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st: re: ANCOVA for pre post designs
In a description of what prepulse inhibition of startle was, I meant to
say *MORE* where I said less,
In an area of schizophrenia research, subjects show a deficit in basic
sensorimotor gating, as measured by prepulse inhibition of the
acoustic startle response. The startle response is simply startle to a
loud noise. Prepulse inhibition is simply inhibition of that startle
response by preceding the loud noise with a soft noise. In both
non-schizophrenics and schizophrenics, startle is comparable, but
prepulse inhibition is _less_ in schizophrenics. That is, both groups
startle comparably to a loud noise, but schizophrenics startle *MORE*
when a startling noise is preceded by a soft noise. So, there are two
brain circuits underlying this behavior and the prepulse inhibition
circuit is compromised in schizophrenics.
Constantine Daskalakis replied to the original email,
This is a question for the biostatisticians on the list.
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
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?
In large trials, (1) should be fine (at least, in terms of no bias).
But (2) or (4) may be more efficient.
Actually, in my data a square root or log transformation makes the raw
data more normal so I'll think about this.
(3) above is similar in flavor to (2) if you view it on the log
(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
Why wouldn't you do it?
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.
Thanks for these points.
The paper I cited was a quick power analysis of the 4 approaches.
ANCOVA is always more efficient. Difference is more efficient than
followup only when corr(B,F) is higher. The F/B ratio is also mentioned
to be very sensitive to changes in the baseline distribution--power
declines when variance in B increases.
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.
OK, let me ask a simpler question: can one have baseline covariates in
within-subjects ANOVAs like we have in ANCOVAs, which are
between-subject ANOVAs but with covariates?
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