seq_williams_bib: Carryover balanced cross-over design specification
In mjg211/xover: Design and analysis of cross-over clinical trials

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

Specifies carryover balanced cross-over designs.

1	seq_williams_bib(sequences, as_matrix = T, summary = T)

`sequences`	A balanced incomplete block design, of class `xover_seq`.
`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_bib() supports the specification of carryover balanced generalized Youden designs, based on any input balanced incomplete block (BIB) design (see sequences). In addition, the designs can be returned in matrix or tibble form (see as_matrix).

Precisely, Patterson (1951) combined BIB designs with Williams designs to get carryover balanced generalized Youden designs. For each sequence in the input BIB design, a Williams design is constructed using the treatments in that sequence. The sequences of the resulting Williams designs are then combined. 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.

Note that the resulting design will only be properly balanced if the input design is actually a BIB design. A warning message will be printed if this is not the case.

BIB designs can be generated using seq_bib.

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.

Patterson HD (1951) Change-over trials. J R Stat Soc B 13:256-271.

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.

seq_bib, seq_williams.

# Find a BIB design
bib                 <- seq_bib()
# Use this to construct a carryover balanced design
williams_bib        <- seq_williams_bib(bib)
# Returning in tibble form
williams_bib_tibble <- seq_williams_bib(bib, as_matrix = F)