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I am working on an individual patient data meta-analysis, using a Cox proportional hazard model, with and without taking into account study identification, in Stata and R.

A reviewer asked me to provide him with a study-wise I-squared (statistical inconsistency) estimate for such patient-level analysis, but I am not aware of any means to do it.

Is it possible at all?

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The ability of reviewers to ask for things without thinking them through never ceases to amaze me.

If your research group had collected all the data as part of a multi-centre study you might have calculated an intra-centre correlation (ICC) and if you had not you might have been asked for an ICC to help other people planning future studies. So, why not offer them that and see how it goes down? To my eyes it answers the scientific question even thought it is not exactly what they asked for.

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  • $\begingroup$ Good hint... one possibility that came to my mind is to use study group as a factor, using the largest trial as the reference one, then obtain effect sizes and corresponding standard errors, and finally check the inconsistency between such effect sizes for study-wise effect. Could it make sense? $\endgroup$
    – Giuseppe Biondi-Zoccai
    Jul 7, 2016 at 13:57
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    $\begingroup$ Effectively then you are doing a two-step meta-analysis as it is becoming called so that seems fine too. $\endgroup$
    – mdewey
    Jul 9, 2016 at 10:58
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Since you've got individual patient data there may be more efficient ways to report study heterogeneity. For completeness: I think the canonical way would be to apply the algorithm used by the Cochrane Collaboration in its RevMan 5 software (see: p.5/6):

"The heterogeneity test statistic is given by

where θ represents the log odds ratio, log risk ratio or risk difference and the w are the weights calculated as rather than the weights used for the Mantel-Haenszel meta-analyses. Under the null hypothesis that there are no differences in intervention effect among studies this follows a chi-squared distribution with k − 1 degrees of freedom (where is the number of studies k contributing to the meta-analysis).

The statistic I^2 is calculated as

This measures the extent of inconsistency among the studies’ results, and is interpreted as approximately the proportion of total variation in study estimates that is due to heterogeneity rather than sampling error."

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