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Re: st: ANCOVA for pre post designs
At 06:12 PM 12/23/2003, David Airey wrote:
This is a question for the biostatisticians on the list.
In large trials, (1) should be fine (at least, in terms of no bias). But
(2) or (4) may be more efficient.
I'm thinking of formulating a commentary on accepted research procedures
in my area that I think could be improved by observing basic statistical
arguments presented to researchers by biostatisticians.
It has been suggested that in a randomized clinical trial design with
baseline (B) and followup (F) test measures comparing a control and
treatment group (G), performing an ANOVA on the ratio pre/post is the
worst choice of the 4 ways to deal with baseline differences:
(1) post: analyze F by G
(2) difference: analyze F-B by G
(3) ratio: analyze F/B by G
(4) ancova: analyze F = constant + b1*B + b2*G, for G differences
In light of biostatisticians' suggestion (e.g., Vickers, BMC Medical
Research Methodology (2001) 1:6,
http://www.biomedcentral.com/1471-2288/1/6) that method (4) above is
preferred most and method (3) is least preferred, does it apply to
"prepulse inhibition" literature?
(3) above is similar in flavor to (2) if you view it on the log scale, i.e.,
(logF-logB) by G (or, equivalently, log(F/B) by G).
A technical question is whether the original measurements (B and F), or
their difference on the original scale, or their log-ratio (ie, difference
of logs) more closely conforms to the assumptions of linear regression
(normality of residuals, homoskedasticity).
Still, I wouldn't do it on (F/B) but rather on log(F/B) if that looks good.
There is a difference in the underlying scientific model and
interpretation, of course.
Does the treatment work additively (ie, adds a fixed amount, no matter
where you start)? If so, the difference (F-B) would be a good choice
(constant additive treatment effect across all values of B). And you'll be
talking about the (arithmetic) mean difference for treatment vs. control.
But if the treatment works multiplicatively (ie, increases/decreases your
original B measurement by a certain percent), then log(F-B) would be
better. And then, by exponentiating the regression coefficients etc, you'll
be talking about geometric mean ratio for treatment vs. control.
Finally, the choice between (2) and (4) depends on the correlation between
baseline and follow-up measurements. I think that when corr(B,F) < 0.5,
then (4) turns out to be more efficient; otherwise, (2) is better. I
believe there's a paper by Liang & Zeger on this.
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Constantine Daskalakis, ScD
Biostatistics Section, Thomas Jefferson University,
211 S. 9th St. #602, Philadelphia, PA 19107
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