bsamsize
you must specify
the fraction of observations in group 1. For power calculations, one
probability (
p1
) must be given, and either the other probability (
p2
),
an
odds.ratio
, or a
percent.reduction
must be given. For
bpower
or
bsamsize
, any or all of the arguments may be vectors, in which case they
return a vector of powers or sample sizes. All vector arguments must have
the same length.
Given
p1, p2
,
ballocation
uses the method of Brittain and Schlesselman
to compute the optimal fraction of observations to be placed in group 1
that either (1) minimize the variance of the difference in two proportions,
(2) minimize the variance of the ratio of the two proportions,
(3) minimize the variance of the log odds ratio, or
(4) maximize the power of the 2-tailed test for differences. For (4)
the total sample size must be given, or the fraction optimizing
the power is not returned. The fraction for (3) is one minus the fraction
for (1).
bpower.sim
estimates power by simulations, in minimal time. By using
bpower.sim
you can see that the formulas without any continuity correction
are quite accurate, and that the power of a continuity-corrected test
is significantly lower. That's why no continuity corrections are implemented
here.
bpower(p1, p2, odds.ratio, percent.reduction, n, n1, n2, alpha=0.05) bsamsize(p1, p2, fraction=.5, alpha=.05, power=.8) ballocation(p1, p2, n, alpha=.05) bpower.sim(p1, p2, odds.ratio, percent.reduction, n, n1, n2, alpha=0.05, nsim=10000)
ballocation
, the
fraction
which optimizes power will not be
returned.
bpower
, if
n
is given,
n1
and
n2
are set to
n/2
.
For
bpower.sim
, all arguments must be of length one.
bpower
, the power estimate; for
bsamsize
, a vector containing
the sample sizes in the two groups; for
ballocation
, a vector with
4 fractions of observations allocated to group 1, optimizing the four
criteria mentioned above. For
bpower.sim
, a vector with three
elements is returned, corresponding to the simulated power and its
lower and upper 0.95 confidence limits.
Fleiss JL, Tytun A, Ury HK (1980): A simple approximation for calculating sample sizes for comparing independent proportions. Biometrics 36:343–6.
Brittain E, Schlesselman JJ (1982): Optimal allocation for the comparison of proportions. Biometrics 38:1003–9.
Gordon I, Watson R (1996): The myth of continuity-corrected sample size formulae. Biometrics 52:71–6.
bpower(.1, odds.ratio=.9, n=1000, alpha=c(.01,.05)) bpower.sim(.1, odds.ratio=.9, n=1000) bsamsize(.1, .05, power=.95) ballocation(.1, .5, n=100) # Plot power vs. n for various odds ratios (base prob.=.1) n <- seq(10, 1000, by=10) OR <- seq(.2,.9,by=.1) plot(0, 0, xlim=range(n), ylim=c(0,1), xlab="n", ylab="Power", type="n") for(or in OR) { lines(n, bpower(.1, odds.ratio=or, n=n)) text(350, bpower(.1, odds.ratio=or, n=350)-.02, format(or)) } # Another way to plot the same curves, but letting labcurve do the # work, including labeling each curve at points of maximum separation pow <- lapply(OR, function(or,n)list(x=n,y=bpower(p1=.1,odds.ratio=or,n=n)), n=n) names(pow) <- format(OR) labcurve(pow, pl=TRUE, xlab='n', ylab='Power') # Contour graph for various probabilities of outcome in the control # group, fixing the odds ratio at .8 ([p2/(1-p2) / p1/(1-p1)] = .8) # n is varied also p1 <- seq(.01,.99,by=.01) n <- seq(100,5000,by=250) pow <- outer(p1, n, function(p1,n) bpower(p1, n=n, odds.ratio=.8)) # This forms a length(p1)*length(n) matrix of power estimates contour(p1, n, pow)