popower computes the power for a two-tailed two sample comparison
of ordinal outcomes under the proportional odds ordinal logistic
model. The power is the same as that of the Wilcoxon test but with
ties handled properly. posamsize computes the total sample size
needed to achieve a given power. Both functions compute the efficiency
of the design compared with a design in which the response variable
is continuous. print methods exist for both functions. Any of the
input arguments may be vectors, in which case a vector of powers or
sample sizes is returned. These functions use the methods of
Whitehead (1993).
pomodm is a function that assists in translating odds ratios to
differences in mean or median on the original scale.
popower(p, odds.ratio, n, n1, n2, alpha=0.05)
# S3 method for popower
print(x, …)
posamsize(p, odds.ratio, fraction=.5, alpha=0.05, power=0.8)
# S3 method for posamsize
print(x, …)
pomodm(x=NULL, p, odds.ratio=1)a vector of marginal cell probabilities which must add up to one.
The ith element specifies the probability that a patient will be
in response level i, averaged over the two treatment groups.
the odds ratio to be able to detect. It doesn't matter which group is in the numerator.
total sample size for popower. You must specify either n or
n1 and n2. If you specify n, n1 and
n2 are set to n/2.
for popower, the number of subjects in treatment group 1
for popower, the number of subjects in group 2
type I error
an object created by popower or posamsize, or a
vector of data values given to pomodm that corresponds to the
vector p of probabilities. If x is omitted for
pomodm, the odds.ratio will be applied and the new
vector of individual probabilities will be returned. Otherwise if
x is given to pomodm, a 2-vector with the mean and
median x after applying the odds ratio is returned.
for posamsize, the fraction of subjects that will be allocated to group 1
for posamsize, the desired power (default is 0.8)
unused
a list containing power and eff (relative efficiency) for popower,
or containing n and eff for posamsize.
Whitehead J (1993): Sample size calculations for ordered categorical data. Stat in Med 12:2257--2271.
Julious SA, Campbell MJ (1996): Letter to the Editor. Stat in Med 15: 1065--1066. Shows accuracy of formula for binary response case.
# NOT RUN {
# For a study of back pain (none, mild, moderate, severe) here are the
# expected proportions (averaged over 2 treatments) that will be in
# each of the 4 categories:
p <- c(.1,.2,.4,.3)
popower(p, 1.2, 1000) # OR=1.2, total n=1000
posamsize(p, 1.2)
popower(p, 1.2, 3148)
# Compare power to test for proportions for binary case,
# proportion of events in control group of 0.1
p <- 0.1; or <- 0.85; n <- 4000
popower(c(1 - p, p), or, n) # 0.338
bpower(p, odds.ratio=or, n=n) # 0.320
# Add more categories, starting with 0.1 in middle
p <- c(.8, .1, .1)
popower(p, or, n) # 0.543
p <- c(.7, .1, .1, .1)
popower(p, or, n) # 0.67
# Continuous scale with final level have prob. 0.1
p <- c(rep(1 / n, 0.9 * n), 0.1)
popower(p, or, n) # 0.843
# Compute the mean and median x after shifting the probability
# distribution by an odds ratio under the proportional odds model
x <- 1 : 5
p <- c(.05, .2, .2, .3, .25)
# For comparison make up a sample that looks like this
X <- rep(1 : 5, 20 * p)
c(mean=mean(X), median=median(X))
pomodm(x, p, odds.ratio=1) # still have to figure out the right median
pomodm(x, p, odds.ratio=0.5)
# }
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