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Commentary | November 25, 2009

Therapeutic Innovations, Diminishing Returns, and Control Rate Preservation

David M. Kent, MD, MS; Thomas A. Trikalinos, MD

JAMA. 2009;302(20):2254-2256. doi:10.1001/jama.2009.1679.

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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.

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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 B_i=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 S_i~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 U_i~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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Kent DM, Trikalinos TA. Therapeutic Innovations, Diminishing Returns, and Control Rate Preservation. JAMA. 2009;302(20):2254-2256. doi:10.1001/jama.2009.1679.

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