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Package
February 17, 2019
Title Calculate Power and Sample Size with BetaPSS
Version 0.0.1
Description Calculate power and sample size(incomplete).
Depends R (>= 3.5.1)
License GPL (>= 2)
Encoding UTF-8
LazyData true
RoxygenNote 6.1.0
Imports betareg,
lmtest,
reshape,
ggplot2,
ggpubr,
Rcpp
Suggests knitr,
rmarkdown
VignetteBuilder knitr

R topics documented:
betapower . . .
betapower_plot
LFL . . . . . .
NH . . . . . . .
sample.size2 . .
samplesize_plot

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1

2

betapower

betapower

Find Power with Beta DBN

Description
Find the power for a given sample size when testing the null hypothesis that the means for the
control and treatment groups are equal against a two-sided alternative.
Usage
betapower(mu0, sd0, mu1.start, mu1.end, mu1.by,
ss.start, ss.end, ss.by, trials, seed, link.type="logit")
Arguments
mu0

the mean for the control group

sd0

the standard deviation for the control group

mu1.start

the starting value of mean for the treatment group under the alternative mu1

mu1.end

the ending value of mean for the treatment group under the alternative mu1

mu1.by

the step length of mean for the treatment group under the alternative mu1

ss.start

the starting value of sample size

ss.end

the ending value of sample size

ss.by

the step length of sample size

trials

the number of trials

seed

the seed used in the simulation

link.type

the type of link used in the beta regression. Default value is "logit", or you
can choose one or more of the following: "logit", "probit", "cloglog", "cauchit",
"log", "loglog", "all"

Details
betapower function allows you to control the number of trials in the simulation, the sample sizes
used, and the alternative means. You can fix the alternative and vary sample size to match a desired
power; You can fix the sample size and vary the alternative to see which will match a desired power;
You can vary both; Start with a small number of trials (say 100) to determine the rough range of
sample sizes or alternatives; Use a larger number of trials (say 1000) to get better estimates.
Value
Return a matrix with 7 to 12 columns:
power.of.GLM: link name
the power using regression method; it will return the power with every links if
you use link.type = "all" statement.
power.of.Wilcoxon.test
the power from Wilcoxon Rank sum test.
sample size

sample size.

mu1

the mean for the treatment group under the alternative.

betapower_plot

3

mu0

the mean for the control group.

sd0

the standard deviation for the control group.

trials

the number of trials.

Examples
betapower(0.56,0.255,.70,.75,.05,30,50, 20,40,610201501)
betapower(0.56,0.255,.60,.75,.05,30,50, 5,100,617201501,"all")
betapower(0.56,0.255,.70,.75,.05,30,50, 20,40,610201501,c("logit","loglog","log"))

betapower_plot

Plots of Beta power

Description
Generate several comparison plots of power.
Usage
betapower_plot(betapower_matrix,link.type)
Arguments
link.type

the type of link used in the beta regression. You can choose one or more of the
following: "logit", "probit", "cloglog", "cauchit", "log", "loglog", "all"

plot.type
the type of plot. see details.
betapower_matrix
a matrix obtained by the function betapower.(the formula was described as the
output formula in the function betapower)
Details
betapower_plot() returns different plots depends on plot.type
plot.type = 1: betapower_plot() returns graphs that plot power against mu1, where mu1 is the mean
for the treatment group under the alternative. The number of plots will vary depending on the number of link types selected with the last plot showing power based on Wilcoxon Rank Sum Test. The
first one or several plots show comparisons of power with different sample size, using GLM method
with one or several link types. The last plot shows a comparison of the power with different sample
size using Wilcoxon Rank Sum Test. Y-axis denotes power and X-axis denotes mu1, the mean for
the treatment group under the alternative.
plot.type = 2: betapower_plot() returns a number of plots equal to the number of sample sizes tested. Each plot compares power calculated with different link types and the Wilcoxon Rank Sum
Test. Y-axis denotes power and X-axis denotes mu1, the mean for the treatment group under the
alternative.
plot.type = 3: betapower_plot() returns a number of plots equal to the number of mu1 used in the
procedure. Each plot compares power calculated with different link types and the Wilcoxon Rank
Sum Test. Y-axis denotes power and X-axis denotes sample size.

4

LFL

Examples
BPmat <- betapower(0.56,0.255,.70,.75,.05,30,50, 20,40,610201501,"all")
betapower_plot(BPmat,link.type = "all",plot.type=1)
betapower_plot(BPmat,link.type = "all",plot.type=2)
betapower_plot(BPmat,link.type = "all",plot.type=3)
BPmat2 <- betapower(0.56,0.255,.560,.76,.05,30,45, 5,200,610201511,c("logit","loglog","log"))
betapower_plot(BPmat2,link.type = c("logit","loglog","log"),plot.type=1)
betapower_plot(BPmat2,link.type = c("logit","loglog","log"),plot.type=2)
betapower_plot(BPmat2,link.type = c("logit","loglog","log"),plot.type=3)

LFL

Check linearity assumption

Description
Check linearity assumption in a model using a given link function.
Usage
LFL(dsn,Y,X,nkat,link.type)
Arguments
dsn

data set name containing X and Y;

Y

outcome variable

X

continuous covariate

nkat

number of categories into which X should be divided (an even number)

link.type

link function to be used: link.type is coded as follows: "identity" = identity
link; "logit" = logit link; "probit" = probit link; "log" = log link; "clog-log" =
complementary log-log link; "log-log" = log-log link; "reciprocal" = reciprocal
link;

outlier

exclude outliers from the plot.

