I am working on a Network Meta-analysis that is aimed at comparing different treatments (medical vs surgery vs percutaneous approach) on short as well as long-term outcomes (including cardiovascular morbidity and mortality at 1 year). We have completed a first pass literature review identifying many studies involving the follow-up of the study population referred to just one treatment (patients just referred to surgery for example) but without a comparison group (controls, or alternative active treatment). Now, considering that, as far as I know, the usual approach of multivariate meta-analysis is based on contrasts so to have direct as well as indirect comparisons, here are my questions: a) is it legitimate/appropriate (from a pure statistical stand-point of course) to include such cohort studies with no comparison group, or is it more straightfoward to exclude them ? b) If we decide to include cohort studies focused at just 1 group with no comparison group what are the pros and cons in doing that, over the alterative strategy of taking out such studies focusing on just those studies in which a comparison (RCT or not) between active treatment and controls or active treatment A vs Active treatment B have been performed ? c) In case it will turn out the inclusion of studies with just 1 group are appropriate or even encouraged, and considering that I am planning to use mvmeta STATA package for the analysis, is that something I should know on how to arrange the dataset or perform such "single arm vs contrasts" analysis ? REFs are of course very wellcome

Thank you all very much in advance,


The idea of how one can use single arm trials is that you assume that outcomes vary across trials, but that they are somewhat similar (assumption of exchangeability). If you have multiple single-arm trials with the same treatment, then you can estimate how much outcomes vary for the same treatment. You might for example assume that this is the same across all treatments. If so, you can then compare the outcomes in different trials - if you do that, the variability in the comparison is not just the within trial sampling variability, but also in addition the between trial variability.

This may be best done in the parameterization given by Piepho et al. (Piepho, H.-P., Williams, E. R., and Madden, L. V. (2012). The use of two-way linear mixed models in multitreatment meta-analysis. Biometrics, 68(4):1269-1277.).

In principle, this works fine (i.e. you can give numbers to a software and results come out), but you must assume that there is no systematic difference between single arm trials for different drugs, as well as between each set of single arm trials and other multi-arm trials. This will definitely be something to caveat a lot in the discussion of your results. You can try - to some extent - to estimate from the data whether there are such differences, but this may be difficult depending on how much data you have. In a Bayesian analysis with (weakly-)informative priors the relevant parameters can usually be estimated, if often not too well, in which case you cannot get much out of across-trial comparisons (which is perhaps quite reasonable).

The most basic vanilla version of this (that is the least robust) can be implemented with any software that can fit random effects GLM with given standard errors (while I don't know STATA, I assume it can do that, but perhaps not in the package you mention). It may be best to get some support for implementing your analyses from a statistician experienced in network meta-analyses.

  • $\begingroup$ This is great Bjorn ! Thank you so very much for the insight, really appreciated. $\endgroup$ – Diego May 3 '17 at 6:04

I will answer your questions labelled as you have them

(a) there is no statistical reason for excluding cohort studies from your analysis but there might be substantive reasons if they are performed on people with a very different case-mix from these in trials (randomised or not). So it is perfectly in order to include a single arm study using a medical treatment and a single study using a surgical treatment. Each arm gives rise to an estimate of effect like the cure rate. Each arm in a trial also gives rise to similar estimates.

(b) I think this has a similar answer to (a). Part of the rationale for network meta-analysis was to develop techniques for indirect comparisons between treatments and single arm studies are an extreme case here. You might want to consider whether you can introduce a study-level covariate to account for case-mix if you can see how to do that. People will always be more sceptical about conclusions if the majority of your information comes from indirect comparisons.

(c) I do not use Stata so cannot comment here.

  • $\begingroup$ First of all, thank you very much for your reply, this is helpful. Let's say study populations are reasonably homogeneous across studies (single arm or trials, does not matter). Still, I do not see how including a single arm population, although possible, will help in improving the (contrasts) analysis, might you please elaborate a little bit more on this ? Thanks again $\endgroup$ – Diego May 1 '17 at 17:16

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