On 16 Márta 2007, at 16:38, Jaroslaw Wechowski wrote:
> Two treatments result in different costs, and the two costs need to be
> compared. The distribution of costs, however, an output of a
> simulation
> model, is trimodal and nonsymmetric, so the mean costs do not seem
> appropriate here.
>
> Simple comparison of medians shows that treatment B is cheaper. To
> test
> the significance, I calculated the Hodges-Lehmann estimate (a
> median of
> all possible differences from the two samples) and then the
> distribution-free confidence interval (Moses) based on Wilcoxon
> Rank Sum
> Test. Strangely, the Hodges-Lehman estimate shows that this time
> treatment A is cheaper and confidence intervals confirm the
> conclusion.
>
> I also tried bootstrapping and obtained CIs individually for each
> group.
> CIs were based on the distribution of means of bootstrap samples.
> Means
> show that treatment A is cheaper but CIs overlap, which is
> inconclusive.
>
> Ideally, perhaps, all approaches should be reported with comments, but
> often there is no space in clinical journals for such details and the
> most appropriate method needs to be chosen.
The H-L is a measure of median slope. This idea can be extended to
the idea of other centile slopes, and this sounds like it might well
be interesting in your case. However, the interpretation of the
median slope makes it more a measure of the effect of treatment on an
individual patient than a comparison of medians (which compares
groups). Since it only describes one quantile, you might complement
the information by calculating the 75%ile and 25%ile slopes as well.
Roger Newson, a tireless advocate of this approach, has a very
interesting paper in the Stata Journal 2006;6(4):497-520 which
introduces Stata programs which do these centile slopes.
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Ronán Conroy
Royal College of Surgeons in Ireland
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