# [R] Odds ratios in logistic regression models with interaction

Laviolette, Michael Michael.Laviolette at dhhs.nh.gov
Wed Aug 3 15:08:52 CEST 2016

```I'm trying to reproduce some results from Hosmer & Lemeshow's "Applied Logistic Regression" second edition, pp. 74-79. The objective is to estimate odds ratios for low weight births with interaction between mother's age and weight (dichotomized at 110 lb.). I can get the point estimates, but I can't find an interval option. Can anyone provide guidance on computing the confidence intervals? Thanks. -Mike L.

library(dplyr)
data(birthwt, package = "MASS")
birthwt <- birthwt %>%
mutate(low = factor(low, 0:1, c("Not low", "Low")),
lwd = cut(lwt, c(0, 110, Inf), right = FALSE,
labels = c("Less than 110", "At least 110")),
lwd = relevel(lwd, "At least 110"))

# p. 77, Table 3.16, Model 3
fit3.16 <- glm(low ~ lwd * age, binomial, birthwt)
# p. 78, interaction plot
visreg::visreg(fit3.16, "age", by = "lwd", xlab = "Age",
ylab = "Estimated logit")
# p. 78, covariance matrix
vcov(fit3.16)
# odds ratios for ages 15, 20, 25, 30
age0 <- seq(15, 30, 5)
df1 <- data.frame(lwd = "Less than 110", age = age0)
df2 <- data.frame(lwd = "At least 110", age = age0)
a1 <- predict(fit3.16, df1, se.fit = TRUE)
a2 <- predict(fit3.16, df2, se.fit = TRUE)
# p. 79, point estimates
exp(a1\$fit - a2\$fit)

# How to get CI's?
# Age    OR     (95% CI)
# ----------------------
# 15   1.04 (0.29, 3.79)
# 20   2.01 (0.91, 4.44)
# 25   3.90 (1.71, 8.88)
# 30   7.55 (1.95, 29.19)

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