We simulate for time-to-event data assuming constant hazards and then investigate whether we can estimate the underlying parameters. Note that the binary variable X is essentially a coin toss and we have used a large variance for the normally distributed U.
You may have to install the required packages the first time you use them. You can install a package by install.packages("package_of_interest") for each package you require.
The assumed causal diagram is reproduced below:
For constant hazards, we can fit (i) Poisson regression, (ii) Cox regression and (iii) flexible parametric survival models.
It may be useful to investigate whether the hazard ratio for X is time-varying hazard ratio and the form for survival.
We now model by excluding the variable U. This variable could be excluded when it is not measured or perhaps when the variable is not considered to be a confounding variable – from the causal diagram, the two variables X and U are not correlated and are only connected through the time variable T.
Again, we suggest investigating whether the hazard ratio for X is time-varying.
What do you see from the time-varing hazard ratio? Is U a potential confounder for X?
We now simulate for rarer outcomes by changing the censoring distribution:
What do you observe?
We now simulate for less heterogeneity by changing the reducing the standard deviation for the random effect U from 3 to 1.
What do you observe?
As an alternative model class, we can fit accelerated failure time models with a smooth baseline survival function. We can use the rstpm2::aft function, which uses splines to model baseline survival. Using the baseline simulation, fit and interpret smooth accelerated failure time models: