Acceptance of therapeutic innovations into practice requires demonstrating and quantifying a treatment effect, measured as the difference in outcome rates between experimental and control groups of a randomized trial. This mathematical dependency of the treatment effect on the control event rate (ie, the rate of events in the control group) creates a dilemma for medical innovation. Although decreasing control rates signal therapeutic progress, sustained innovation theoretically requires an inexhaustible control rate. For industries dependent on therapeutic innovations, reducing outcome rates becomes both a primary goal and an existential threat.
When sequentially testing treatments with similar relative risk reductions (efficacy, E), the absolute risk reduction (incremental benefit, B) for i th therapeutic trial in the series can be described by the declining exponential function Bi=B1(1−E)i −1. In turn, the required sample size (S) for the i th trial approximates an increasing exponential function, described by the equation Si~S1/(1−E)i −1, and the number of trial participants for each incremental 1% benefit (unit cost, U) increases at twice this rate, described by the equation Ui~U1/(1−E)2(i −1). The rate of change of unit costs, U, is sensitive to the magnitude of the risk reduction, E. The derivation of the formulas used to calculate B, S, and U at the i th generation of treatment trial is available from the author upon request. In this example, the baseline mortality rate is 8% and the relative risk reduction with each therapy is 25% (and B1 is thus 2%).
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