Value
Return a matrix with 6 columns:
X

intervals of continuous covariate.

Frequency

number of observations in each group.

mean

group means of outcome variable.

link

name of link function.

gmu

group means of outcome variable with link function.

midpt

median of continuous covariate in each group.

NH

5

Examples
Data.X <- runif(1000)
Data.Y <- exp(Data.X+1)+rnorm(1000,0,1)
Data <- data.frame(cbind(Data.X,Data.Y))
LFL(Data,"Data.Y","Data.X",20,4)
##Use NH data:
NH$quality_rating <- (scale(NH$quality_rating)/2+0.5)
LFL(dsn = NH,Y = "quality_rating", X = "RNHRD", nkat = 40, link.type = "logit", outlier = T)

NH

Nursing homes data on Nursing Home Compare site.

Description
These are the official datasets used on the Medicare.gov Nursing Home Compare Website provided
by the Centers for Medicare & Medicaid Services. These data allow you to compare the quality of
care at every Medicare and Medicaid-certified nursing home in the country, including over 15,000
nationwide. This data set only used 3 variables of original data.
Usage
data(NH)
Format
An object of data frame.
Source
Nursing homes data
Examples
data(NH)
summary(NH)

sample.size2

Find minimum sample size with Beta DBN

Description
Find minimum sample sizes with Beta DBN and given mu0,sd0,mu1 and target powers.
Usage
sample.size(mu0, sd0, mu1.start, mu1.end, mu1.by, power.start, power.end, power.by,
sig.level = 0.05, N = 100, accuracy = NuLL, seed = 1, link.type = "logit")

6

samplesize_plot

Arguments
mu0

the mean for the control group

sd0

the standard deviation for the control group

mu1.start

the starting value of mean for the treatment group under the alternative mu1

mu1.end

the ending value of mean for the treatment group under the alternative mu1

mu1.by

the step length of mean for the treatment group under the alternative mu1

power.start

the starting value of target power

power.end

the ending value of target power

power.by

the step length of target power

sig.level

significant level; default value is 0.05

N

the number of trials; default value is 100

accuracy

the accuracy of the result; must be integer

seed

the seed used in the simulation

link.type

link options include: "logit", "probit", "cloglog", "cauchit", "log", "loglog". Default link is "logit".

Details
The sample.size function allows you to control the number of trials in the simulation, the target
power, accuracy, and the alternative means. You can fix the alternative and vary power to match a
desired sample size; Use default values for the number of trials and accuracy for a quick view; Use
a larger number of trials (say 1000) and a smaller accuracy (say 1) to get better estimates.
Examples
sample.size2(mu0=0.56, sd0=0.255, mu1.start = 0.60,
power.start = 0.7, power.end = 0.9, power.by = 0.1)
sample.size2(mu0=0.56, sd0=0.255, mu1.start = 0.60,
power.start = 0.7, power.end = 0.9, power.by = 0.1,
sample.size2(mu0=0.56, sd0=0.255, mu1.start = 0.60,
power.start = 0.7, power.end = 0.9, power.by = 0.1,

samplesize_plot

mu1.end = 0.70, mu1.by = 0.05,
mu1.end =
link.type
mu1.end =
link.type

0.70, mu1.by = 0.05,
= c("logit","loglog","log"))
0.70, mu1.by = 0.05,
= "all")

Plots by mu1

Description
Generate the comparison plots using GLM method and Wilcoxon Rank Sum Test with different
mu1.
Usage
samplesize_plot(SS_matrix,link.type)

samplesize_plot

7

Arguments
link.type

the type of link used in the beta regression(or Wilcoxon Rank Sum Test). You
can choose one or more of the following: "logit", "probit", "cloglog", "cauchit",
"log", "loglog", "wilcoxon", "all"

SS_matrix

the matrix obtained by the function sample.size2.(the formula was described as
the output formula in the function sample.size2)

Details
samplesize_plot() returns a series of plots equal to the number of mu1 used in the procedure. Y-axis
denotes minimum sample size and X-axis denotes minimum power.
Examples
SSmat <- sample.size2(mu0=0.56, sd0=0.255, mu1.start = 0.60, mu1.end = 0.70, mu1.by = 0.05,
power.start = 0.7, power.end = 0.9, power.by = 0.1, link.type = "all")
samplesize_plot(SSmat, "all")
SSmat2 <- sample.size2(mu0=0.56, sd0=0.255, mu1.start = 0.60, mu1.end = 0.70, mu1.by = 0.05,
power.start = 0.7, power.end = 0.9, power.by = 0.1, link.type = c("logit","loglog","log"))
samplesize_plot(SSmat2,link.type = c("logit","loglog","log"))

Index
∗Topic datasets
NH, 5
betapower, 2
betapower_plot, 3
LFL, 4
NH, 5
sample.size2, 5
samplesize_plot, 6

8



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