getDesignOneMultinom: Power and Sample Size for One-Sample Multinomial Response

Description

Obtains the power given sample size or obtains the sample size given power for one-sample multinomial response.

Usage

getDesignOneMultinom(
  beta = NA_real_,
  n = NA_real_,
  ncats = NA_integer_,
  piH0 = NA_real_,
  pi = NA_real_,
  rounding = TRUE,
  alpha = 0.05
)

Value

An S3 class designOneMultinom 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.
piH0: The prevalence of each category under the null hypothesis.
pi: The prevalence of each category.
effectsize: The effect size for the chi-square test.
rounding: Whether to round up sample size.

Arguments

beta: The type II error.
n: The total sample size.
ncats: The number of categories of the multinomial response.
piH0: The prevalence of each category under the null hypothesis. Only need to provide the values for the first ncats-1 categories.
pi: The prevalence of each category. Only need to provide the values for the first ncats-1 categories.
rounding: Whether to round up sample size. Defaults to 1 for sample size rounding.
alpha: The two-sided significance level. Defaults to 0.05.

Author

Kaifeng Lu, kaifenglu@gmail.com

Details

A single-arm multinomial response design is used to test whether the prevalence of each category is different from the null hypothesis prevalence. The null hypothesis is that the prevalence of each category is equal to $\pi_{0i}$, while the alternative hypothesis is that the prevalence of each category is equal to $\pi_i$, for $i=1,\ldots,C$, where $C$ is the number of categories.

The sample size is calculated based on the chi-square test for multinomial response. The test statistic is given by $$X^2 = \sum_{i=1}^{C} \frac{(n_i - n\pi_{0i})^2}{n\pi_{0i}}$$ where $n_i$ is the number of subjects in category $i$, and $n$ is the total sample size.

Under the null hypothesis, $X^2$ follows a chi-square distribution with $C-1$ degrees of freedom.
Under the alternative hypothesis, $X^2$ follows a non-central chi-square distribution with non-centrality parameter $$\lambda = n \sum_{i=1}^{C} \frac{(\pi_i - \pi_{0i})^2}{\pi_{0i}}$$

The sample size is chosen such that the power to reject the null hypothesis is at least $1-\beta$ for a given significance level $\alpha$.

Examples

Run this code


(design1 <- getDesignOneMultinom(
  beta = 0.1, ncats = 3, piH0 = c(0.25, 0.25),
  pi = c(0.3, 0.4), alpha = 0.05))

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