seq_williams: Williams cross-over design specification
In mjg211/xover: Design and analysis of cross-over clinical trials

Description Usage Arguments Details Value Author(s) References Examples

Specifies Williams cross-over designs.

1	seq_williams(D = 2, labels = 0:(D - 1), as_matrix = T, summary = T)

`D`	The number of treatments. Must be a single `numeric` integer greater than or equal to two. Defaults to `2`.
`labels`	A `vector` of labels for the treatments. Should be of `length` `D`, containing unique elements. Defaults to `0:(D - 1)`.
`as_matrix`	A `logical` variable indicating whether the design should be returned as a `matrix`, or a `tibble`. Defaults to `T`.
`summary`	A `logical` variable indicating whether a summary of the function's progress should be printed to the console. Defaults to `T`.

seq_williams() supports the specification of Williams designs. Sequences for any number of treatments (see D) are supported, for any chosen treatment labels (see labels). In addition, the designs can be returned in matrix or tibble form (see as_matrix).

Precisely, Williams designs are (generalized) Latin squares that are balanced for first order carryover effects. Generally, carryover balance is achieved with very few sequences. Ultimately, the (k,j)th element of the cross-over design matrix corresponds to the treatment a subject on the kth sequence would receive in the jth period.

Either a matrix if as_matrix = T (with rows corresponding to sequences and columns to periods), or a tibble if as_matrix = F (with rows corresponding to a particular period on a particular sequence). In either case, the returned object will have class xover_seq.

Based on code from the crossdes package by Oliver Sailer.

Jones B, Kenward MG (2014) Design and Analysis of Cross-Over Trials. Chapman and Hall: London, 3rd Edition.

Wakeling IN, MacFie HJH (1995) Designing consumer trials balanced for first and higher orders of carry-over effect when only a subset of k samples from t may be tested. Food Qual Prefer 6:299-308.

Williams EJ (1949) Experimental designs balanced for the estimation of residual effects of treatments. Aust J Sci Res Ser A 2:149-168.

# A Williams design for three treatments
williams        <- seq_williams(D = 3)
# Using different labels
williams_ABC    <- seq_williams(D = 3, labels = LETTERS[1:3])
# Returning in tibble form
williams_tibble <- seq_williams(D = 3, as_matrix = F)