binomRRci {MCPAN}

Simultaneous confidence intervals for ratios of independent binomial proportions

Description

Simultaneous asymptotic CI for contrasts of binomial proportions, assuming that standard normal approximation holds on the log scale. Confidence intervals for ratios of (weighted geometric means) of proportions are calculated based on differences of log-proportions, and normal approximation on the log-scale.

Usage

binomRRci(x,...)

## Default S3 method:
binomRRci(x, n, names=NULL,
 type="Dunnett", cmat=NULL,
 alternative="two.sided", conf.level=0.95,
 dist="MVN", ...)

## S3 method for class 'formula'
binomRRci(formula, data,
 type="Dunnett", cmat=NULL,
 alternative="two.sided", conf.level=0.95,
 dist="MVN",...)

## S3 method for class 'table'
binomRRci(x, type="Dunnett",
 cmat=NULL, alternative="two.sided",
 conf.level=0.95, dist="MVN",...)

## S3 method for class 'matrix'
binomRRci(x, type="Dunnett",
 cmat=NULL, alternative="two.sided",
 conf.level=0.95, dist="MVN",...)

Arguments

x

a numeric vector, giving the number of successes in I independent samples, or an object of class "table", representing the 2xk-table, or an object of class "matrix", representing the 2xk-table

n

a numeric vector, giving the number of trials (i.e. the sample size) in each of the I groups (only required if x is a numeric vector, ignored otherwise)

names

an optional character string, giving the names of the groups/ sample in x, n; if not specified the possible names of x are taken as group names (ignored if x is a table or matrix)

formula

a two-sided formula of the style 'response ~ treatment', where 'response' should be a categorical variable with two levels, while treatment should be a factor specifying the treatment levels

data

a data.frame, containing the variables specified in formula

type

a character string, giving the name of a contrast method, as defined in contrMat(multcomp); ignored if cmat is specified

cmat

a optional contrast matrix

alternative

a single character string, one of "two.sided", "less", "greater"

conf.level

a single numeric value, simultaneous confidence level

dist

a character string, "MVN" invokes multiplicity adjustment via the multivariate normal distribution, "N" invokes use of quantiles of the univariate normal distribution

...

arguments to be passed to binomest, currently only success labelling the event which should be considered as success

Details

The interval for the ratio of two independent proportions, described in section "Crude Methods using first-order variance estimation" in Gart and Nam (1988) are extended to multiple contrasts. Confidence intervals are constructed based on contrasts for differences of lp=log (x+0.5)/(n+0.5), using quantiles of the multivariate normal or normal approximation. Applying the exponential functions to the bounds results in intervals for the risk ratio. In case that 0 occur in both, the numerator and denominator of the ratio, the interval is expanded to [0,Inf], in case that only 0s numerator go to the numerator, the lower bound is expanded to 0, in case that only 0s go to the denominator, the upper bound is expanded to Inf.

See the examples for different usages.

Value

A object of class "binomRDci", a list containing:

conf.int

a matrix with 2 columns: lower and upper confidence bounds, and M rows

alternative

character string, as input

conf.level

single numeric value, as input

quantile

the quantile used to construct the confidence intervals

estimate

a matrix with 1 column: containing the estimates of the contrasts

x

the observed number of successes in the treatment groups

n

the number of trials in the treatment groups

p

the estimated proportions in the treatment groups

success

a character string labelling the event considered as success

names

the group names

method

a character string, specifying the method of interval construction

cmat

the contrast matrix used

Note

Note, that all implemented methods are approximate only. The coverage probability of the intervals might seriously deviate from the nominal level for small sample sizes and extreme success probabilities.

References

Gart, JJ and Nam,J-m (1988): Approximate interval estimation of the ratio of binomial parameters: a review and corrections for skewness. Biometrics 44, 323-338.

See Also

summary.binomRDci for the risk difference, summary.binomORci for the odds ratio, plot.sci for plotting

Examples

# In simple cases, counts of successes
# and number of trials can be just typed:

ntrials <- c(40,20,20,20)
xsuccesses <- c(1,2,2,4)
names(xsuccesses) <- LETTERS[1:4]
ex1D<-binomRRci(x=xsuccesses, n=ntrials,
 type="Dunnett")
ex1D

ex1W<-binomRRci(x=xsuccesses, n=ntrials,
 type="Williams", alternative="greater")
ex1W

# results can be plotted:
plot(ex1D, main="Comparisons to control group A")

# summary gives a more detailed print out:
summary(ex1W)

# if data are represented as dichotomous variable
# in a data.frame one can make use of table:


data(liarozole)

head(liarozole)

# here, it might be important to define which level of the
# variable 'Improved' is to be considered as success

binomRRci(Improved ~ Treatment, data=liarozole,
 type="Dunnett", success="y", base=4, alternative="greater")

# If data are available as a named kx2-contigency table:

tab<-table(liarozole)
tab

binomRRci(tab, type="Dunnett", success="y", base=4, alternative="greater")


# Performance for extreme cases:


binomRRci(x=c(0,0,20,5),n=c(20,20,20,20),names=c("A","B","C","D"),
 type="Dunnett", alternative="greater")