[R] Incomplete Factorial design

[Spencer Graves]

      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
>>
>>
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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
>>>
>>>
>>>
>>>	[[alternative HTML version deleted]]
>>>
>>>______________________________________________
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>>>https://www.stat.math.ethz.ch/mailman/listinfo/r-help
>>>PLEASE do read the posting guide! 
>>>      
>>>
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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 
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