getDesignUnorderedBinom {lrstat} | R Documentation |
Power and Sample Size for Unordered Multi-Sample Binomial Response
Description
Obtains the power given sample size or obtains the sample size given power for the chi-square test for unordered multi-sample binomial response.
Usage
getDesignUnorderedBinom(
beta = NA_real_,
n = NA_real_,
ngroups = NA_integer_,
pi = NA_real_,
allocationRatioPlanned = NA_integer_,
rounding = TRUE,
alpha = 0.05
)
Arguments
beta |
The type II error. |
n |
The total sample size. |
ngroups |
The number of treatment groups. |
pi |
The response probabilities for the treatment groups. |
allocationRatioPlanned |
Allocation ratio for the treatment groups. |
rounding |
Whether to round up sample size. Defaults to 1 for sample size rounding. |
alpha |
The two-sided significance level. Defaults to 0.05. |
Details
A multi-sample binomial response design is used to test whether the
response probabilities differ among multiple treatment arms.
Let \pi_{g}
denote the response probability in group
g = 1,\ldots,G
, where G
is the total number of
treatment groups.
The chi-square test statistic is given by
X^2 = \sum_{g=1}^{G} \sum_{i=1}^{2}
\frac{(n_{gi} - n_{g+}n_{+i}/n)^2}{n_{g+} n_{+i}/n}
where n_{gi}
is the number of subjects in category i
for group g
, n_{g+}
is the total number of subjects
in group g
, and n_{+i}
is the total number of subjects
in category i
across all groups, and
n
is the total sample size.
Let r_g
denote the randomization probability for group g
, and
define the weighted average response probability across all groups as
\bar{\pi} = \sum_{g=1}^{G} r_g \pi_g
Under the null hypothesis,
X^2
follows a chi-square distribution withG-1
degrees of freedom.Under the alternative hypothesis,
X^2
follows a non-central chi-square distribution with non-centrality parameter\lambda = n \sum_{g=1}^{G} \frac{r_g (\pi_{g} - \bar{\pi})^2} {\bar{\pi} (1-\bar{\pi})}
The sample size is chosen such that the power to reject the null
hypothesis is at least 1-\beta
for a given
significance level \alpha
.
Value
An S3 class designUnorderedBinom
object with the following
components:
-
power
: The power to reject the null hypothesis. -
alpha
: The two-sided significance level. -
n
: The maximum number of subjects. -
ngroups
: The number of treatment groups. -
pi
: The response probabilities for the treatment groups. -
effectsize
: The effect size for the chi-square test. -
allocationRatioPlanned
: Allocation ratio for the treatment groups. -
rounding
: Whether to round up sample size.
Author(s)
Kaifeng Lu, kaifenglu@gmail.com
Examples
(design1 <- getDesignUnorderedBinom(
beta = 0.1, ngroups = 3, pi = c(0.1, 0.25, 0.5), alpha = 0.05))