optbdmaeAT {optbdmaeAT}

Optimal block designs for two-colour cDNA microarray experiments

Description

Used to compute A-, MV-, D- or E-optimal or near-optimal block designs for two-colour cDNA microarray experiments under either the linear fixed effects model or the linear mixed effects model settings using either the array exchange or treatment exchange algorithms of Debusho, Gemechu and Haines (2016).

Usage

optbdmaeAT(trt.N, blk.N, theta, nrep, itr.cvrgval, Optcrit = "", Alg = "", ...)

## Default S3 method:
optbdmaeAT(trt.N, blk.N, theta, nrep, itr.cvrgval, Optcrit = "", Alg = "", ...)
## S3 method for class 'optbdmaeAT'
print(x, ...)
## S3 method for class 'optbdmaeAT'
summary(object, ...)

Arguments

trt.N

integer, specifying number of treatments, v.

blk.N

integer, specifying number of arrays, b.

theta

numeric, representing a function of the ratio of random array variance and random error variance. It takes any value between 0 and 1, inclusive.

nrep

integer, specifying number of replications of the optimization procedure.

itr.cvrgval

integer, specifying number of iterations required for convergence during the exchange procedure.

Optcrit

character, specifying the optimality criteria to be used. Optcrit takes the letter "A", "MV","D" and "E" for A-, MV-, D- and E-optimal or near-optimal block designs, respectively.

x

the object to be printed.

object

an object of class "optbdmaeAT".

Alg

character string used to specify the algorithm to be used. Possible values of Alg are Alg="trtE" for the treatment exchange algorithm and Alg="arrayE" for the array exchange algorithm: see 'Details'.

...

not used.

Details

optbdmaeAT computes optimal or near-optimal block design for the two-colour cDNA microarray experiments where the interest is in a comparison of all possible elementary treatment contrasts. The function computes A-, MV-, D- and E-optimal or near optimal block designs via calling of eight sub-functions Aoptbd.maeT, Aoptbd.maeA, MVoptbd.maeT, MVoptbd.maeA, Doptbd.maeT, Doptbd.maeA, Eoptbd.maeT and Eoptbd.maeA, respectively. Each function requires an initial connected block designs, generated using the function intcbd.mae.

The minimum value of trt.N and blk.N is 3 and trt.N should be less than or equal to blk.N - 1. The linear fixed effects model results for given trt.N and blk.N are obtained by setting theta = 0.0.

Alg specifies the exchange algorithm of Debusho, Gemechu and Haines (2016). If Alg = "trtE", the function optbdmaeAT perform the treatment exchange procedure through deletion and addition of treatments at a time and selects a design with best treatment exchange with respect to the optimality criterion value. If Alg = "arrayE", the function optbdmaeAT perform the array exchange procedure through deletion and addition of candidate arrays at a time and selects a design with best array exchange with respect to the optimality criterion value.

nrep takes a value of greater than or equal to 2. However, to ensure optimality of the resultant design, the nrep should be greater than or equal to 10 and in addition, as trt.N and blk.N increase, to ensure optimality of resultant design, it is advised to further increase the value of nrep up to greater than or equal to 100. However, it has to be noted that as trt.N or blk.N or nrep or all of them increses, computer time required to generate optimal or near-optimal block design increases.

itr.cvrgval number of iterations during exchange procedure. It takes a value between 2 and blk.N. It is used to speedup the computer search time by setting how long should the user should wait for the exchange process to obtain any different (if any) design than the one that was produced as the result of the preceding exchange of the current array in the initial design with candidate array. This is mainly effective if blk.N is very large. For example itr.cvrgval = 2, means the exchange procedure will jump to the next array test if the exchange of the two preceding arrays with candidate arrays results with the same efficient designs. The function will not give error message if the users set itr.cvrgval > blk.N and it will automatically set itr.cvrgval = blk.N. The smaller the itr.cvrgval means the faster the exchange procedure is, but this will reduce the chance of getting optimal block design and users are advised to set itr.cvrgval closer to blk.N.

Value

Returns the resultant A-, MV-, D- or E-optimal or near-optimal block design with its corresponding score value and parametric combination saved in excel file in a working directory. In addition, the function optbdmaeAT displays the graphical layout of the resultant optimal or near-optimal block designs. Specifically:

call

the method call.

v

number of treatments.

b

number of blocks

theta

theta value.

nrep

number of replications of the optimization procedure.

itr.cvrgval

number of iterations required for convergence during the exchange procedure.

Optcrit

optimality criteria.

Alg

algorithm used.

OptdesF

a 2 x blk.N obtained optimal or near-optimal block design.

Optcrtsv

score value of the optimality criteria 'Optcrit' of the resultant optimal or near-optimal block design 'OptdesF'.

file_loc, file_loc2

location where the summary of the resultant optimal or near-optimal block design is saved in .csv format.

equireplicate

logical value indicating whether the resultant optimal or near-optimal block design is equireplicate or not.

vtrtrep

vector of treatment replication of the resultant optimal or near-optimal block design.

Cmat

the C-matrix or treatment information matrix of the optimal or near-optimal block design.

The graphical layout of the resultant optimal or near-optimal block design.

NB: The function optbdmaeAT also saves the summary of the resultant optimal or near-optimal block design in .csv format in the working directory. Furthermore, the function reports only one final optimal or near-optimal block design, however, there is a possibility of more than one optimal or near-optimal block designs for a given parametric combination. The function graphoptbd.mae can be used to view and rearrange the graphical layout of the resultant optimal or near-optimal block design on tcltk window. Alternative to the function optbdmaeAT, a GUI tcltk window can be used to generate optimal or near-optimal block designs, see mmenubd.mae and fixparbd.mae.

Author(s)

Dibaba Bayisa Gemechu, Legesse Kassa Debusho, and Linda Haines

References

Debusho, L. K., Gemechu, D. B., and Haines, L. M. (2016). Algorithmic construction of optimal block designs for two-colour cDNA microarray experiments using the linear mixed model. Under review.

Gemechu D. B., Debusho L. K. and Haines L. M. (2014). A-optimal designs for two-colour cDNA microarray experiments using the linear mixed effects model. Peer-reviewed Proceedings of the Annual Conference of the South African Statistical Association for 2014 (SASA 2014), Rhodes University, Grahamstown, South Africa. pp 33-40, ISBN: 978-1-86822-659-7.

See Also

mmenubd.mae, fixparbd.mae, intcbd.mae

Examples

  
  ##To obtain the A-optimal or near-optimal block design using treatment exchange algorithm, set
  trt.N <- 3 #Number of treatments
  blk.N <- 3 #Number of blocks
  theta <- 0 #theta value
  nrep <- 5  #Number of replications
  itr.cvrgval <- 6 #Number of iterations required during the exchange procedure
  Optcrit <- "A"   #Optimality criteria
  Alg <- "trtE"    #Algorithm
  
  Aoptexample <- optbdmaeAT(trt.N = 3, blk.N = 3, theta = 0, nrep = 5, 
                            itr.cvrgval = 6, Optcrit = "A", Alg = "trtE")
  
  summary(Aoptexample)