Yes. Remembered the very sensible Genstat convention in my reply but read it as SAS in the question! So Cattle_group_Season might be the random effect.
Stephen
From: Nicholas Galwey <[log in to unmask]>
Sent: 14 December 2020 09:42
To: Open discussion list for the statistical system Genstat <[log in to unmask]>; Marie Smith <[log in to unmask]>; Stephen Senn <[log in to unmask]>
Subject: RE: meta analysis advice
Dear Stephen and Marie,
I don’t think Marie is specifying interaction as the main focus. If I’m understanding her email correctly, she is following the convention
Cattle_group*Season = Cattle_group + Season + Cattle_group.Season
where Cattle_group.Season represents the interaction effect, following the notation of
Wilkinson, G.N. and Rogers, C.E. (1973) Symbolic description of factorial models for analysis of variance. Applied Statistics 22:392-399.
@Marie Smith<mailto:[log in to unmask]>, have I understood correctly?
Best wishes,
Nick
N.W. Galwey, PhD
Statistics Leader, Research Statistics
Biostatistics, R&D
GSK Medicines Research Centre, Gunnels Wood Road, Stevenage, Hertfordshire, SG1 2NY, UK
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From: GENSTAT-Request <[log in to unmask]<mailto:[log in to unmask]>> On Behalf Of Stephen Senn
Sent: 14 December 2020 09:30
To: [log in to unmask]<mailto:[log in to unmask]>
Subject: Re: meta analysis advice
EXTERNAL
Dear Marie,
It is unusual to choose an interaction as the main focus of interest in a meta-analysis. For example in a meta-analysis of treatments in clinical trials, TRIAL would be a block effect and THERAPY (often at two levels, drug and placebo) would be the treatment effect. The main effect of THERAPY would be the focus of interest. The fixed effects meta-analysis would (implicitly) remove the THERAPY.TRIAL effect from the error term and the residual error term would be based on TRIAL/PATIENT. In a random effects meta-analysis the interaction would contribute to the error term. The difference between the two philosophies is that in the former a causal analysis of what actually happened in the set of trials is being attempted, whereas in the random effects analysis some sort of general predictions is attempted. See Senn SJ. The many modes of meta. Drug Information Journal. 2000;34:535-549.
Can you say more about what the data-structure is?
Regards
Stephen
From: GENSTAT-Request <[log in to unmask]<mailto:[log in to unmask]>> On Behalf Of Marie Smith
Sent: 14 December 2020 08:04
To: [log in to unmask]<mailto:[log in to unmask]>
Subject: meta analysis advice
Dear Genstat colleagues
I would really appreciate advice on the following complex data set. It is performance data from several cattle groups over 8 years and 4 seasons sourced from 5 feedlots. The objective of the study was to compare the performance of the cattle groups per season by means of a meta analysis over feedlots. The FIXED effects will be Cattle_group*Season, but what I am unsure of is what I should define as the RANDOM effects?
Kind regards
Marie F. Smith
Biometrician, stats4science
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