Transform Odds Ratio to Relative Risk

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Description

Transform a given odds-ratio (OR) to the respective relative risk (RR).

Usage

1
ORToRelRisk(or, p0)

Arguments

or

numeric vector: OR (odds-ratio).

p0

numeric vector: incidence of the outcome of interest in the nonexposed group.

Details

The function transforms a given odds-ratio (OR) to the respective relative risk (RR). It can also be used to transform the limits of confidence intervals.

It uses the formula of Zhang and Yu (1998).

Value

relative risk.

Author(s)

Matthias Kohl <matthias.kohl@stamats.de>

References

Zhang, J. and Yu, K. F. (1998). What's the relative risk? A method of correcting the odds ratio in cohort studies of common outcomes. JAMA, 280(19):1690-1691.

Examples

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## We use data from Zhang and Yu (1998)

## single OR to RR
ORToRelRisk(14.1, 0.05)

## OR and 95% confidence interval
ORToRelRisk(c(14.1, 7.8, 27.5), 0.05)

## Logistic OR and 95% confidence interval
logisticOR <- rbind(c(14.1, 7.8, 27.5),
                    c(8.7, 5.5, 14.3),
                    c(27.4, 17.2, 45.8),
                    c(4.5, 2.7, 7.8),
                    c(0.25, 0.17, 0.37),
                    c(0.09, 0.05, 0.14))
colnames(logisticOR) <- c("OR", "2.5%", "97.5%")
rownames(logisticOR) <- c("7.4", "4.2", "3.0", "2.0", "0.37", "0.14")
logisticOR

## p0
p0 <- c(0.05, 0.12, 0.32, 0.27, 0.40, 0.40)

## Compute corrected RR
## helper function
ORToRelRisk.mat <- function(or, p0){
  res <- matrix(NA, nrow = nrow(or), ncol = ncol(or))
  for(i in seq_len(nrow(or)))
    res[i,] <- ORToRelRisk(or[i,], p0[i])
  dimnames(res) <- dimnames(or)
  res
}
RR <- ORToRelRisk.mat(logisticOR, p0)
round(RR, 2)

## Results are not completely identical to Zhang and Yu (1998)
## what probably is caused by the fact that the logistic OR values
## provided in the table are rounded and not true values.

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