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Re: A note on the usage of cost-effectiveness acceptability curves

Dear Editor,

In a recent article in this journal by Struijs and colleagues [1], the cost-effectiveness of physiotherapy, braces, and a combination of the two for treatment of tennis elbow has been studied. Unfortunately, the cost-effectiveness acceptability curve (Figure 3 of the article) could not be correct. As the cost-effectiveness plane and the authors' comments in the results section indicate, bootstrap cost-effect pairs were equally distributed in all quadrants of the cost-effectiveness plane. This means that in roughly 1/4 of times the incremental cost-effectiveness ratio (ICER) falls in quadrant II (upper left quadrant); that is, the treatment is more costly (∆e<_0 and="and" less="less" effective="effective" _8710e0="_8710e0" hence="hence" is="is" dominated="dominated" by="by" the="the" alternative="alternative" strategy.="strategy." for="for" any="any" positive="positive" value="value" of="of" ceiling="ceiling" ratio="ratio" willingness="willingness" to="to" pay="pay" estimates="estimates" that="that" lie="lie" in="in" this="this" quadrant="quadrant" should="should" never="never" be="be" economically="economically" acceptable="acceptable" posing="posing" an="an" upper="upper" limit="limit" on="on" acceptability="acceptability" curve.="curve." plotted="plotted" curve="curve" approaches="approaches" _1="_1" as="as" increases="increases" which="which" clear="clear" contradiction="contradiction" with="with" above="above" constraint.="constraint." p="p" /> We believe the source of this error is that the authors have plotted the proportion of incremental cost-effectiveness ratios that fell below the value of the ceiling ratio (∆c/∆e<K).

The incorrectness of this method has been discussed in detail elsewhere [2]. In brief, this method can not distinguish between estimates that fall in the second (upper left) and forth (lower right) quadrants as they both take negative ∆c/∆e values despite the fact that these two quadrants represent the dominated and dominant strategies, respectively.

The correct way of generating the cost-effectiveness acceptability curve is to calculate the proportion of ratios that satisfy the inequality ∆c-K.∆e<_0 _2.="_2." this="this" method="method" will="will" properly="properly" exclude="exclude" the="the" dominated="dominated" and="and" include="include" dominant="dominant" estimates.="estimates." p="p" /> References

[1] Struijs PA, Korthals-de Bos IB, van Tulder MW, van Dijk CN, Bouter LM, Assendelft WJ, Pluim BM. Cost effectiveness of brace, physiotherapy, or both for treatment of tennis elbow. Br J Sports Med 2006;40:637-643.

[2] O'Hagan A, Stevens JW, Montmartin J. Inference for the cost- effectiveness acceptability curve and cost-effectiveness ratio. Pharmacoeconomics. 2000 Apr;17(4):339-49