A technique for population pharmacodynamic analysis of concentration-binary response data

Background: Pharmacodynamic data frequently consist of the binary assessment (a ''yes'' or ''no'' answer) of the response to a defined stimulus (verbal stimulus, intubation, skin incision, and so on) for multiple patients. The concentration--effect relation is usually reported in terms of C-50, the drug concentration associated with a 50% probability of drug effect, and a parameter the authors denote gamma, which determines the shape of the concentration-probability of effect curve. Accurate estimation of gamma, a parameter describing the entire curve, is as important as the estimation of C-50, a single point on this curve. Pharmacodynamic data usually are analyzed without accounting for interpatient variability. The authors postulated that accounting for interpatient variability would improve the accuracy of estimation of gamma and allow the estimation of C-50 variability. Methods: A probit-based model for the Individual concentration-response relation was assumed, characterized by two parameters, C-50 and gamma. This assumption was validated by comparing probit regression with the more commonly used logistic regression of data from individual patients found in the anesthesiology literature. The model was then extended to analysis of population data by assuming that C-50 has a log-normal distribution. Population data were analyzed in terms of three parameters, [C-50], the mean value of C-50 in the population; omega, the standard deviation of the distribution of the logarithm of C-50; and gamma. The statistical characteristics of the technique were assessed using simulated data. The data were generated for a range of gamma and omega values, assuming that C-50 and gamma had a log-normal distribution. Results: The probit-based model describes data from individual patients and logistic regression does. Population analysis using the extended probit model accurately estimated [C-50], gamma, and omega for a range of values, despite the fact that the technique accounts for C-50 variability but not gamma variability. Conclusion: A probit-based method of pharmacodynamic analysis of pooled population data facilitates accurate estimation of the concentration-response curve.