USE OF RESAMPLING TECHNIQUES TO ESTIMATE THE VARIANCE OF PARAMETERS IN PHARMACOLOGICAL ASSAYS WHEN EXPERIMENTAL PROTOCOLS PRECLUDE INDEPENDENT REPLICATION - AN EXAMPLE USING SCHILD REGRESSIONS

Estimates of variance in pharmacological assays are usually made by re peating the experiment with different tissues. Biological factors, suc h as the inability to wash a drug from tissue, may preclude the type o f replication that is appropriate for the statistics of interest. For example, in Schild regressions, replication is usually done at each co ncentration of antagonist. In some test systems, replication of dose-r esponse curves is not possible. For example, some persistent agonists cannot be removed from tissues after exposure, while in other systems, rapid desensitization severely alters tissue sensitivity to repeated challenge with agonist. In this paper, we demonstrate how a statistica l resampling method, bootstrapping, can be used to derive estimates of the confidence intervals for pA(2), pK(B), and slope from Schild plot s. This method utilizes the speed of the computer to estimate variance by repeatedly resampling the data. The advantage to this method is th at it can be used for many different experimental designs. For a data set obtained from a Schild regression of atenolol antagonism of isopro terenol in the guinea pig left atrium, bootstrap estimates of confiden ce limits were calculated for cases where dose ratios were derived fro m the same tissue and randomly paired tissues. These estimates showed good agreement with estimates obtained using conventional analytical m ethods, thus suggesting that this method may be useful in practice.