OR: Odds ratio for binary regression models fit with 'glm'
In LogisticDx: Diagnostic Tests for Models with a Binomial Response

Description Usage Arguments Value Note See Also Examples

Odds ratio for binary regression models fit with glm

OR(x, ...)

## Default S3 method:
OR(x, ...)

## S3 method for class 'glm'
OR(x, ..., newdata = rep(1L, length(stats::coef(x))),
  ci = TRUE, alpha = 0.95, what = c("model", "all", "data"))

`x`	A numeric object containing probabilities P. I.e. the range of P must be 0 to 1. The odds ratio OR is given by: OR = P[i] / (1-P[i]) = odds[1] / odds[0] There is a method for regression models with `class(x)==glm` and `x$family$family == "binomial"`.
`...`	Not used.
`newdata`	A `vector` of new variables to use. There should be one value, in sequence, for each coefficient in the model. By default, values are calculated for a change in the value of the coefficient for the predictor from 0 to 1. For continuous predictors changes of > 1 unit may have more practical significance.
`ci`	If `ci=TRUE` (the default), include a confidence interval for P[i] and OR[i] in the returned values.
`alpha`	Used to cacluate the confidence interval, which is: CI = x +- Z[1-alpha].SD where the normal distribution Z = N(0,1) and SD is the standard deviation.
`what`	See Value below.

A data.table. Columns give the model, the value of the link function and the associated probability P[i] and odds ratio OR[i].

If ci=TRUE, will also give upper and lower bounds of the confidence intervals for these values.

Rows are determined by what:

`what="model"`	The value of the link function is given for the full model. If an intercept term is included, the value if given with and without the intercept.
`what="all"`	The value of the link function is given for each combination of coefficients in the model.
`what="data"`	The value of the link function is given for each set of predictors in the data with which the model was fit. This option will ignore the argument `newdata`.

In the model formulas, the intercept term is specified as 0 (absent) or 1 (present).
The variance of the values of the link function is:

Var = SUM(x[i]^2.var(B[i])) + SUM(2.x[i][x[j]].cov(B[i], B[j]))

where Var is the variance and cov is the covariance.

?stats::predict.glm

if(require("graphics")){
    plot(x <- seq(from=0.1, to=0.9, by=0.05), y=OR(x))}
## H&L 2nd ed. Table 1.3. Page 10.
data(ageChd)
summary(g1 <- glm(chd ~ age, data=ageChd, family=binomial))
OR(g1)
attributes(OR(g1))
## Table 1.4. Page 20.
stats::vcov(g1)
## Table 2.3. Page 38.
data(lbw)
summary(g1 <- glm(LOW ~ LWT + RACE, data=lbw, family=binomial))
## Table 2.4. Page 42.
vcov(g1)
ageChd$gr54 <- ageChd$age > 54
OR(glm(chd ~ gr54, data=ageChd, family=binomial))