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I hope this is an ok place to post this. I am an epidemiologist looking at 14 studies on a particular topic (e.g. chemical exposure on semen parameters). All the studies performed similar semen analysis methods, but their analyses were varied. Some used a continuous outcome (with continuous or categorical exposure), some used a dichotomous outcome (all with categorical exposure).That difference feels manageable to me.

However, they also didn't all report the same effect estimates (betas for continuous, betas for high vs. low quartiles, correlation coefficient, % change, mean difference, means, odds ratios) or use the same transformations of the variables (ln, log10, cubic root, Box-Cox of outcome, ln, log10 of exposure).

Ideally, if all the studies used the same techniques, I would put them all in a forest plot. But this is just a mess. There are hardly any that did things they same. But they are all looking at the same question.

Does anyone have any suggestions for displaying this mess in such a way that the reader can easily see what the findings were across studies and can understand what the general trend is? There is also the additional complication of different studies having different median exposures, so wanting to preferably sort by that.

Currently, I just have a big old table with all the continuous outcome studies first, then all the categorical outcomes, and with information about what the transformation and effect estimate is. I just don't think it is very effective.

Thanks so much (and sorry for the wall of text)!

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There are ways of converting between standardised mean differences and (log) odds ratios

@ARTICLE{chinn00,
  author = {Chinn, S},
  year = 2000,
  title = {A simple method for converting an odds ratio to effect size for use
          in meta--analysis},
  journal = {Statistics in Medicine},
  volume = 19,
  pages = {3127--3131}
}

which may help to put more of them onto the same footing.

You presumably know that you can convert between logarithms to different bases fairly simply $\log_a{N} = \log_a{b} \times \log_b{N}$.

If you have the correlation and the standard deviations then by calculating from them the covariance you can estimate the $\beta$.

Apart from that you could always try writing to the authors. In my experience there are two sorts of reply: (a) silence, (b) the enormously helpful.

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  • $\begingroup$ Thanks for this, it is very helpful. I will spend some time looking at the paper. One quick question: I have converted between logarithms when the predictor was transformed (dividing beta by ln10 to covert base from 10 to e, for example). Can I do this when the outcome is transformed as well? $\endgroup$ Jun 29 '16 at 15:26
  • $\begingroup$ @OrangeTrout I do not see why not. $\endgroup$
    – mdewey
    Jun 29 '16 at 16:03

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