Balancing dataset for survival analysis

Question

So I'm using survival analysis to help identify customers at risk of churning. As of now, I've been using a hugely imbalanced dataset that consists of 99.5% of customers in the majority class (i.e. not churned) and 0.5% churned. To improve my model I've randomly undersampled the majority class such that the ratio between the minority and majority classes is only 1/3, which resulted in improvements when compared to using the full dataset.

However, in order to avoid removing data points which can be important, I would like to try oversampling techniques such as SMOTE, etc but I don't know how well this would suit survival models, because the duration (target variable) depends on a churn date/time which is the result of the difference of two variables in the dataset (date_client_churned + date_client_joined). Isn't generating new examples going to mess with the distribution of these two variables and as such produce erratic results? Has anybody dealt with this kind of imbalance in the dataset for survival analysis, and if so what was your approach? Is it really necessary to balance the dataset for survival analysis?

For reference, the survival models that I've used are: Cox Proportional Hazards, Random Survival Forests and Gradient Boosted Trees with Cox loss.

Just to clarify how I compute the duration variable: For time t = 0 I'm using the date a customer signs a contract with the company, given by t_born, and for the end date I'm using either a) the churn date t_churn if t_churn < t_study, where t_study represents the end of the study period (t_study=t_born+6, t_study=t_born+12, t_study=t_born+24 months); b) t_study otherwise. The duration column will then be given by the difference t_churn - t_born if t_churn < t_study; t_study - t_born otherwise.

Answer 1

I would like to try oversampling techniques such as SMOTE, etc but I don't know how well this would suit survival models...

As the comments on this question and many pages like this one demonstrate on this site, it's not clear that SMOTE or any type of biased over/under-sampling suits any type of model well. You then necessarily bias the intercept of the model and thus all probability estimates (unless you back-correct for the biased resampling). It's not clear that even relative log-odds or log-hazard estimates are improved, as you don't have any more cases than you started with.

Unbiased resampling by bootstrapping at the original sample size, however, is a very useful technique for validating and calibrating models, including survival models. See the validate() and calibrate() functions of Frank Harrell's rms package for example. Provided that you resample by case so that each set of t_born, t_churn and t_study is kept together, there is no problem.

I suspect that your apparent improvement with SMOTE would disappear if you evaluated performance of the modeling process by bootstrap resampling or (with tens of thousands of cases) repeated train/test splits.

Finally, it's not clear that a continuous-time survival model like a Cox model is the best choice for data like yours, where there is apparently a very large ratio of cases to observation times. A discrete-time model--a set of binary regressions, including time as a predictor, on appropriately structured data--could be preferable. In particular, it would naturally handle your large proportion of censored cases that might be considered "cured" in a survival model. At the least you should consider a cure model that combines survival over time with a binary "cured" outcome, as the types of model you have used implicitly assume that every case eventually experiences the event in question.