epi.interaction {epiR}R Documentation

Relative excess risk due to interaction in a case-control study

Description

Computes the relative excess risk due to interaction, the proportion of disease among those with both exposures attributable to interaction, and the synergy index for case-control data. Confidence interval calculations are based on those described by Hosmer and Lemeshow (1992).

Usage

epi.interaction(model, coeff, conf.level = 0.95)

Arguments

model an object of class glm.
coeff a vector specifying the position of the two coefficients of their interaction term in the model.
conf.level magnitude of the returned confidence interval. Must be a single number between 0 and 1.

Details

Interaction is defined as a departure from additivity of effects in epidemiologic studies. This function calculates three indices defined by Rothman (1998): (1) the relative excess risk due to interaction (RERI), (2) the proportion of disease among those with both exposures that is attributable to their interaction (AP[AB]), and (3) the synergy index (S). The synergy index measures the interaction between two risk factors expressed as the ratio of the relative excess risk for the combined effect of the risk factors and the sum of the relative excess risks for each separate effect of the two risk factors. In the absence of interaction both RERI and AP[AB] = 0 and S = 1.

These measures can be used to assess additive interaction when the odds ratio estimates the risk ratio. However, it is recognised that odds ratios from case-control studies that are not designed to directly estimate the risk or rate ratio (and only do so well when the outcome is rare).

Value

A list containing the following:

reri the relative excess risk due to interaction.
apab the proportion of disease among those with both exposures that is attributable to interaction.
S the synergy index.

References

Chen S-C, Wong R-H, Shiu L-J, Chiou M-C, Lee H (2008). Exposure to mosquito coil smoke may be a risk factor for lung cancer in Taiwan. Journal of Epidemiology 18: 19 - 25.

Hosmer DW, Lemeshow S (1992). Confidence interval estimation of interaction. Epidemiology 3: 452 - 456.

Kalilani L, Atashili J (2006). Measuring additive interaction using odds ratios. Epidemiologic Perspectives & Innovations doi:10.1186/1742-5573-3-5.

Rothman K, Greenland S (1998). Modern Epidemiology. Lippincott - Raven Philadelphia, USA.

Rothman K, Keller AZ (1972). The effect of joint exposure to alcohol and tabacco on risk of cancer of the mouth and pharynx. Journal of Chronic Diseases 23: 711 - 716.

Examples

## Data from Rothman and Keller (1972) evaluating the effect of joint exposure 
## to alcohol and tabacco on risk of cancer of the mouth and pharynx (cited in
## Hosmer and Lemeshow, 1992):

can <- c(rep(1, times = 231), rep(0, times = 178), rep(1, times = 11), 
   rep(0, times = 38))
smk <- c(rep(1, times = 225), rep(0, times = 6), rep(1, times = 166), 
   rep(0, times = 12), rep(1, times = 8), rep(0, times = 3), rep(1, times = 18), 
   rep(0, times = 20))
alc <- c(rep(1, times = 409), rep(0, times = 49))
dat <- as.data.frame(cbind(alc, smk, can))

## Table 2 of Hosmer and Lemeshow (1992):

dat.glm01 <- glm(can ~ alc + smk + alc:smk, family = binomial, data = dat)
summary(dat.glm01)

## Rothman suggested an alternative coding scheme to be employed for
## parameterising an interaction term. Using this approach, instead of using
## two risk factors and one product term to represent the interaction (as 
## above) the risk factors are combined into one variable with four levels:

## a.neg b.neg: 0 0 0
## a.pos b.neg: 1 0 0
## a.neg b.pos: 0 1 0
## a.pos b.pos: 0 0 1

dat$d <- rep(NA, times = nrow(dat))
dat$d[dat$alc == 0 & dat$smk == 0] <- 0
dat$d[dat$alc == 1 & dat$smk == 0] <- 1
dat$d[dat$alc == 0 & dat$smk == 1] <- 2
dat$d[dat$alc == 1 & dat$smk == 1] <- 3
dat$d <- factor(dat$d)

## Table 3 of Hosmer and Lemeshow (1992):

dat.glm02 <- glm(can ~ d, family = binomial, data = dat)
summary(dat.glm02)

epi.interaction(model = dat.glm02, coeff = c(2,3,4), conf.level = 0.95)

## Page 455 of Hosmer and Lemeshow (1992):
## RERI: 3.73 (95% CI -1.83 -- 9.31).
## AP[AB]: 0.41 (95% CI -0.07 -- 0.90).
## S: 1.87 (95% CI 0.54 -- 5.41).

[Package epiR version 0.9-15 Index]