multiCA (version 1.2.0)

power.multiCA.test: Power calculations for the multinomial Cochran-Armitage trend test

Description

Given the probabilities of outcomes, compute the power of the overall multinomial Cochran-Armitage trend test or determine the sample size to obtain a target power.

Usage

power.multiCA.test(
  N = NULL,
  power = NULL,
  pmatrix = NULL,
  p.ave = NULL,
  p.start = NULL,
  p.end = NULL,
  slopes = NULL,
  scores = 1:G,
  n.prop = rep(1, G),
  G = length(p.ave),
  sig.level = 0.05
)

Value

object of class "power.htest"

Arguments

N

integer, the total sample size of the study. If NULL then power needs to be specified.

power

target power. If NULL then N needs to be specified.

pmatrix

numeric matrix of hypothesized outcome probabilities in each group, with the outcomes as rows and ordered groups as columns. The columns should add up to 1.

p.ave

numeric vector of average probability of each outcome over the groups weighted by n.prop.

p.start, p.end

numeric vectors of the probability of each outcome for the first / last ordered group

slopes

numeric vector of the hypothesized slope of each outcome when regressed against the column scores with weights n.prop. The values should add up to zero, as the total probability is always 1 and has no trend.

scores

non-decreasing numeric vector of the same length as the number of ordered groups giving the trend test scores. Defaults to linearly increasing values.

n.prop

numeric vector describing relative sample sizes of the ordered groups. Will be normalized to sum to 1. Defaults to equal sample sizes.

G

integer, number of ordered groups

sig.level

significance level

Details

The sample size calculation depends only on p.ave - the weighted average probability of each outcome, and slopes - the weighted regression slope of each outcome.

The values of these two key inputs can be specified in three ways:

1. directly passing p.ave and slopes, or

2. specifying exactly two of the parameters p.ave, slopes, p.start, and p.end. In this case the full matrix of outcome probabilities will be inferred assuming linearity within each outcome.

3. specifying the full matrix of outcome probabilities pmatrix.

The calculation is based on approximating the distribution of the test statistic under the alternative with a non-central chi-squared distribution instead of the correct weighted mixture of multiple non-central chi-squares. This results in bias in the power away from 50 underestimated.

References

Szabo, A. (2018). Test for Trend With a Multinomial Outcome. The American Statistician, 73(4), 313–320.

See Also

power.CA.test for simpler (and more precise) power calculation with a binomial outcome

Examples

power.multiCA.test(power=0.8, p.start=c(0.1,0.2,0.3,0.4), p.end=c(0.4, 0.3, 0.2, 0.1), 
                     G=5, n.prop=c(3,2,1,2,3))

## Power of stroke study with 100 subjects per year and observed trends
data(stroke)
strk.mat <- xtabs(Freq ~ Type + Year, data=stroke)
power.multiCA.test(N=900, pmatrix=prop.table(strk.mat, margin=2))