R: Odds Ratio Estimation and Confidence Intervals

OddsRatio {DescTools}

R Documentation

Odds Ratio Estimation and Confidence Intervals

Description

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).

Usage

OddsRatio(x, y = NULL, conf.level = NA, method = c("wald", "mle", "midp"),
          interval = c(0, 1000), ...)

Arguments

`x`	a vector or a 2 x 2 numeric matrix, resp. table.
`y`	NULL (default) or a vector with compatible dimensions to `x`. If y is provided, `table(x, y, ...)` will be calculated.
`method`	method for calculating odds ratio and confidence intervals. Can be one out of "`wald`", "`mle`", "`midp`". Default is `"wald"` (not because it is the best, but because it is the most commonly used.)
`conf.level`	confidence level. Default is `NA`, meaning no confidence intervals will be reported.
`interval`	interval for the function `uniroot` that finds the odds ratio median-unbiased estimate and `midp` exact confidence interval.
`...`	further arguments are passed to the function `table`, allowing i.e. to set `useNA`. This refers only to the vector interface.

Details

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         n11

however, for odds ratios the following table is equivalent:

                    disease=1   disease=0
    exposed=1          n11         n10
    exposed=0          n01         n00

If 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.

Value

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

Author(s)

Andri Signorell <andri@signorell.net>, strongly based on code from Tomas Aragon, <aragon@berkeley.edu>

References

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

Examples

# 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, direction="column")

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))

[Package DescTools version 0.99.24 Index]