Antihypertensive effect of drugs: statistical distribution of the trough-to-peak ratio.

Explicit formulas for the distribution function, the expectation, and the variance of the ratio X/Y were calculated, where X and Y are dependent variables. We assumed that the pair (X, Log Y) has a bivariate normal distribution. The work was motivated by a recent draft from the American Food and Drug Administration (FDA) on the treatment of high blood pressure (FDA, 1990, Draft of the Proposed Guidelines for the Clinical Evaluation of Antihypertensive Drugs). The effect of antihypertensive drugs on blood pressure usually achieves a peak level and then decreases to a trough level before the next dose. The FDA recommended that the ratio of trough-to-peak effects should be at least 0.5. It is well known that trough and peak effects are correlated.