designMA {daMA} | R Documentation

## DESIGN OF FACTORIAL MICROARRAY EXPERIMENTS

### Description

designMA computes efficient factorial microarray experimental designs for two-colour microarrays based on a list of user-defined design matrices, a matrix describing the experimental questions (contrasts), a vector to discern vectorial contrasts from contrasts given in matrix form and a design optimality criterion.

### Usage

    designMA(design.list, cmat, cinfo, type = c("d", "e", "t"), tol = 1e-06)

### Arguments

`design.list` | a named list of design matrices. Each design matrix should have nrow = number of arrays and ncol= number of experimental conditions. With p columns, the first two columns describe the dye labeling (green and red), the remaining columns describe the experimental conditions.
`cmat` | a matrix describing the experimental questions (contrasts) to be analysed in the experiment. The matrix can be composed of vectorial contrasts (a single row of the matrix) and of contrasts in matrix form (several rows of the matrix), e.g. an A times B interaction effect in a 3 times 2 design. All contrasts have to be combined into one matrix (using rbind for instance).
`cinfo` | a vector describing the grouping of the contrast matrix rows in vector or matrix form. E.g. if the design matrix contains three contrasts in vector form, cinfo = rep(1,3), if it contains two vectorial contratst and one as matrix with three rows, cinfo=c(1,1,3).
`type` | a quoted letter indicating the optimality criterion that shoul be used. "d" - determinant, "e" - eigenvalue, "t" - trace.
`tol` | A value indicating the tolerance for contrast estimability check.

### Details

The choice of the optimality criterion influences the design defined as best. We propose the trace criterion because of its straightforward interpretability. For a detailed description of optimality criteria cf. Pukelsheim, F. "Optimal Design of Experiments", New York 1993.

### Value

a list with the following components

`alleff` | a matrix giving the absolute efficiency values (cols) for each contrast (rows). NA if contrast is not estimatable.
`alleffrel` | a matrix giving the relative efficiency values (cols) for each contrast (rows). The values are obtained by dividing the absolute values by the by the maximal efficiency value for a given contrast. NA if contrast is not estimatable.
`alleffave` | a vector giving the average efficiency for each design over all contrasts.
`effdesign` | the name of the design with the highest alleffave value.
`df` | a vector with the degrees of freedom of the F-statistics obtained by the designs.

### Note

### Author(s)

Jobst Landgrebe (jlandgr1@gwdg.de) and Frank Bretz (bretz@bioinf.uni-hannover.de)

### References

Bretz, F and Landgrebe J and Brunner E (2003):"Design and analysis of two colour factorial microarray experiments", submitted. http://www.microarrays.med.uni-goettingen.de/

### See Also

### Examples

          ## Not run: designs.basic # look at typical basic designs
                    ## Not run: designs.composite  #look at comlpex composite designs
                    ## Not run:
    t.eff.3x2.B.AB <-  designMA(designs.composite,
                                                cmatB.AB,cinfoB.AB,type="t")# compute design efficiencies for
                                                                            # a \eqn{3 \times 2} factorial experiment
                                                                            # using 18 microarrays and asking for
                                                                            # the main effect B and the interaction effect \eqn{A \times B}

    ## End(Not run)
                    ## Not run:
    t.eff.3x2.all <-  designMA(designs.composite,
                                                        cmat,cinfo,type="t")

    ## End(Not run)                                                      #compute design efficiencies design for
                                                                            # a \eqn{3 \times 2} factorial
                                                                            # experiment using 18
                                                                            # microarrays and asking for
                                                                            # the the simple B
                                                                            # effects, the main effects
                                                                            # A, B and the interaction
                                                                            # effect \eqn{A  \times B}

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