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Appendix II: Comparison of Slopes and Testing of Linearity: Determination of Relative Potency

A common problem in bioassay, or when comparing the potency of compounds such as in drug screening programs, is the assessment of the relative potency of the comparative drugs. The problems in this analysis consist of (a) obtaining a function of dose and response which is linear, (b) testing the lines for each compound for parallelism (i.e., equality of slopes), and (c) determining the relative potency. We will discuss some elementary concepts for a comparison of two antiinflammatory compounds, a standard drug (St) and an experimental compound (Ex). The experiment consists of measuring the reduction in volume after treatment of initially inflamed paws of two animals at each of three doses for each compound. The results are shown in Table II.1 and plotted in Fig. II.1. The figure shows that the plot of log dose versus response is approximately linear. A transformation of dose and/ or response is often necessary to achieve linearity in dose-response relationships. The response is usually considered to be a linear function of log dose (see Chapter 10). Transformations to obtain linearity are desirable because straight-line relationships are more easily analyzed and interpreted than are more complex functions.