[R] data analysis for partial two-by-two factorial design

David Winsemius dwinsemius at comcast.net
Tue Mar 6 00:54:54 CET 2018 

> On Mar 5, 2018, at 3:04 PM, Bert Gunter <bgunter.4567 at gmail.com> wrote:
> 
> But of course the whole point of additivity is to decompose the combined effect as the sum of individual effects.

Agreed. Furthermore your encoding of the treatment assignments has the advantage that the default treatment contrast for A+B will have a statistical estimate associated with it. That was a deficiency of my encoding that Ding found problematic. I did have the incorrect notion that the encoding of Drug B in the single drug situation would have been NA and that the `lm`-function would produce nothing useful. Your setup had not occurred to me.

Best;
David.

> 
> "Mislead" is a subjective judgment, so no comment. The explanation I provided is standard. I used it for decades when I taught in industry.
> 
> Cheers,
> Bert
> 
> 
> 
> Bert Gunter
> 
> "The trouble with having an open mind is that people keep coming along and sticking things into it."
> -- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )
> 
> On Mon, Mar 5, 2018 at 3:00 PM, David Winsemius <dwinsemius at comcast.net> wrote:
> 
> > On Mar 5, 2018, at 2:27 PM, Bert Gunter <bgunter.4567 at gmail.com> wrote:
> >
> > David:
> >
> > I believe your response on SO is incorrect. This is a standard OFAT (one factor at a time) design, so that assuming additivity (no interactions), the effects of drugA and drugB can be determined via the model you rejected:
> 
> >> three groups, no drugA/no drugB, yes drugA/no drugB, yes drugA/yes drug B, omitting the fourth group of no drugA/yes drugB.
> 
> >
> > For example, if baseline control (no drugs) has a response of 0, drugA has an effect of 1, drugB has an effect of 2, and the effects are additive, with no noise we would have:
> >
> > > d <- data.frame(drugA = c("n","y","y"),drugB = c("n","n","y"))
> 
> d2 <- data.frame(trt = c("Baseline","DrugA_only","DrugA_drugB")
> >
> > > y <- c(0,1,3)
> >
> > And a straighforward inear model recovers the effects:
> >
> > > lm(y ~ drugA + drugB, data=d)
> >
> > Call:
> > lm(formula = y ~ drugA + drugB, data = d)
> >
> > Coefficients:
> > (Intercept)       drugAy       drugBy
> >   1.282e-16    1.000e+00    2.000e+00
> 
> I think the labeling above is rather to mislead since what is labeled drugB is actually A&B. I think the method I suggest is more likely to be interpreted correctly:
> 
> > d2 <- data.frame(trt = c("Baseline","DrugA_only","DrugA_drugB"))
> >  y <- c(0,1,3)
> > lm(y ~ trt, data=d2)
> 
> Call:
> lm(formula = y ~ trt, data = d2)
> 
> Coefficients:
>    (Intercept)  trtDrugA_drugB   trtDrugA_only
>      2.564e-16       3.000e+00       1.000e+00
> 
> --
> David.
> >
> > As usual, OFAT designs are blind to interactions, so that if they really exist, the interpretation as additive effects is incorrect.
> >
> > Cheers,
> > Bert
> >
> >
> > Bert Gunter
> >
> > "The trouble with having an open mind is that people keep coming along and sticking things into it."
> > -- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )
> >
> > On Mon, Mar 5, 2018 at 2:03 PM, David Winsemius <dwinsemius at comcast.net> wrote:
> >
> > > On Mar 5, 2018, at 8:52 AM, Ding, Yuan Chun <ycding at coh.org> wrote:
> > >
> > > Hi Bert,
> > >
> > > I am very sorry to bother you again.
> > >
> > > For the following question, as you suggested, I posted it in both Biostars website and stackexchange website, so far no reply.
> > >
> > > I really hope that you can do me a great favor to share your points about how to explain the coefficients for drug A and drug B if run anova model (response variable = drug A + drug B). is it different from running three separate T tests?
> > >
> > > Thank you so much!!
> > >
> > > Ding
> > >
> > > I need to analyze data generated from a partial two-by-two factorial design: two levels for drug A (yes, no), two levels for drug B (yes, no);  however, data points are available only for three groups, no drugA/no drugB, yes drugA/no drugB, yes drugA/yes drug B, omitting the fourth group of no drugA/yes drugB.  I think we can not investigate interaction between drug A and drug B, can I still run  model using R as usual:  response variable = drug A + drug B?  any suggestion is appreciated.
> >
> > Replied on CrossValidated where this would be on-topic.
> >
> > --
> > David,
> >
> > >
> > >
> > > From: Bert Gunter [mailto:bgunter.4567 at gmail.com]
> > > Sent: Friday, March 02, 2018 12:32 PM
> > > To: Ding, Yuan Chun
> > > Cc: r-help at r-project.org
> > > Subject: Re: [R] data analysis for partial two-by-two factorial design
> > >
> > > ________________________________
> > > [Attention: This email came from an external source. Do not open attachments or click on links from unknown senders or unexpected emails.]
> > > ________________________________
> > >
> > > This list provides help on R programming (see the posting guide linked below for details on what is/is not considered on topic), and generally avoids discussion of purely statistical issues, which is what your query appears to be. The simple answer is yes, you can fit the model as described,  but you clearly need the off topic discussion as to what it does or does not mean. For that, you might try the stats.stackexchange.com<http://stats.stackexchange.com> statistical site.
> > >
> > > Cheers,
> > > Bert
> > >
> > >
> > > Bert Gunter
> > >
> > > "The trouble with having an open mind is that people keep coming along and sticking things into it."
> > > -- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )
> > >
> > > On Fri, Mar 2, 2018 at 10:34 AM, Ding, Yuan Chun <ycding at coh.org<mailto:ycding at coh.org>> wrote:
> > > Dear R users,
> > >
> > > I need to analyze data generated from a partial two-by-two factorial design: two levels for drug A (yes, no), two levels for drug B (yes, no);  however, data points are available only for three groups, no drugA/no drugB, yes drugA/no drugB, yes drugA/yes drug B, omitting the fourth group of no drugA/yes drugB.  I think we can not investigate interaction between drug A and drug B, can I still run  model using R as usual:  response variable = drug A + drug B?  any suggestion is appreciated.
> > >
> > > Thank you very much!
> > >
> > > Yuan Chun Ding
> > >
> > >
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> > > ______________________________________________
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> > > and provide commented, minimal, self-contained, reproducible code.
> >
> > David Winsemius
> > Alameda, CA, USA
> >
> > 'Any technology distinguishable from magic is insufficiently advanced.'   -Gehm's Corollary to Clarke's Third Law
> >
> >
> >
> >
> >
> >
> 
> David Winsemius
> Alameda, CA, USA
> 
> 'Any technology distinguishable from magic is insufficiently advanced.'   -Gehm's Corollary to Clarke's Third Law
> 
> 
> 
> 
> 
> 

David Winsemius
Alameda, CA, USA

'Any technology distinguishable from magic is insufficiently advanced.'   -Gehm's Corollary to Clarke's Third Law

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