Semiparametric analysis of non-steady-state pharmacodynamic data

Abstract

We present an approach to the analysis of pharmacodynamic (PD) data arising from non-steadystate experiments, meant to be used when only PD data, not pharmacokinetic (PK) data, are available. The approach allows estimation of the steady-state relationship between drug input and effect. The analysis is based on a model describing the time dependence of drug effect (E) on (unobserved) drug concentration (Ce) in an hypothetical effect compartment. The model consists of (i) a known model for the input rate of drug I(t), (ii) a parametric model; L(t, a) (a function of time t, and vector of parameters a), relating I to an observed variable X, (iii) a nonparametric model relating X to E. Ce is proportional to X. X(t) is given by I(X) * L(t, a)/AL, where L(t,α)=e ^−α ₁ ^t * ∑ _k=1 ^m , α_2k e ^−α _2k+1 ^t, ∑ _k=1 ^m α_2k=1, AL=∫ ₀ ^∞ L(t) dt, and * indicates convolution.The nonparametric model relating X to Eis a cubic spline, a function of X and a vector of (linear) parameters β. The values of α and β are chosen to minimize the sum of squared residuals between predicted and observed E. We also describe a similar model, generalizing a previously described one, to analyze PK/PD data. Applications of the approach to different drug-effect relationships (verapamil-PR interval, hydroxazine-wheal and flare, flecainide and/or verapamil-PR, and left ventricular ejection fraction) are reported.