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:dwinsem...@comcast.net] Sent: Monday, March 05, 2018 3:55 PM To: Bert Gunter Cc: Ding, Yuan Chun; r-help@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.4...@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 <dwinsem...@comcast.net> > wrote: > > > On Mar 5, 2018, at 2:27 PM, Bert Gunter <bgunter.4...@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 <dwinsem...@comcast.net> > > wrote: > > > > > On Mar 5, 2018, at 8:52 AM, Ding, Yuan Chun <ycd...@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.4...@gmail.com] > > > Sent: Friday, March 02, 2018 12:32 PM > > > To: Ding, Yuan Chun > > > Cc: r-help@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 > > > <ycd...@coh.org<mailto:ycd...@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@r-project.org<mailto:R-help@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@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 ______________________________________________ R-help@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.
