R help - Mar 2018 - data analysis for partial two-by-two factorial design

But of course the whole point of additivity is to decompose the combined
effect as the sum of individual effects.

"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
> > >
> > >
> > >
---------------------------------------------------------------------
> > > -SECURITY/CONFIDENTIALITY WARNING-
> > > This message (and any attachments) are intended solely
> f...{{dropped:28}}
> > >
> > > ______________________________________________
> > > R-help at r-project.org<mailto:R-help at r-project.org>
mailing list -- To
> UNSUBSCRIBE and more, see
> > > https://stat.ethz.ch/mailman/listinfo/r-help
> > > PLEASE do read the posting guide http://www.R-project.org/
> posting-guide.html
> > > and provide commented, minimal, self-contained, reproducible
code.
> > >
> > >
> > >       [[alternative HTML version deleted]]
> > >
> > > ______________________________________________
> > > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more,
see
> > > https://stat.ethz.ch/mailman/listinfo/r-help
> > > PLEASE do read the posting guide http://www.R-project.org/
> posting-guide.html
> > > 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
>
>
>
>
>
>
	[[alternative HTML version deleted]]

> 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
> > >
> > >
> > >
---------------------------------------------------------------------
> > > -SECURITY/CONFIDENTIALITY WARNING-
> > > This message (and any attachments) are intended solely
f...{{dropped:28}}
> > >
> > > ______________________________________________
> > > R-help at r-project.org<mailto:R-help at r-project.org>
mailing list -- To UNSUBSCRIBE and more, see
> > > https://stat.ethz.ch/mailman/listinfo/r-help
> > > PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> > > and provide commented, minimal, self-contained, reproducible
code.
> > >
> > >
> > >       [[alternative HTML version deleted]]
> > >
> > > ______________________________________________
> > > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more,
see
> > > https://stat.ethz.ch/mailman/listinfo/r-help
> > > PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> > > 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

Thanks a lot, after reading this message, I think I got the advantage of
Bert's coding. Those two drugs indeed do not interact with each other, so
additive assumption is valid.

I learned a lot today. Thanks again.

Ding

-----Original Message-----
From: David Winsemius [mailto:dwinsemius at comcast.net] 
Sent: Monday, March 05, 2018 3:55 PM
To: Bert Gunter
Cc: Ding, Yuan Chun; r-help at r-project.org
Subject: Re: [R] data analysis for partial two-by-two factorial design

> 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
> > >
> > >
> > >
------------------------------------------------------------------
> > > --- -SECURITY/CONFIDENTIALITY WARNING- This message (and any 
> > > attachments) are intended solely f...{{dropped:28}}
> > >
> > > ______________________________________________
> > > R-help at r-project.org<mailto:R-help at r-project.org>
mailing list --
> > > To UNSUBSCRIBE and more, see 
> > > https://stat.ethz.ch/mailman/listinfo/r-help
> > > PLEASE do read the posting guide 
> > > http://www.R-project.org/posting-guide.html
> > > and provide commented, minimal, self-contained, reproducible
code.
> > >
> > >
> > >       [[alternative HTML version deleted]]
> > >
> > > ______________________________________________
> > > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more,
see
> > > https://stat.ethz.ch/mailman/listinfo/r-help
> > > PLEASE do read the posting guide 
> > > http://www.R-project.org/posting-guide.html
> > > 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