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Re: Fixed effects versus random effects models - idiot's guide?

From:

Doggett, David

Date:

Wed, 22 Aug 2001 10:46:27 -0400

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 ```I agree with Steve Simon that when there is an apparent clumping, it is best to try to explain that, and to treat the clumps separately. I also agree with him that for very homogeneous study results, the fixed and random effects methods give similar results. The more heterogeneity there is, the further appart the results will be with the two methods (the point estimates will differ somewhat, but mainly, the confidence interval will be wider for the random effects method. Therefore, the most conservative thing is to always use the random effects method. When there is truly no heterogeneity, the random method will give the same result as the fixed, and the more heterogeneity is present, the more the random effets method will be appropriate. Philosophically, the way to decide which method applies is to ask this question. If all of the studies (or centers) expanded their sample sizes many-fold, would one expect all of the results to converge to the same point estimate? If so, then one believes all of the variability between study results comes from scatter because of small study sizes. Then weighting should be solely on the basis of study size (or variance), and the fixed effects model is appropriate. If on the other hand one would not expect the different study results to converge to the same point estimate, because of real differences in the populations being sampled, then the random effects model is appropriate. As you can see, this is a sort of philosophical expectation that one is guessing at. The only emipirical way to address the question is with heterogeneity analysis. Unfortunately, with small numbers of studies (or centers) heterogeneity analysis is underpowered, so that "non-significant" heterogeneity may be found in a situation in which there is some real heterogeneity. For this reason it may be wise to use the random effects model even when no "significant" heterogeneity is found. As mentioned above, the results will be very similar, but the random effects model will give a more conservative, wider confidence interval. However, there is a potential problem with any random effects analysis. If the different studies (or centers) have different populations, but the studies are not a random sample of the different population centers, then the result will be biased to the extent that the sample is biased. Other than using many studies (or centers), there is no remedy for this problem. However, the larger confidence interval of the random effects model again seems to be more appropriate and conservative than the fixed effects approach. Actually, presentation of the simple range of study (or center) results may be the most appropriate way to deal with this sampling problem. That way having more samples toward one end of the range does not bias the result. But of course, an extreme outlier can shift the range. Thus, outliers must be examined carefully for explanations of the heterogeneity. The bottom line is that, even with the more conservative random effects method, the results of a meta-analysis (or a multi-center study) will be biased to the extent that the studies (or centers) are not representative. David L. Doggett, Ph.D. Senior Medical Research Analyst Health Technology Assessment and Information Services ECRI, a non-profit health services research organization 5200 Butler Pike Plymouth Meeting, Pennsylvania 19462, U.S.A. Phone: (610) 825-6000 x5509 FAX: (610) 834-1275 http://www.ecri.org e-mail: [log in to unmask] -----Original Message----- From: Simon, Steve, PhD [mailto:[log in to unmask]] Sent: Monday, August 20, 2001 7:57 PM To: [log in to unmask] Subject: Re: Fixed effects versus random effects models - idiot's guide? Andrew Booth writes: >Does anyone have a simple explanation or "rule of thumb" for explaining to people >when a fixed effects or a random effects method should be used for a systematic review. There is a fair amount of controversy about this. I like to think of a meta-analysis as a multi-center trial where each center uses a different protocol. Since the multi-center trial requires random effects, so should a meta-analysis. The controversy occurs because many times there will be a sharp disagreement between studies where some of them will cluster at one point and others will cluster at a different point. This violates the assumption of normality for the random effects model. A new trend is to look for trends that might explain the underlying heterogeneity (e.g., baseline risk) and incorporate these trends into a model. This sometimes goes by the name of meta-regression. Some people test for heterogeneity and then choose. I don't like this approach--if there is little heterogeneity, the random and fixed models will be close anyway, so why not always choose the random effects model? I am not an expert in meta-analysis--just an informed consumer. So take my comments with a grain of salt. Steve Simon, [log in to unmask], Standard Disclaimer. STATS: STeve's Attempt to Teach Statistics. http://www.cmh.edu/stats Watch for a change in servers. On or around June 2001, this page will move to http://www.childrens-mercy.org/stats ```

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