Odds Ratio Estimation and Confidence Intervals
Calculates odds ratio by unconditional maximum likelihood estimation (wald),
conditional maximum likelihood estimation (mle) or median-unbiased estimation (midp).
Confidence intervals are calculated using normal approximation (wald) and exact methods
(midp, mle).
OddsRatio(x, conf.level = NULL, ...)
## S3 method for class 'glm'
OddsRatio(x, conf.level = NULL, digits = 3, use.profile = TRUE, ...)
## S3 method for class 'multinom'
OddsRatio(x, conf.level = NULL, digits = 3, ...)
## S3 method for class 'zeroinfl'
OddsRatio(x, conf.level = NULL, digits = 3, ...)
## Default S3 method:
OddsRatio(x, conf.level = NULL, y = NULL, method = c("wald", "mle", "midp"),
interval = c(0, 1000), ...)x |
a vector or a 2 x 2 numeric matrix, resp. table. |
y |
NULL (default) or a vector with compatible dimensions to |
digits |
the number of fixed digits to be used for printing the odds ratios. |
method |
method for calculating odds ratio and confidence intervals. Can be one out of
" |
conf.level |
confidence level. Default is |
interval |
interval for the function |
use.profile |
logical. Defines if profile approach should be used, which normally is a good choice. Calculating profile can however take ages for large datasets and not be necessary there. So we can fallback to normal confidence intervals. |
... |
further arguments are passed to the function |
If a 2 x 2 table is provided the following table structure is preferred:
disease=0 disease=1
exposed=0 (ref) n00 n01
exposed=1 n10 n11however, for odds ratios the following table is equivalent:
disease=1 disease=0
exposed=1 n11 n10
exposed=0 n01 n00If the table to be provided to this function is not in the
preferred form, the function Rev() can be used to "reverse" the table rows, resp.
-columns. Reversing columns or rows (but not both) will lead to the inverse of the odds ratio.
In case of zero entries, 0.5 will be added to the table.
a single numeric value if conf.level is set to NA
a numeric vector with 3 elements for estimate, lower and upper confidence interval if conf.level is provided
Andri Signorell <andri@signorell.net>, strongly based on code from Tomas Aragon, <aragon@berkeley.edu>
Kenneth J. Rothman and Sander Greenland (1998): Modern Epidemiology, Lippincott-Raven Publishers
Kenneth J. Rothman (2002): Epidemiology: An Introduction, Oxford University Press
Nicolas P. Jewell (2004): Statistics for Epidemiology, 1st Edition, 2004, Chapman & Hall, pp. 73-81
Agresti, Alan (2013) Categorical Data Analysis. NY: John Wiley and Sons, Chapt. 3.1.1
# Case-control study assessing whether exposure to tap water
# is associated with cryptosporidiosis among AIDS patients
tab <- matrix(c(2, 29, 35, 64, 12, 6), 3, 2, byrow=TRUE)
dimnames(tab) <- list("Tap water exposure" = c("Lowest", "Intermediate", "Highest"),
"Outcome" = c("Case", "Control"))
tab <- Rev(tab, margin=2)
OddsRatio(tab[1:2,])
OddsRatio(tab[c(1,3),])
OddsRatio(tab[1:2,], method="mle")
OddsRatio(tab[1:2,], method="midp")
OddsRatio(tab[1:2,], method="wald", conf.level=0.95)
# in case of zeros consider using glm for calculating OR
dp <- data.frame (a=c(20, 7, 0, 0), b=c(0, 0, 0, 12), t=c(1, 0, 1, 0))
fit <- glm(cbind(a, b) ~ t, data=dp, family=binomial)
exp(coef(fit))
# calculation of log oddsratios in a 2x2xk table
migraine <- xtabs(freq ~ .,
cbind(expand.grid(treatment=c("active","placebo"),
response=c("better","same"),
gender=c("female","male")),
freq=c(16,5,11,20,12,7,16,19))
)
log(apply(migraine, 3, OddsRatio))
# OddsRatio table for logistic regression models
r.glm <- glm(type ~ ., data=MASS::Pima.tr2, family=binomial)
OddsRatio(r.glm)
plot(OddsRatio(r.glm), xlim=c(0.5, 2), main="OddsRatio - glm", pch=NA,
lblcolor=hred, args.errbars=list(col=horange, pch=21, col.pch=hblue,
bg.pch=hyellow, cex.pch=1.5))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.