Including trials reporting medians in meta-analysis

I’ve been thinking a lot about how best to include trials that report incomplete stats (or just not the stats you want) in a meta-analysis. This led me to a 2005 paper by Hozo, Djulbegovic & Hozo. It’s a worthwhile read for all meta-analysts. They set out estimators for the mean & variance given the median, range & sample size. The process by which they got these estimators was a cunning use of inequalities.
However, I was left wondering about uncertainty around the estimates. Because I’ve been taking a Bayesian approach, I really want a conditional distribution for the unknown stats given what we do know. There is one point where the authors try a little sensitivity analysis by varying the mean and standard deviation that came from their estimators, and they found a change in the pooled estimate from their exemplar meta-analysis that is too big to ignore. They do give upper and lower bounds, but that’s not the same thing.
Another interesting problem is that the exemplar meta-analysis seems to have some substantial reporting bias; the studies reporting medians get converted to smaller means than those that reported means. A fully Bayesian approach would allow you to incorporate some prior information about that.


1 Comment

  1. A comment from K? O’Rourke left over on some other, vastly more popular blog:

    In my thesis I made these comments after communicating to one of the authors

    “In the given reference, the example purported to demonstrate the value of such a method that was based on using medians and ranges of within patient change scores, but these were actually unavailable to the authors. Instead the authors “imputed” values using information on group mean scores over various treatment applications on different days, even when considerable drop out occurred [private communication]. Furthermore, the non-parametric conversions they used were based on inequalities between
    sample medians and ranges and SAMPLE means and standard deviations which are only indirectly relevant – it is population means and standard deviations that are of inferential relevance.”

    So authors don’t make corrections their papers (it was keep on misleading folks).

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