st: ANCOVA for pre post designs

[David Airey <david.airey@vanderbilt.edu>]

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 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?

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 less 
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.

Across the board, prepulse inhibition papers generally employ method 
(3). That is, each subject is measured with trials for startle, and 
also (at the same testing session) with trials for prepulse inhibition, 
and then a ratio is formed for that subject 
100*(startle-prepulse)/(startle) to represent the percent prepulse 
inhibition relative to startle. That percent (%PPI) is then analyzed as 
the response measure. I'm thinking the baseline measure discuss at the 
top of this email is analogous to the startle trial response, and the 
followup is analogous to the prepulse trial response. A difference is 
that both trial types are given pre and post to any (e.g., drug) 
intervention. An additional complication is that the %PPI ratio is 
analyzed in the context of both between-subject designs and 
within-subject designs.

Is method (4) applicable to prepulse inhibition studies, and is it 
applicable to both between and within designs?

By way of example, let's suppose we have the following between-subjects 
data:

group, startle, prepulse, ppi

where group indicates a between-subjects design where one group had a 
placebo and another group had the drug. Then, method (4) says to 
analyze group difference by the regression (ANCOVA) model, prepulse = 
constant + b1*startle + b2*group, and in Stata, this would be "anova 
prepulse group startle, continuous(startle)". The usual ANOVA on %PPI 
by method (3) would be "anova ppi group".

Next we could have the same question but using within-subjects data:

subject, startle, prepulse, ppi, treatment

where treatment indicates that each subject is exposed to the placebo 
and drug at different times in random order. Is it also possible to use 
a within-subjects design with the advantages of method (4) 
incorporated? Usually, one would do "anova ppi subject treatment" on 
%PPI. Does the model "anova prepulse subject treatment startle, 
continuous(startle)" make sense?

-Dave

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