Comments on Using the Time of Maximum Effect Site Concentration to Combine Pharmacokinetics and Pharmacodynamics: In Reply

On behalf of the our coauthors of the article “Using the time of maximum effect site concentration to combine pharmacokinetics and pharmacodynamics,”1we welcome the comments and observations in the letter by Drs. Nigrovic and Amann and the letter by Dr. Van Meurs, Mr. Nikkelen, and Dr. Good. The letter by Drs. Nigrovic and Amann raises several points, which are addressed in the order presented:In response to the letter from Dr. Van Meurs, Mr. Nikkelen, and Dr. Good, we acknowledge their excellent manuscript on keoand tpeakand appreciate their consistency with the definition of tpeakintroduced by Shafer and Gregg 6(reference 5 of their manuscript). Although we share many of the same conclusions, in particular, their observation on page 586 that “this result justifies the use of tpeakas a parameter to base a keoestimate on.” What particularly distinguishes their article is the thoughtful and novel sensitivity analysis. Their article describes development of their own software for this purpose. STANPUMP, which has been available over the Internet since 1989, provides a mean for nonprogrammers to perform the same simulations.We do not know how the authors responded to their reviewer, but the reviewer is not quite correct. Assuming that effect has been continuously sampled (getting around the issue of discrete sample times that concerned Drs. Nigrovic and Amann), there is a one-to-one relation between keoand tpeak. When analyzing a population of patients, variability in keocan be determined directly from variability in tpeak. What the reviewer may have intended was that when analyzing an individual patient, the uncertainty (e.g. , SE) about the estimate of tpeakmay be greater than the uncertainty about an estimate of keo, because tpeakis a single observation that may have considerable variability, whereas an estimate of keois based on analysis of all points in the hysteresis curve and thus may be known with greater certainty. If one has access to multiple concentrations and measures of drug effect, the standard approach should be used to estimate keo. We would never advocate using tpeakto estimate keowhen one has access to a full set of concentration and effect measures. Nevertheless, comparing the calculated tpeakfrom the resulting model with the observed time of peak effect provides a quick verification that the modeling was done correctly.We certainly agree that the fact that different keos, combined with different pharmacokinetic parameter sets, demonstrated nearly identical values for tpeak(figs. 1 and 2) in our article could be serendipitous. The purpose of our article was to present a theoretical concept and show some examples of the concept. It was not known before our analysis that the tpeakwould be the same for figures 1 and 2. It is not clear how a sensitivity analysis could address the question of serendipity.Again, on behalf of our coauthors, we appreciate the thoughtful letter of Drs. Nigrovic and Amann and that of Dr. Van Meurs, Mr. Nikkelen, and Dr. Good and hope that this discussion on a moderately arcane topic is of interest to the readers of Anesthesiology.Palo Alto Veterans Affairs Health Care System, Palo Alto, California; Stanford University School of Medicine, Stanford, California; and University of California at San Francisco, San Francisco, California. steven.shafer@stanford.edu