popower
Power and Sample Size for Ordinal Response
popower
computes the power for a twotailed 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).
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
i
th element specifies the probability that a patient will be in response leveli
, 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 eithern
orn1
andn2
. If you specifyn
,n1
andn2
are set ton/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
orposamsize
 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 12:22572271.
Julious SA, Campbell MJ (1996): Letter to the Editor. Stat in Med 15: 10651066. Shows accuracy of formula for binary response case.
See Also
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)