Package 'WMWssp'

Sample size calculation for the Wilcoxon-Mann-Whitney test.

Description

This function calculates the sample size for a given power, type-I error rate and allocation rate t = n_1/N. Additionally, the actual achieved power can be simulated.

Usage

WMWssp(x, y, alpha = 0.05, power = 0.8, t = 1/2,
  simulation = FALSE, nsim = 10^4)

Arguments

x	prior information for the first group
y	prior information for the second group
alpha	two sided type I error rate
power	power
t	proportion of subjects in the first group; or use t = "min" to use optimal proportion rate
simulation	TRUE if a power simulation should be carried out
nsim	number of simulations for the power simulation

Value

Returns an object from class WMWssp containing

result	A dataframe with the results.
t	The allocation rate which was used.
alpha	The type-I error rate which was used.
simulation	The achieved power in a simulation.
power	The power which was used.
N	The sample size needed.

References

Brunner, E., Bathke A. C. and Konietschke, F. Rank- and Pseudo-Rank Procedures in Factorial Designs - Using R and SAS. Springer Verlag. to appear.

Happ, M., Bathke, A. C., & Brunner, E. (2019). Optimal Sample Size Planning for the Wilcoxon-Mann-Whitney-Test. Statistics in medicine, 38(3), 363-375.

Examples

# Prior information for the reference group
x <- c(315,375,356,374,412,418,445,403,431,410,391,475,379)
# generate data for treatment group based on a shift effect
y <- x - 20

# calculate sample size
ssp <- WMWssp(x, y, alpha = 0.05, power = 0.8, t = 1/2)
summary(ssp)

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Maximizing power for a given Type I error rate and prior information x and y

Description

This function maximizes the power of the Wilcoxon-Mann-Whitney test for a given total sample size N and type-I error rate with respect to the allocation rate t = n_1/N.

Usage

WMWssp_maximize(x, y, alpha = 0.05, N)

Arguments

x	a vector of prior information for the first group
y	a vector of prior information for the second group
alpha	Type I error rate
N	total sample size

Value

Returns an object from class WMWssp containing

result	A dataframe with the results.
t	The optimal allocation rate.
alpha	The type-I error rate which was used.
power	The maximized power.
N	The total sample size which was used.

References

Brunner, E., Bathke A. C. and Konietschke, F. Rank- and Pseudo-Rank Procedures in Factorial Designs - Using R and SAS. Springer Verlag. to appear.

Happ, M., Bathke, A. C., & Brunner, E. (2019). Optimal Sample Size Planning for the Wilcoxon-Mann-Whitney-Test. Statistics in medicine, 38(3), 363-375.

Examples

# Prior information for the reference group
x <- c(315,375,356,374,412,418,445,403,431,410,391,475,379)
# generate data for treatment group based on a shift effect
y <- x - 20

#
N <- 112

# calculate optimal t
ssp <- WMWssp_maximize(x, y, alpha = 0.05, N)
summary(ssp)

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Minimizing samplesize for a given Type I and II error rate and prior information x and y

Description

This function minimizes the sample size for a given power and type-I error rate with respect to the allocation rate t = n_1/N.

Usage

WMWssp_minimize(x, y, alpha = 0.05, power = 0.8, simulation = FALSE,
  nsim = 10^4)

Arguments

x	a vector of prior information for the first group
y	a vector of prior information for the second group
alpha	Type I error rate
power	Power to detect a relative effect based on the prior information
simulation	TRUE if a power simulation should be carried out
nsim	number of simulations for the power simulation

Value

Returns an object from class WMWssp containing

result	A dataframe with the results.
t	The optimal allocation rate for minimizing the sample size.
alpha	The type-I error rate which was used.
power	The power which was used.
N	The minimized sample size.

References

Brunner, E., Bathke A. C. and Konietschke, F. Rank- and Pseudo-Rank Procedures in Factorial Designs - Using R and SAS. Springer Verlag. to appear.

Happ, M., Bathke, A. C., & Brunner, E. (2019). Optimal Sample Size Planning for the Wilcoxon-Mann-Whitney-Test. Statistics in medicine, 38(3), 363-375.

Examples

# Prior information for the reference group
x <- c(315,375,356,374,412,418,445,403,431,410,391,475,379)
# generate data for treatment group based on a shift effect
y <- x - 20

# calculate optimal t
ssp <- WMWssp_minimize(x, y, alpha = 0.05, power = 0.8)
summary(ssp)

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Sample size calculation for the Wilcoxon-Mann-Whitney test using the Noether formula

Description

This function calculates the sample size for given type-I and type-II error probabilities using Noether's formula. If ties are present then prior information is needen.

Usage

WMWssp_noether(alpha, power, t, p, x = c(0), ties = FALSE)

Arguments

alpha	two sided type I error rate
power	power: detect a relative effect p at least with the specified power
t	proportion of subjects in the first group (between 0 and 1)
p	relative effect
x	prior information is only needed in case of ties
ties	TRUE if ties are possible (non continuous distribution), otherwise FALSE

Value

Returns an object from class WMWssp containing

result	A dataframe with the results.
t	The allocation rate which was used.
alpha	The type-I error rate which was used.
power	The power which was used.
N	The sample size needed.

References

Noether, G. E. (1987). Sample Size Determination for Some Common Nonparametric Tests. Journal of the American Statistical Association 85, 645.647.

Examples

# Prior information for the reference group
x <- c(315,375,356,374,412,418,445,403,431,410,391,475,379)
# generate data for treatment group based on a shift effect
y <- x - 20
# this data leads to a relative effect of p = 0.349

# calculate sampe size for a balanced design
ssp <- WMWssp_noether(alpha = 0.05, power = 0.8, t =1/2, p = 0.349)
summary(ssp)

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