soptdmaeA {soptdmaeA}

Sequential optimal designs for two-colour cDNA microarray experiments

Description

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

Usage

soptdmaeA(trt.N, blk.N, theta, nrep, strt, sary, des0, dtype, Optcrit = "", ...)


## Default S3 method:
soptdmaeA(trt.N, blk.N, theta, nrep, strt, sary, des0, dtype, Optcrit = "",...)
## S3 method for class 'soptdmaeA'
print(x, ...)
## S3 method for class 'soptdmaeA'
summary(object, ...)

Arguments

trt.N

integer, specifying number of treatments v of initial design, des0.

blk.N

integer, specifying number of arrays (blocks or columns) b of initial design, des0.

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.

strt

a non-negative integer, specifying number of added treatments/conditions to the initial design.

sary

a non-negative integer, specifying number of added arrays to the initial design.

des0

matrix, a 2 x blk.N or blk.N x 2 initial block or row-column design. The initial design must be treatment connected and the number of treatments and arrays should also coincides with trt.N and blk.N inserted by the user, if this conditions are not satisfied, the package will stop running with an error message.

dtype

character, specifying the design type. For block designs, dtype = "blkd" and for row-column deigns, dtype = "rcd".

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 or row-column designs, respectively.

x

the object to be printed.

object

an object of class "soptdmaeA".

...

not used.

Details

soptdmaeA computes sequential optimal or near-optimal block or row-column designs for the two-colour cDNA microarray experiments where the interest is in a comparison of all possible elementary treatment contrasts for a given initial optimal or near-optimal designs. The function computes sequential A-, MV-, D- and E-optimal or near optimal block or row-column designs via calling of four sub-functions seqAoptbrcd.maeA, seqMVoptbrcd.maeA, seqDoptbrcd.maeA, and seqEoptbrcd.maeA, respectively. These functions uses the array exchange algorithm of Debusho, Gemechu and Haines (2016). Thus, once the parametric combinations of interest are sated, these functions will first compute, randomly, a new connected initial design with a new number of arrays and, optionally, a new number of treatments. Then they 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. The candidate arrays are lists of possible arrays with different treatment combinations and their lists are dependent of the number of arrays and treatments added to the initial optimal or near-optimal design. For example, if only one treatment and one array are to be added to the initial optimal or near-optimal design, then the candidate arrays will be only those arrays that consists of a new treatment together with the old treatments in the initial optimal or near-optimal design with or without considering their position within the array for row-column or block designs, respectively.

The minimum value of trt.N and blk.N is 3 and trt.N should be less than or equal to blk.N - 1. Thus, the least initial design should be of a design with 3 number of treatments and number of arrays. The minimum number of sary and strt are 1 and 0, respectively, and sary should be greater than or equal to strt. The linear fixed effects model results for given parametric combinations and initial design are obtained by setting theta = 0.0.

nrep takes a value of greater than or equal to 1. However, to ensure optimality of the resultant design, for sary - strt > 0, the nrep should be greater than or equal to 10. In addition, as trt.N or blk.N or sary and/or strt or all of them increase, to ensure optimality of resultant design, it is advised to further increase the value of nrep up to greater than or equal to 50. However, it has to be noted that as trt.N or blk.N or nrep or all of them increase, computer time required to generate sequential optimal or near-optimal design increases.

Value

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

call

the method call.

v

number of treatments of obtained sequential design.

b

number of arrays of obtained sequential design.

theta

theta value.

nrep

number of replications of the optimization procedure.

strt

number of added treatments.

sary

number of added arrays.

Optcrit

optimality criteria.

optdes0

a 2 x blk.N initial optimal or near-optimal block or row-column design.

optcrtsv0

score value of the optimality criteria 'Optcrit' of the initial optimal or near-optimal block or row-column design 'optdes0'.

soptdesF

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

soptcrtsv

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

file_loc, file_loc2

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

equireplicate0

logical value indicating whether the initial optimal or near-optimal block or row-column design is equireplicate or not.

vtrtrep0

vector of treatment replication of the initial optimal or near-optimal block or row-column design.

equireplicate

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

vtrtrep

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

Cmat

the C-matrix or treatment information matrix of the obtained sequential optimal or near-optimal block or row-column design.

The output also includes graphical layouts of the initial and resultant sequential optimal or near-optimal block or row-column design. The new edges (arrays) and vertices (treatments) added to the initial design are coloured in red and brown, respectively, for identification purpose.

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

mmenusoptd.mae, fixparsoptd.mae

Examples

  
  ##To obtain sequential A-optimal or near-optimal block design for a given
  ##initial A-optimal or near-optimal block design, set
  
  trt.N <- 3  #Number of treatments
  blk.N <- 3  #Number of blocks
  theta <- 0  #theta value
  nrep <- 10  #Number of replications
  strt <- 2   #Number of added treatments
  sary <- 3   #Number of added arrays
  des0 <- rbind(1:3, c(2, 3, 1)) #Initial design
  dtype = "blkd" #Design type
  Optcrit <- "A"   #Optimality criteria

  seqAoptbd <- soptdmaeA(trt.N = 3, blk.N = 3, theta = 0, nrep = 10, 
                            strt = 2, sary = 3, des0, dtype = "blkd", Optcrit = "A")
  
  summary(seqAoptbd)

  ##To obtain sequential A-optimal or near-optimal row-column design for a given
  ##initial A-optimal or near-optimal row-column design des0 (stated above), set
  
  dtype = "rcd" #Design type

  seqAoptrcd <- soptdmaeA(trt.N = 3, blk.N = 3, theta = 0, nrep = 10, 
                            strt = 2, sary = 3, des0, dtype = "rcd", Optcrit = "A")
  
  summary(seqAoptrcd)