I'm performing survival analysis on time to drop out of a certain program. However, the censoring of each case depends heavily on the length of the program. For example, some programs only last 3 months, while some can last up to 18 months. Programs of length 6, 9, and 12 months account for 80% of the observations. They are censored only if they do not drop out at the end of the program, therefore the time of censoring depends greatly on program length

I would like to ask for best practices on creating an appropriate estimation when censoring depends on one of the covariates. So far these are the options that I came up with

  1. Create one estimator for all observations, but it feels odd when a person joining a 3-month program would have a survival function of 18 months
  2. Create one estimator for each group of program length, but some groups only have a small number of observations, so I'm not sure if it can produce a good estimator. The large number of estimators can also be a problem
  3. Bin the programs by length, then create one estimator for each bin. This seems more sensible but I'm not sure if there's any caveat.

1 Answer 1


It sounds like you need to engage in some exploratory data analysis. The choice of model will depend on your understanding of the factors that contribute to dropout. If the rate of dropout isn't a function of program length per se (except that you can't drop out of a program after it's ended), you might be able to put all of the data together in a single model, even though some interpretations might seem odd (precisely because you can't drop out of a program after it's ended). That might work well if most dropouts are early in time regardless of program length. An alternative would be to express the time-to-dropout as a fraction of the program length. Including the program length as a covariate would be wise in either case.

This might also be handled with a cure model, where you explicitly model the failure to have an event along with the time-to-event for those who do.


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