```
## Same data available online:
## Hosmer and Lemeshow (2000) Applied Logistic Regression
## http://www.umass.edu/statdata/statdata/data/index.html
## description: http://www.umass.edu/statdata/statdata/data/icu.txt
## text format: http://www.umass.edu/statdata/statdata/data/icu.dat
## Excel format: http://www.umass.edu/statdata/statdata/data/icu.xls
icu <- read.table("http://www.umass.edu/statdata/statdata/data/icu.dat",
skip = 8, col.names = c("id","status","age","sex","race","service","cancer","renal","inf","cpr","sys","heart","prevad","type","frac","po2","ph","pco2","bic","cre","loc")
)
## Recode variables
icu <- within(icu, {
status <- factor(status, levels = 0:1, labels = c("Lived","Died"))
sex <- factor(sex, levels = 0:1, labels = c("Male","Female"))
race <- factor(race, levels = 1:3, labels = c("White","Black","Other"))
service <- factor(service, levels = 0:1, labels = c("Medical","Surgical"))
type <- factor(type, levels = 0:1, labels = c("Elective","Emergency"))
po2 <- factor(po2, levels = 0:1, labels = c(">60","<=60"))
ph <- factor(ph, levels = 0:1, labels = c(">=7.25","<7.25"))
pco2 <- factor(pco2, levels = 0:1, labels = c("<=45",">45"))
bic <- factor(bic, levels = 0:1, labels = c(">=18","<18"))
cre <- factor(cre, levels = 0:1, labels = c("<=2.0",">2.0"))
loc <- factor(loc, levels = 0:2, labels = c("No Coma or Deep Stupor","Deep Stupor","Coma"))
})
## Recode No-Yes variables
no.yes.variables <- c("cancer","renal","inf","cpr","prevad","frac")
icu[,no.yes.variables] <-
lapply(icu[,no.yes.variables],
function(var) {
var <- factor(var, levels = 0:1, labels = c("No","Yes"))
})
## summary(icu)
```

```
cdplot(status ~ age, icu)
```

```
age_quantiles <- quantile(icu$age, 0:5/5)
icu$age_cat <- cut(icu$age, breaks = age_quantiles, include.lowest = TRUE)
table(icu$age_cat)
```

```
[16,40] (40,57.6] (57.6,67] (67,75] (75,92]
41 39 43 44 33
```

If the age variable is used as a continuous variable, the effect of age is uniform across the range of the variable. If it is transformed into a categorical variable, it can have different effects depending on the position in the distribution of the variable.

**One effect for age variable**

```
## Fit age model (linearity assumption)
logit.age <- glm(status ~ age, icu, family = binomial)
coef(logit.age)
```

```
(Intercept) age
-3.05851 0.02754
```

**Three different effect for 1st vs 2nd, 1st vs 3rd, and 1st vs 4th age quantiles**

```
## Fit categorical age model
logit.age_cat <- glm(status ~ age_cat, icu, family = binomial)
coef(logit.age_cat)
```

```
(Intercept) age_cat(40,57.6] age_cat(57.6,67] age_cat(67,75] age_cat(75,92]
-2.539 1.184 1.210 1.440 1.558
```

```
## Extract coefficients for categorical age variable. Add 0 for reference level.
coef.age_cat <- c(0, coef(logit.age_cat)[-1])
coef.age_cat
```

```
age_cat(40,57.6] age_cat(57.6,67] age_cat(67,75] age_cat(75,92]
0.000 1.184 1.210 1.440 1.558
```

```
midValue <- function(x) {
x <- (x[-1] + x[-1 * length(x)]) / 2
names(x) <- NULL
x
}
## Get mid values of each quartile
midValue(age_quantiles)
```

```
[1] 28.0 48.8 62.3 71.0 83.5
```

```
## Plot coefficients against each mid values
plot(y = coef.age_cat, x = midValue(age_quantiles), type = "b")
```