# Time-to-event data with low censoring

I have data on individuals, consisting of an individual identifier column, starting date column and length date column. This indicates an individual being in financial distress for a specific period of days.

ID    STARTDATE    LENGTH_DAYS
1     2016-05-01   12
1     2016-03-12   7
2     2016-01-08   33
3     2016-06-01   24
3     2016-07-23   12
...   ...          ...


I have about 100.000 observations such as these and I'm aiming to predict the length of days in financial distress, when entering financial distress, based on some variables. As this is basically time-to-event data, I wanted to model this using a survival model. However, for 1000 to 2000 observations (the more recent observations) I do not yet know how may days the individual will be in financial distress. Which lets me doubt whether a survival model will be appropriate as only between 1% and 2% of my observations are censored. As far as I know, the presence of censoring is the main reason for using survival models.

Due to the low amount of censoring I thought maybe a panel data approach may therefore be a more suitable and easier approach. From what I've read implementing a survival model seems more involved than using standard regression techniques. Furthermore, if I discard the last month of data from my dataset (which is about 3%), less than 1% of the data is censored. Although discarding this data seems like bad practice, I'm wondering how much information is actually discarded as I have 18 months of data.

So my questions basically are:

• Is there a rule of thumb as to how much censoring needs to be present for time-to-event data to use survival models?
• If so, what would the downsides of a (panel data) approach using standard regression techniques be? (Except for discarding possible valuable information)

Survival analysis is not strictly about censoring, but rather modeling time to event data. Censoring is a very common feature of the data analyzed with survival models, and so the two topics are often paired together. But they are not equivalent. For example, if you are looking at time to event data, and all subjects experienced an event, you have survival data with no censoring. Conversely, consider measuring particles in the air: under a certain level, many instruments are unable to detect the particles, resulting in left censoring. But this is not survival data!

Generally speaking, censoring is bad, not good. Survival models are often designed to account for censoring (since it is so common with time to event data), but none that I know of require censoring. In fact, every model I know of would do better if all the data were uncensored rather than censored.

If you had zero censoring, you would have the freedom to use models that do not account for censoring, but nothing is wrong with survival models. As the professor who taught my survival analysis course put it "the best thing to do about censoring is to not have it". So don't worry if you don't have enough censoring; that's a good thing!

• Thanks, it does sound quite logical putting it that way. One more question, although I am not sure whether this is the correct place to ask it. When I am aiming to predict the length of the period at its start for data unknown to the model, would I only consider the values of my covariates at the start of periods in my "training set". That is, when I make a prediction at the start I only know the covariate values at that moment. It seems to me therefore I should only consider the covariate values at the start of a period for the estimation unless I want to update my prediction during a period. – Andrew Nov 15 '16 at 20:38
• As a rule of thumb, in a predictive model, you should only use the covariates that you will have access to when you are trying to make the prediction. – Cliff AB Nov 15 '16 at 20:40

If you are trying to compute a distribution of the duration of financial stress times, you can certainly employ censoring techniques. Seems as though "time-to-event" may not be as accurate as "duration of event"?