Baseline hazard function is the hazard function obtained when all covariates are set to zero

Question

I am trying to learn Cox proportional hazard model but I have hit a wall with the basehaz function.

Lets suppose for example I have some data that I want to use but there is a column such as BMI. The BMI has 3 levels: Underweight, normal weight and fat. How could one of these levels be set to zero?

In addition lets suppose I have a continuous variable such as IQ. Does that mean the model wants to take the base for the IQ to be 0?

Answer 1

1) There are different ways to include categorical variables into the analysis. The most popular and default in most packages is so called dummy coding where the first category is the "reference" category and the other are code 1 if the observation is from the category and 0 otherwise. Below is an example with R where "a" is the reference category and the columns x1b and x1c would enter the analysis. The coefficients for these variables would than indicate differences compared to category "a".

# create example data set
df <- data.frame(x1 = sample(letters[1:3], 6, replace = TRUE))
df
#>   x1
#> 1  b
#> 2  c
#> 3  a
#> 4  b
#> 5  a
#> 6  c
# dummy coding
cbind(df, model.matrix(~x1, df)[,-1])
#>   x1 x1b x1c
#> 1  b   1   0
#> 2  c   0   1
#> 3  a   0   0
#> 4  b   1   0
#> 5  a   0   0
#> 6  c   0   1

2) For the baseline hazard continuous variables have to be set to 0 as you suspect, which is why the baseline hazard often does not have a useful interpretation and not the focus of the analysis. What is done sometimes is to center the continuous variable. That way the baseline hazard corresponds to the mean value.

^{Created on 2019-06-08 by the reprex package (v0.3.0)}