Incomplete Factorial design
Hi, Simon: Excellent observation, reinforcing the point that
interpretation of confounded effects depends on the context.
Best Wishes,
spencer graves
Simon Fear wrote:
One could also fit fit <- lm(y~A*B - 1, data.frame(y=..., A=..., B=..,) which will give a direct a:b term (as the negative of the intercept in Spenser's formulation). Arguably this is more natural in a setting where there is no placebo so that an intercept term has a less obvious interpretation.
-----Original Message----- From: Spencer Graves [mailto:spencer.graves at pdf.com] Sent: 06 February 2004 14:39 To: parrinel at med.unibs.it Cc: R-help at stat.math.ethz.ch Subject: Re: [R] Incomplete Factorial design Security Warning: If you are not sure an attachment is safe to open please contact Andy on x234. There are 0 attachments with this message.
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I assume that means you have two treatments, say A and
B, can be
either absent or present. The standard analysis codes them
as -1 or +1
for absent or present, respectively. If you have
observations in all 4
cells, you can write the following equation:
y(A,B) = b0 + b1*A + b2*B + b12*A*B + error.
This equation has 4 unknowns, b1, b1, b2 and b12. If
you have all
4 cells in the 2x2 table, then you can estimate all 4
unknowns. If you
have data for only 3 cells, the standard analysis pretends
that b12 = 0
and estimates the other three. If you have only 2 cells, say (both
absent) and (both present), the standard analysis can
estimate b0 plus
either of b1 or b2. However, in fact, these really estimate (b0+b12)
and (b1+b2). To understand this, consult any good book that
discusses
confounding with 2-level fractional factorial designs.
To do this in R, use "lm", as
fit <- lm(y~A+B, data.frame(y=..., A=..., B=..,)
hope this helps.
spencer graves
parrinel at med.unibs.it wrote:
Hello,
I am planning a study with the main point to evaluate the
interaction of two treatments,
but for ethical reasons one cell is empty, that with
patients receaving no treatment at all
Treatment B
+
-
Treatment A
+
a
b
-
c
-------
I am looking for functions in R to estimate the sample size
and/or to conduct the
analysis. I have just found an article from Byar in
Statistics in Medicine for a 2^3
incomplete factorial design, but I would like not to
discover again the wheel..
TIA
dr. Giovanni Parrinello
Section of Medical Statistics
Department of Biosciences
University of Brescia
25127 Viale Europa, 11
Brescia Italy
Tel: +390303717528
Fax: +390303701157
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