[R-meta] Sample size and continuity correction

Gerta Ruecker ruecker @end|ng |rom |mb|@un|-|re|burg@de
Thu Aug 27 18:21:09 CEST 2020

Dear Nelly and all,

With respect to (only) the first question (sample size):

I think nothing is wrong, at least in principle, with a meta-analysis of 
two studies. We analyze single studies, so why not combining two of 
them? They may even include hundreds of patients.

Of course, it is impossible to obtain a decent estimate of the 
between-study variance/heterogeneity from two or three studies. But if 
the confidence intervals are overlapping, I don't see any reason to 
mistrust the pooled effect estimate.



Am 27.08.2020 um 16:07 schrieb ne gic:
> Many thanks for the insights Wolfgang.
> Apologies for my imprecise questions. By "agreed upon" & "what
> conclusions/interpretations", I was thinking if there is a minimum sample
> size whose pooled estimate can be considered somewhat reliable to produce
> robust inferences e.g. inferences drawn from just 2 studies can be
> drastically changed by the publication of a third study for instance - but
> it seems like there isn't. But I guess readers have to then check this for
> themselves to access how much weight they can place on the conclusions of
> specific meta-analyses.
> Again, I appreciate it!
> Sincerely,
> nelly
> On Thu, Aug 27, 2020 at 3:43 PM Viechtbauer, Wolfgang (SP) <
> wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
>> Dear nelly,
>> See my responses below.
>>> -----Original Message-----
>>> From: R-sig-meta-analysis [mailto:
>> r-sig-meta-analysis-bounces using r-project.org]
>>> On Behalf Of ne gic
>>> Sent: Wednesday, 26 August, 2020 10:16
>>> To: r-sig-meta-analysis using r-project.org
>>> Subject: [R-meta] Sample size and continuity correction
>>> Dear List,
>>> I have general meta-analysis questions that are not
>>> platform/software related.
>>> *=======================*
>>> *1. Issue of few included studies *
>>> * =======================*
>>> It seems common to see published meta-analyses with few studies e.g. :
>>> (A). An analysis of only 2 studies.
>>> (B). In another, subgroup analyses ending up with only one study in one of
>>> the subgroups.
>>> Nevertheless, they still end up providing a pooled estimate in their
>>> respective forest plots.
>>> So my question is, is there an agreed upon (or rule of thumb, or in your
>>> view) minimum number of studies below which meta-analysis becomes
>>> unacceptable?
>> Agreed upon? Not that I am aware of. Some may want at least 5 studies (per
>> group or overall), some 10, others may be fine with if one group only
>> contains 1 or 2 studies.
>>> What interpretations/conclusions can one really draw from such analyses?
>> That's a vague question, so I can't really answer this in general. Of
>> course, estimates will be imprecise when k is small (overall or within
>> groups).
>>> *===================*
>>> *2. Continuity correction *
>>> * ===================*
>>> In studies of rare events, zero events tend to occur and it seems common
>> to
>>> add a small value so that the zero is taken care of somehow.
>>> If for instance, the inclusion of this small value via continuity
>>> correction leads to differing results e.g. from non-significant results
>>> when not using correction, to significant results when using it, what does
>>> make of that? Can we trust such results?
>> If this happens, then the p-value is probably fluctuating around 0.05 (or
>> whatever cutoff is used for declaring results as significant). The
>> difference between p=.06 and p=.04 is (very very unlikely) to be
>> significant (Gelman & Stern, 2006). Or, to use the words of Rosnow and
>> Rosenthal (1989): "[...] surely, God loves the .06 nearly as much as the
>> .05".
>> Gelman, A., & Stern, H. (2006). The difference between "significant" and
>> "not significant" is not itself statistically significant. American
>> Statistician, 60(4), 328-331.
>> Rosnow, R.L. & Rosenthal, R. (1989). Statistical procedures and the
>> justification of knowledge in psychological science. American Psychologist,
>> 44, 1276-1284.
>>> If one instead opts to calculate a risk difference instead, and test that
>>> for significance, would this be a better solution (more reliable result?)
>>> to the continuity correction problem above?
>> If one is worried about the use of 'continuity corrections', then I think
>> the more appropriate reaction is to use 'exact likelihood' methods (such as
>> using (mixed-effects) logistic regression models or beta-binomial models)
>> instead of switching to risk differences (nothing wrong with the latter,
>> but risk differences are really a fudamentally different effect size
>> measure compared to risk/odds ratios).
>>> Looking forward to hearing your views as diverse as they may be in cases
>>> where there is no consensus.
>>> Sincerely,
>>> nelly
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Dr. rer. nat. Gerta Rücker, Dipl.-Math.

Institute of Medical Biometry and Statistics,
Faculty of Medicine and Medical Center - University of Freiburg

Stefan-Meier-Str. 26, D-79104 Freiburg, Germany

Phone:    +49/761/203-6673
Fax:      +49/761/203-6680
Mail:     ruecker using imbi.uni-freiburg.de
Homepage: https://www.uniklinik-freiburg.de/imbi-en/employees.html?imbiuser=ruecker

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