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I am starting to work on a meta-analysis project and I have received the data. The data includes both randomized trial and observational studies. Is there any article, book, or website that explains how to deal with both studies? Is it simply impossible to deal with them together? Is there different way to deal with them separately and compare the results?

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    $\begingroup$ When you say you have received data what exactly do you mean? What sort of data? Individual participant data? Some sort of summary statistic, and if so which? $\endgroup$
    – mdewey
    Nov 11 '16 at 12:54
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Meta-analysis of randomized and non-randomized trials is possible, but I recommend caution, as the exercise might lead to biased results, especially if the non-randomized trials weigh excessively on the overall effect estimates.

However, it can be useful for instance as a sensitivity analysis, in order to confirm in a more real-world patient set (as typically provided by non-randomized trials) the findings obtained in more selected subjects (as typically enrolled in randomized trials).

The common yet incorrect approach is to pool crude event rates from both types of studies. This is very misleading as confounders in non-randomized trials are not taken into account.

Conversely, the correct approach is to use crude event rates from randomized trials, for instance as odds ratios or relative risks (or, if provided hazard ratios [HR]), and use multivariable adjusted risk estimates from non-randomized trials, for instance those generated by logistic regression, Cox proportional hazard analysis, or propensity score matching.

Once all individual study effect estimates are provided in a similar fashion, for instance as log HR with corresponding standard errors, they can be pooled with several methods, including frequentist, Bayesian, fixed-effect, and random-effect.

There are several potentially useful examples from the literature, such as Vlaar et al, and Biondi-Zoccai et al.

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