power.multiCA.test {multiCA} | R Documentation |
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
)
Arguments
N |
integer, the total sample size of the study. If |
power |
target power. If |
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 |
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 |
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.
Value
object of class "power.htest"
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))