getDesignTwoMultinom {lrstat} | R Documentation |
Power and Sample Size for Difference in Two-Sample Multinomial Responses
Description
Obtains the power given sample size or obtains the sample size given power for difference in two-sample multinomial responses.
Usage
getDesignTwoMultinom(
beta = NA_real_,
n = NA_real_,
ncats = NA_integer_,
pi1 = NA_real_,
pi2 = NA_real_,
allocationRatioPlanned = 1,
rounding = TRUE,
alpha = 0.05
)
Arguments
beta |
The type II error. |
n |
The total sample size. |
ncats |
The number of categories of the multinomial response. |
pi1 |
The prevalence of each category for the treatment group.
Only need to specify the valued for the first |
pi2 |
The prevalence of each category for the control group.
Only need to specify the valued for the first |
allocationRatioPlanned |
Allocation ratio for the active treatment versus control. Defaults to 1 for equal randomization. |
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 two-arm multinomial response design is used to test whether the
prevalence of each category differs between two treatment arms.
Let \pi_{gi}
denote the prevalence of category i
in group g
, where g=1
for the treatment group and
g=2
for the control group.
The chi-square test statistic is given by
X^2 = \sum_{g=1}^{2} \sum_{i=1}^{C}
\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 both groups, and
n
is the total sample size.
Under the null hypothesis,
X^2
follows a chi-square distribution withC-1
degrees of freedom.Under the alternative hypothesis,
X^2
follows a non-central chi-square distribution with non-centrality parameter\lambda = n r (1-r) \sum_{i=1}^{C} \frac{(\pi_{1i} - \pi_{2i})^2} {r \pi_{1i} + (1-r)\pi_{2i}}
where
r
is the randomization probability for the active treatment.
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 designTwoMultinom
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. -
ncats
: The number of categories of the multinomial response. -
pi1
: The prevalence of each category for the treatment group. -
pi2
: The prevalence of each category for the control group. -
effectsize
: The effect size for the chi-square test. -
allocationRatioPlanned
: Allocation ratio for the active treatment versus control. -
rounding
: Whether to round up sample size.
Author(s)
Kaifeng Lu, kaifenglu@gmail.com
Examples
(design1 <- getDesignTwoMultinom(
beta = 0.1, ncats = 3, pi1 = c(0.3, 0.35),
pi2 = c(0.2, 0.3), alpha = 0.05))