assess, using both simulations and tools of asymptotic statistics, the impact of lagged effect on the estimates obtained with the standard PKPD models routinely used for assessment of concentration – QT relationships.
Methods: The true model assumes a linear relationship between time-matched QT change and the lagged PK concentration, whereas the working analysis concentration – QT model is the standard mixed linear model using time-matched QT change as dependant variable, the observed PK concentration plus a time effect (considered as a factor) as independent variable. Methods of asymptotic statistics are used to derive the limit value of the slope and time effects parameters in the mis-specified model. These results are illustrated with simulations exploring behaviour of the estimates in a non-asymptotic setting.
Results: Both asymptotic calculations and simulations confirm systematic under-estimation of slope parameter when the true model involves a lagged effect but not the working analysis model: the bias, which depends on the covariance structure of the PK profile, grows as the lag time increases. Also the lag time impacts the time effect parameter in the working analysis model: the magnitude of this time effect could be then used as quantitative diagnostics for the presence of lagged effect.
Conclusions: Ignoring a lag-time effect induces systematic underestimation of the concentration effect through biased estimation of slope parameter in direct analysis model. Also, as complementary sensitivity analyses, approximate lag-time corrected slope estimates can be computed in considering lag time as tuning parameter instead of a parameter to be estimated. These corrected estimates can have some usefulness as exploratory results, but cannot probably fully replace comprehensive PKPD modelling of both PK and PD parameters when hysteresis is suspected.
References:
[1] P. Glomb and A. Ring, Delayed Effects In The Exposure-Response Analysis Of Clinical Qtc Trials, Journal of Biopharmaceutical Statistics, 22: pp 387-400, 2012.
[2] H. White, Maximum Likelihood Estimation of Misspecified Models. Econometrica, pp 1-25, 1982
Reference: PAGE 21 (2012) Abstr 2499 [www.page-meeting.org/?abstract=2499]
Poster: Safety (e.g. QT prolongation)