Description Usage Arguments Details Value Author(s) References See Also Examples

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).

1 2 3 4 5 6 7 8 9 |

`trt.N` |
integer, specifying number of treatments |

`blk.N` |
integer, specifying number of arrays (blocks or columns) |

`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 |

`dtype` |
character, specifying the design type. For block designs, |

`Optcrit` |
character, specifying the optimality criteria to be used. |

`x` |
the object to be printed. |

`object` |
an object of class |

`...` |
not used. |

`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.

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 |

`optcrtsv0` |
score value of the optimality criteria |

`soptdesF` |
a |

`soptcrtsv` |
score value of the optimality criteria |

`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`

.

Dibaba Bayisa Gemechu, Legesse Kassa Debusho, and Linda Haines

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.

`mmenusoptd.mae`

, `fixparsoptd.mae`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 | ```
##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)
``` |

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