Detecting dose response with contrasts

Analyses of dose response studies should separate the question of the existence of a dose response relationship from questions of functional form and finding the optimal dose. A well-chosen contrast among the estimated effects of the studied doses can make a powerful test for detecting the existence of a dose response relationship. A contrast-based test attains its greatest power when the pattern of the coefficients has the same shape as the true dose response relationship. However, it loses power when the contrast shape and the true dose response shape are not similar. Thus, a primary test based on a single contrast is often risky. Two (or more) appropriately chosen contrasts can assure sufficient power to justify the cost of a multiplicity adjustment. An example shows the success of a two-contrast procedure in detecting dose response, which had frustrated several standard procedures.