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Dear Marie,
I don’t think there’s likely to be such a thing as a ‘correct’ model for a data set like this, of considerable complexity and not collected with research in mind (though
there certainly are ‘incorrect’ models). I think probably the best you can hope to achieve is a reasonable model – and that may require exploring different possibilities, in which case you have to bear in mind that the process of exploration and selection
introduces bias into your final estimates and p-values. So the whole analysis then becomes exploratory, hypothesis-generating – not hypothesis-validating.
I don’t see anything incorrect in the model you have specified for your cattle data, but I wonder if it may be too complicated. Bearing in mind the unbalanced data
structure, do you have enough information to get good estimates of Year and Season effects in the RANDOM model? If I’m understanding the data correctly, the important thing is that each Cattle_group is within a single Year and Season, and the Cattle_group
values themselves may be sufficient to specify this, in which case the model
RANDOM=Feedlot/Cattle_group
might suffice. You could compare it with your proposed model to see if there was evidence of a substantial Year and/or Season-within-Year variance component. If there are duplicate
Cattle_group values that actually refer to different groups in different Years and/or Seasons, you can take account of this, without estimating Year and/or Season-within-Year variance components, by specifying
RANDOM=Feedlot/Year.Season.Cattle_group
By the way, for the classic example of meta-analysis that you cite, you need to consider the possibility that the main effect of TRIAL should be specified as a fixed-effect
term, and correspondingly that in your study the main effect of Feedlot should be a fixed-effect term. This may seem perverse, but if you specify TRIAL as random, then the estimate of the effect of THERAPY (I think) includes information from the between-trials
variation, which you may not want, as patients are randomised to a level of THERAPY only within each trial. (See Section 8.4, ‘A random-effect interaction between two fixed-effect terms’, in the second edition of my mixed modelling book, for a discussion
of this issue.)
I say ‘I think’ because it may be that the option setting ‘EXPERIMENT = TRIAL’ is sufficient to specify within-trial estimation of the THERAPY effect. Does anyone
else on the discussion list know if this is the case?
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
Tel +44 208 047 6878
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From: Marie Smith <[log in to unmask]>
Sent: 15 December 2020 07:37
To: Stephen Senn <[log in to unmask]>
Cc: Nicholas Galwey <[log in to unmask]>; Open discussion list for the statistical system Genstat <[log in to unmask]>
Subject: Re: meta analysis advice
EXTERNAL
Dear Stephen & Nick
Thank you for responding so soon. Apologies for not giving more detailed information! Yes, I was using the Genstat algorithm for more than one factor and its interactions.
In this country many feedlots record for each of hundreds of animals per year data as follows:
AnimalID, Cattle_group, Sex, Season, Year, ADG, etc., where ADG is average daily gain, other growth performance measures, also health status.
For the classic example of meta-analysis the VCOMPONENT statement, in Stephen's example, will be:
VCOMP [FIXED=THERAPY;EXP=TRIAL] RANDOM=TRIAL/THERAPY.
In this study, the data from 5 feedlots were sourced from a certain area, that included the cattle groups of interest. To my understanding, the data from each feedlot is of a nested origin, such as a split-plot
design, where animals are nested within seasons that are nested within years. How do I correctly define the RANDOM effects term in this case, if the main interest is in growth performance of different cattle groups and the possible seasonal effect?
VCOMP [FIXED=Cattle_group*Season;EXP=Feedlot] RANDOM=Feedlot/Year/Season/Cattle_group?
Note also that the data are very unbalanced. This is my concern, that I define the correct random effects term!
Marie
On Mon, 14 Dec 2020 at 12:00, Stephen Senn <[log in to unmask]> wrote:
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, 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
Tel +44 208 047 6878
gsk.com | Twitter | YouTube | Facebook | Flickr
From: GENSTAT-Request <[log in to unmask]> On Behalf Of Stephen Senn
Sent: 14 December 2020 09:30
To: [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]> On Behalf Of Marie Smith
Sent: 14 December 2020 08:04
To: [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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