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A Formula for Determining Sample Sizes to Study Dose-Response

Determining the appropriate sample size for a clinical trial requires careful deliberation. Cost and ethical considerations dictate that a minimum number of patients be enrolled to study the safety and efficacy of a new chemical entity, yet the probability of not observing a true treatment effect is overly high if too few patients are enrolled. Recent results regarding adequate sample size for dose-response (DR) studies were based on Monte Carlo simulation. Application of such results is limited to planning DR studies that match the simulation protocol with respect to the desired power, number and spacing of dose levels, level of significance, and actual DR relationship. Complete flexibility in planning DR studies requires a formula relating power to sample size and other design parameters. This paper describes such a formula that is applicable when standard analyses are planned. An example is given to suggest possible alternative hypotheses and to illustrate application of the sample size formula.