# Using the tmerge() function to structure time-dependent covariates for survival analysis

The tmerge() function in the survival package is used to structure data to represent time-dependent variables in a survival analysis. This post shows a minimal example of how to use tmerge.
Author

Max Rohde

Published

March 31, 2022

Code

## Why do we need tmerge?

In survival analysis, we differentiate between time-independent covariates and time-dependent covariates. Time-independent covariates are constant over time, while time-dependent covariates can vary over time.

As an example, assume we are modeling time-to-death in years, with exposure to a chemical as our time-dependent covariate of interest. Assume that we can quantify the exposure as 0, 1, or 2. We will use this exposure and the sex of the subject as covariates in our model.

To represent time-dependent covariates, we need to have multiple rows for each subject, where each row represents a different value of the time dependent covariates.

Take for example a subject who started with exposure = 1. Then at 4 years, their exposure status changed to exposure = 0. Then at 7 years, their exposure status changed to exposure = 2. Then the subject died at 10 years (i.e., status = 1). We would need three rows to represent this subject, since there are 3 distinct time periods: 0-4, 4-7, and 7-10. The survival package uses the names tstart and tstop to denote the beginning and end of each time period. So when structuring data from time-dependent variables, the rows for this subject would look like this:

id tstart tstop exposure status
1 0 4 1 0
1 4 7 0 0
1 7 10 2 1

## Using tmerge

### Creating example data

First, we need our data in two data frames, one for the time-independent covariates and one for the time-dependent covariates.

Here’s some example data for the time-independent covariates. We have 3 subjects, and each row contains their id, sex, survival time, and whether or not they experience the event of interest (in this case, death). We use event = 1 to indicate death, and event = 0 to indicate censoring.

Code
df_time_ind <-
tibble(id = c(1,2,3),
sex = c("M","F","F"),
surv_time = c(5,10,15),
event = c(1,1,0))
id sex surv_time event
1 M 5 1
2 F 10 1
3 F 15 0

And here’s some example time-dependent data. Each subject has a record for their exposure status at time = 0, and another record whenever their exposure status changes. For example, in the data below, subject 1 has

• exposure status 0 from time 0 to 2
• exposure status 1 from time 2 to 4
• exposure status 2 from time 4 onwards
Code
df_time_dep <-
tibble(id = c(1,1,1,2,2,3),
time = c(0,2,4,0,7,0),
exposure = c(0,1,2,0,1,0))
id time exposure
1 0 0
1 2 1
1 4 2
2 0 0
2 7 1
3 0 0

We will use the tmerge function to turn these data frames in a single data frame to use in a time-dependent survival analysis. The tmerge function is used multiple times in the process of formatting data for time-dependent covariates.

First, we use tmerge with the independent variables. Note that we call tmerge with df_time_ind as both the data1 and data2 argument. We must also specify the id variable and the event variable using the syntax event(survival_time_variable, event_indicator_variable). Using the name event on the left of the expression is optional.

Code
df_time_ind <-
tmerge(data1=df_time_ind,
data2=df_time_ind,
id=id,
event=event(surv_time, event))

Now the df_time_ind data frame looks like this:

id sex surv_time event tstart tstop
1 M 5 1 0 5
2 F 10 1 0 10
3 F 15 0 0 15

Notice that the tstart, tstart, and event variables have been added.

Now to add the time-dependent variables, we call tmerge again, now with df_time_ind as the data1 argument and df_time_dep as the data2 argument. To specify the time-dependent exposure variable, we use the tdc function with the syntax time_dependent_variable = tdc(time, time_dependent_variable).

Code
df_final <-
tmerge(data1=df_time_ind,
data2=df_time_dep,
id=id,
exposure=tdc(time, exposure))

Below we have our completed dataset with properly structured time-dependent variables.

id sex surv_time event tstart tstop exposure
1 M 5 0 0 2 0
1 M 5 0 2 4 1
1 M 5 1 4 5 2
2 F 10 0 0 7 0
2 F 10 1 7 10 1
3 F 15 0 0 15 0

Finally, fitting a model with the survival package uses the general syntax Surv(tstart, tstop, event_indicator_variable) as shown below, where we fit a Cox proportional hazard model.

Code
coxph(Surv(tstart, tstop, event) ~ exposure, data=df_final)

## References

For more details, see this presentation and this report on further features of tmerge.