SEMIPARAMETRIC ANALYSIS OF NON-STEADY-STATE PHARMACODYNAMIC DATA

We present an approach to the analysis of pharmacodynamic (PD) data arising from non-steady-state 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, alpha) (a function of time t, and vector of parameters-alpha), 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(t) * L(t, alpha)/AL, where L(t, alpha) = e(-alpha(1)t * SIGMA(k = 1)m alpha(2k)e(-alpha(2k)+1t, SIGMA(k = 1)m alpha(2k) = 1, AL = integral(0)infinity L(t) dt, and * indicates convolution. The nonparametric model relating X to E is a cubic spline, a function of X and a vector of (linear) parameters beta. The values of alpha and beta 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.