# popower

0th

Percentile

##### Power and Sample Size for Ordinal Response

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).

Keywords
htest, category
##### Usage
popower(p, odds.ratio, n, n1, n2, alpha=0.05)
"print"(x, ...)
posamsize(p, odds.ratio, fraction=.5, alpha=0.05, power=0.8)
"print"(x, ...)
##### Arguments
p
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.
odds.ratio
the odds ratio to be able to detect. It doesn't matter which group is in the numerator.
n
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.
n1
for popower, the number of subjects in treatment group 1
n2
for popower, the number of subjects in group 2
alpha
type I error
x
an object created by popower or posamsize
fraction
for posamsize, the fraction of subjects that will be allocated to group 1
power
for posamsize, the desired power (default is 0.8)
...
unused
##### Value

a list containing power and eff (relative efficiency) for popower, or containing n and eff for posamsize.

##### References

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.

bpower, cpower

##### Aliases
• popower
• posamsize
• print.popower
• print.posamsize
##### Examples
#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)

Documentation reproduced from package Hmisc, version 4.0-2, License: GPL (>= 2)

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