On Thu, 6 Feb 2014, Joseph Shaw wrote: > Hi Gordon, > > Thanks for your response - I believe it has cleared everything up. > > So, for example, for experimental design (d), the simple saturated > direct design, we have the design matrix (1 0; 0 1; -1, -1). > > The first coefficient represents B-A, hence the first row (1 0); the > second coefficient represents C-B, hence the second row (0 1) and > because the third row represents the third array (A-C), we have: > > (-1 -1) = -(B-A)-(C-B) = -B+A-C+B = A-C > > which is what we wanted. Is this correct? Yes. > I have one last question. In practice, is this approach identical to a > 3x3 diagonal matrix (of ones) where each column represents and array > contrast? > > More specifically: > > 1 0 0 ---> B-A > 0 1 0 ---> C-B > 0 0 1 ---> A-C No, it is not equivalent. The three pairwise comparisons are inter-related, and this must be represented by the design matrix. Gordon > Joseph > > On Wed, Feb 5, 2014 at 11:28 PM, Gordon K Smyth <smyth at="" wehi.edu.au=""> wrote: >> Dear Joseph, >> >>> Date: Tue, 4 Feb 2014 18:11:50 -0800 (PST) >>> From: "Joseph Shaw [guest]" <guest at="" bioconductor.org=""> >>> To: bioconductor at r-project.org, josph.sh at gmail.com >>> Subject: [BioC] Design/Contrast Matrix for Two Channel Microarray >>> >>> >>> Hi all, >>> >>> Could somebody explain the process used in developing the design matrix >>> for two channel microarray experiments in Limma; in particular, those given >>> for each experiment in Figure 1 in the empirical Bayes paper >>> (http://www.statsci.org/smyth/pubs/ebayes.pdf). >>> >>> For single channel arrays, the design matrix seems to assume the form of >>> standard linear model design matrices; that is, 1 where an array treatment >>> is present and 0 otherwise. From here, the resulting model parameters can be >>> tested with the implementation of an appropriate contrast matrix (where, >>> typically, each contrast effect sums to zero). This does not appear to be >>> the case for two-channel experiments. >>> >>> In the above paper, the aforementioned experiments are given in Kerr and >>> Churchill arrow notation (where the arrow head points toward the RNA sample >>> labelled with red dye and the sample at the arrow base is labelled green). >>> >>> The experiments can be summarised as follows: >>> >>> (a) >>> Red Green >>> RNA1 RNA2 >>> >>> For this experiment, it seems to me that only parameter of interest (let's >>> call it mu1) is the response value (or mean of the response values if we >>> have more than one identical replicate); because the response is estimated >>> by the (mean of) the log2 fold change between red and green channels, in >>> this instance, the design "matrix" is simply (1); this becomes a column of 1 >>> values if there is more than one identical replicate. >>> >>> (b) >>> Red Green >>> RNA1 RNA2 >>> RNA2 RNA1 >>> >>> In this experiment, although there are two arrays, similarly to in >>> experiment (a), it seems that there is only one comparison of interest >>> (namely, the difference between RNA1 and RNA2); because the dyes in the >>> second array are inverted (relative to the first array in the experiment), >>> the ratio, too, is inverted. Inverting the term inside the logarithm will >>> yield a response which is the negative of the response from the first >>> replicate (i.e. log2(RNA2/RNA1) = -log2(RNA1/RNA2)); therefore, the second >>> replicate will yield the negative relative of the response from the first >>> replicate. For consistency, we must multiply the response value by -1. As a >>> result, we have the design matrix: (1, -1). >>> >>> I'm confused about how the design matrices are formed for experiments in >>> (c) and (d). >>> >>> In (c), RNA1 and RNA2 are compared through a common reference. >>> >>> (c) >>> Red: Green: >>> Ref RNA1 >>> RNA1 Ref >>> RNA2 Ref >>> >>> The design matrix is given by (-1 0; 1 0; 1 1) -- where ";" denotes the >>> end of the matrix row; the first coefficient estimates the difference >>> between the RNA1 and the reference sample, whilst the second coefficient >>> estimates the the difference between RNA1 and RNA2. >> >> >> It isn't easy to explain how this design matrix was derived, but it is easy >> to confirm that it works. Consider the third array for example, which >> estimates RNA2-Ref (Red minus Green). As you say, the first coef is >> >> coef1 = RNA1-Ref >> >> and the second is >> >> coef2 = RNA2-RNA1 >> >> The third array estimates >> >> RNA2-Ref = coef1 + coef2 >> >> Hence the two coefficients have to be c(1,1). >> >> You can easily compute these design matrices in limma. Here is the code for >> Figure 1(c) in the paper: >> >> > targets >> Cy3 Cy5 >> 1 A Ref >> 2 Ref A >> 3 Ref B >> > parameters >> AvsRef BvsA >> Ref -1 0 >> A 1 -1 >> B 0 1 >> > modelMatrix(targets,parameters=parameters) >> Found unique target names: >> A B Ref >> AvsRef BvsA >> 1 -1 0 >> 2 1 0 >> 3 1 1 >> >> Best wishes >> Gordon >> >>> Experiment (d) is a saturated direct design comparing three samples. >>> >>> (d) >>> Red Green >>> B A >>> A C >>> C B >>> >>> The design matrix is given by (1 0; 0 1; -1 -1); where the first >>> coefficient compares the difference between B - A and the second coefficient >>> compares the difference between C - B. >>> >>> Also, on page 39 of the Limma user guide >>> (http://www.bioconductor.org/packages/release/bioc/vignettes/limma /inst/doc/usersguide.pdf), >>> you can find a design and contrast matrix for a direct two-colour design. >>> The experiment compares CD4, CD8 and DN. I'm not really sure how this >>> design/contrast works. >>> >>> Explanation of the above structures would be greatly appreciated. >>> >>> Joseph >>> >>> -- output of sessionInfo(): >>> >>> -- >>> >>> -- >>> Sent via the guest posting facility at bioconductor.org. >> >> >> ______________________________________________________________________ >> The information in this email is confidential and intended solely for the >> addressee. >> You must not disclose, forward, print or use it without the permission of >> the sender. >> ______________________________________________________________________ > ______________________________________________________________________ The information in this email is confidential and intend...{{dropped:4}}