# [R] Incomplete Factorial design

Spencer Graves spencer.graves at pdf.com
Fri Feb 6 16:47:49 CET 2004

```      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:
>>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]]
>>>
>>>______________________________________________
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>>>https://www.stat.math.ethz.ch/mailman/listinfo/r-help
>>>
>>>
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>
>
>>
>>
>>
>>
>
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>
>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
>
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