binMto {binMto}

Confidence intervals for many-to-one comparisons of proportions

Description

Approximate simultaneous confidence intervals for many-to-one comparisons of proportions. The add-4, add-2, Newcombes Hybrid Score interval for the difference of proportions can be calculated using either quantiles of the multivariate normal distributrion (Dunnett) standard normal quantiles (Bonferroni or unadjusted.)

Usage

## Default S3 method:
binMto(x, n, names = NULL,
 base = 1, conf.level = 0.95, alternative = "two.sided",
 method = "Add4", adj = "Dunnett", ...)

## S3 method for class 'formula'
binMto(formula, data, base=1, conf.level=0.95,
 alternative="two.sided", method="Add4", adj="Dunnett", ...)

Arguments

x

vector giving the number of success in the groups

n

vector giving the number of trials, i.e. the sample size of each group

names

(character-)vector specifying the names of groups given in x and n, ignored if formula and data.frame are used

formula

a formula specifying a response and treatment variable like: response~treatment; the response must consist of 0,1 (failure and success)

data

data.frame containing the response and treatment variable specified in formula

base

a numeric value specifying which group to be treated as control group

conf.level

confidence level

alternative

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

method

character string specifying the method of CI construction to used, one of: "Add4": adding-4-method (Agresti and Caffo, 2000), conservative, recommended for small sample sizes, "Add2": adding-2-method (Brown and Li, 2005),less conservative, recommended for one-sided limits, "NHS": Newcombes Hybrid Score method (Newcombe, 1998), "Wald": Wald method, not recommended, only for large sample sizes and not too extreme proportions.

adj

character string, specifying the adjustment for multiplicity, one of: "Dunnett": Recommended, using quantiles of the multivariate normal distribution adjusting for multiplicity and correlation between comparisons depending on sample size and estimated proportion (Piegorsch, 1991), "Bonf": Simple Bonferroni-adjustment, conseravtive for large number of comparisons, "Unadj": Unadjusted interval, i.e. each with local confidence level = conf.level

...

arguments to be passed to the methods binMto.formula and binMto.default

Details

All methods only asymptotically hold the nominal confidence level. Thus they can not be recommended if sample size is combined with extreme proportions of success (close to 0 or 1). Among the available methods Add-4 is most appropriate for small sample sizes, if conservative performance is acceptable.

Value

A list containing:

conf.int

a matrix containg estimates, lower and upper confidence limits

and further values specified in the function call, apply str() to the output for details

Author(s)

Frank Schaarschmidt

References

Schaarschmidt, F., Biesheuvel, E., Hothorn, L.A. (2009) Asymptotic simultaneous confidence intervals for many-to-one comparisons of binary proportions in randomized clinical trials, Journal of Biopharmaceutical Statistics 19(2):292-310.

Examples

# 1)Simultaneous CI for Dunnett contrasts for
# the example in Table 1 of Bretz F and Hothorn LA (2002):
#  Detecting dose-response using contrasts: asymptotic
#  power and sample size determination for binomial data.
#  Statistics in Medicine 21, 3325-3335.

binMto(x=c(9,19,21,21,24),
 n=c(20,43,42,42,41),
 names = c("Placebo", 0.125, 0.5, 0.75, 1) )

#########################################################

# 2) Berth-Jones, J., Todd, G., Hutchinson, P.E.,
# Thestrup-Pedersen, K., Vanhoutte, F.P. (2000):
# Treatment of Psoriasis with oral liarozole:
# a dose-ranging study.
# British Journal of Dermatology 143 (6), 1170-1176.

# Three doses of a compound (liarozole) were compared
# to a group treated with placebo. The primary variable
# was defined as the proportion of patients with an at
# least marked improvement of psoriasis symptoms. 
# A total of 139 patients were assigned to the 4 treatment
# groups, sample sizes were 34,35,36,34, for the Placebo,
# 50mg, 75mg, and 150mg treatments, respectively.
# The number of patients with marked improvement of
# symptoms was 2,6,4,13 in the 4 treatment groups.

# two-sided Add-4 95-percent confidence intervals:

binMto(x=c(2,6,4,13),
 n=c(34,35,36,34),
 names = c("Placebo","50mg","75mg","150mg") )