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
[[alternative HTML version deleted]]
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
>
>
>
> [[alternative HTML version deleted]]
>
>______________________________________________
>R-help at stat.math.ethz.ch mailing list
>https://www.stat.math.ethz.ch/mailman/listinfo/r-help
>PLEASE do read the posting guide!
http://www.R-project.org/posting-guide.html
>
>
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. > ________________________________________________________________ > > 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 > > > > > > > > [[alternative HTML version deleted]] > > > >______________________________________________ > >R-help at stat.math.ethz.ch mailing list > >https://www.stat.math.ethz.ch/mailman/listinfo/r-help > >PLEASE do read the posting guide!http://www.R-project.org/posting-guide.html> >______________________________________________ R-help at stat.math.ethz.ch mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Simon Fear Senior Statistician Syne qua non Ltd Tel: +44 (0) 1379 644449 Fax: +44 (0) 1379 644445 email: Simon.Fear at synequanon.com web: http://www.synequanon.com Number of attachments included with this message: 0 This message (and any associated files) is confidential and\...{{dropped}}