optrcdmaeAT: Optimal row-column designs for two-colour cDNA microarray...

In optrcdmaeAT: Optimal Row-Column Designs for Two-Colour cDNA Microarray Experiments

Description

Used to compute A-, MV-, D- or E-optimal or near-optimal row-column 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) after adjusting to the row-column setup.

Usage

optrcdmaeAT(trt.N, col.N, theta, nrep, itr.cvrgval, Optcrit = "", Alg = "", ...)

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

Arguments

trt.N	integer, specifying number of treatments, v.
col.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 row-column designs, respectively.
x	the object to be printed.
object	an object of class "optrcdmaeAT".
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

optrcdmaeAT computes optimal or near-optimal row-column 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 row-column designs via calling of eight sub-functions Aoptrcd.maeT, Aoptrcd.maeA, MVoptrcd.maeT, MVoptrcd.maeA, Doptrcd.maeT, Doptrcd.maeA, Eoptrcd.maeT and Eoptrcd.maeA, respectively. Each function requires an initial connected row-column designs, generated using the function intcrcd.mae.

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

Alg specifies the array exchange and treatment exchange algorithm to be used that is adopted from Debusho, Gemechu and Haines (2016) after adjusting for the row-column designs setup. If Alg = "trtE", the function optrcdmaeAT 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 optrcdmaeAT 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 col.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 col.N or nrep or all of them increase, computer time required to generate optimal or near-optimal row-column design increases.

itr.cvrgval number of iterations during exchange procedure. It takes a value between 2 and col.N. It is used to speedup the computer search time by setting how long 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 col.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 > col.N and it will automatically set itr.cvrgval = col.N. The smaller the itr.cvrgval means the faster the exchange procedure is, but this will reduce the chance of getting optimal row-column design and users are advised to set itr.cvrgval closer to col.N.

Remark: After the treatment exchange or array exchange procedure is completed, a dye-flip procedure is added to the internal functions of optrcdmaeAT stated above to further insure the optimality of the resulting optimal or near-optimal row-column designs. Thus, the procedure will flip (interchange) the treatments position within each array (column) and select the optimal dye-flip based on the optimality criteria of interest. This step is effective only for the large number of arrays and is efficient if itr.cvgval < col.N and there is a jump in the array exchange or treatment exchange procedure as stated above under the detail description of itr.cvrgval.

Value

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

call	the method call.
v	number of treatments.
b	number of arrays.
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 col.N obtained optimal or near-optimal row-column design.
Optcrtsv	score value of the optimality criteria 'Optcrit' of the resultant optimal or near-optimal row-column design 'OptdesF'.
file_loc, file_loc2	location where the summary of the resultant optimal or near-optimal row-column design is saved in .csv format.
equireplicate	logical value indicating whether the resultant optimal or near-optimal row-column design is equireplicate or not.
vtrtrep	vector of treatment replication of the resultant optimal or near-optimal row-column design.
Cmat	the C-matrix or treatment information matrix of the optimal or near-optimal row-column design.

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

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

Author(s)

Legesse Kassa Debusho, Dibaba Bayisa Gemechu, and Linda Haines

References

Debusho, L. K., Gemechu, D. B., and Haines, L. M. (2016). Algorithmic construction of optimal row-column 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.

Gemechu, D. B., Debusho, L. K., and Haines, L. M. (2015). A-and D-optional row-column designs for two-colour cDNA microarray experiments using linear mixed effects models. South African Statistical Journal, 49, 153-168.

See Also

mmenurcd.mae, fixparrcd.mae, intcrcd.mae

Examples

  
  ##To obtain the A-optimal or near-optimal row-column design 
  ##using treatment exchange algorithm, set
  trt.N <- 3 #Number of treatments
  col.N <- 3 #Number of arrays
  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
  
  Aoptrcdes <- optrcdmaeAT(trt.N = 3, col.N = 3, theta = 0, nrep = 5, 
                            itr.cvrgval = 6, Optcrit = "A", Alg = "trtE")
  
  summary(Aoptrcdes)

optrcdmaeAT documentation built on May 1, 2019, 7:56 p.m.