williams: Construct sequences of a Williams design

Description

The function constructs the sequences of a Williams design via the algorithm given by Sheehe and Bross.

Usage

williams(ntmt = 4, tmts = NULL)

Value

Returns a character vector of the sequences.

Arguments

ntmt: Number of treatments. Must be an integer >1.
tmts: NULL or a vector of treatment codes.

Author

D. Labes

Details

A Williams design is a crossover design in which each subject receives each treatment. The design is balanced over periods. The design has additionally the further feature that every treatment follows every other treatment the same number of times. It is said that these designs are balanced for first order carry over effects.
For an even number of treatments the design is a Latin square. For an odd number the design is a combination of two Latin squares.

Although the balance to first order carry over effects is not absolutely necessary in well planned BE studies with sufficient washout the Williams designs were traditionally used in "3x6x3" "4x4" crossover studies.

The sequences are created originally within the ABC... notation. If tmts are given the sequences are returned based on these treatment codes.

References

Williams, E. J. (1949) "Experimental designs balanced for the estimation of residual effects of treatments" Australian J. of Scientific Research, Ser. A 2, 149-168.

Sheehe PR, Bross IDJ (1961) "Latin Squares to Balance Immediate Residual and Other Effects." Biometrics, 17, 405-414.

Jones B, Kenward MG (2003). "Design and Analysis of Cross-Over Trials" 2nd edition. Chapman & Hall, London.

Bing-Shun Wang, Xiao-Jin Wang, Li-Kun Gong (2009) "The Construction of a Williams Design and Randomization in Cross-Over Clinical Trials Using SAS" J. of Statistical Software, Volume 29, Code Snippet 1

Examples

Run this code

# Williams design for 4 treatments in ABC... notation
williams()
# The 6 sequences of the Williams design for 3 treatments
# same as sequences(design="3x6x3") except the ordering
williams(ntmt=3)

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