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I have a transaction history of loans. Each row represents a monthly update/payment made on a loan, where the columns are loan ID, features like current principal, house value, days since the loan was started, and finally a boolean label indicating whether the load is prepaid (the survival analysis analogue of 'death' here) or not. So it's a right censored dataset. My goal is to predict when (if ever) a loan might be prepaid, given its current history.

My concern is that the dataset is just 2 years old, and so a model might not properly pick up on patterns that differentiate normally paid off loans and those that are paid off early. Since these loans are mortgages, the normally paid off ones would take 15 or 30 years. Is it worth trying to predict when a loan might get paid off given the constraints of my data? Might it be more tractable to just predict whether a loan will get paid off given its history?

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When you say the data set is just 2 years old, does that mean the follow-up is at most 2 years for any subject in the data set? Does it instead mean that there is much more follow-up for many subjects, but the data set was built starting 2 years ago?

If the former is true, i.e. the largest non-censored times are near 2 years, then a time-to-event regression could be performed using a parametric approach with the vast majority of the survival curve being extrapolated. For a binary regression the censored events would need to be accounted for with imputation using a missing data assumption. This type of analysis is doable, but would not inspire much confidence in the results and conclusions.

If the latter is true then the amount of extrapolation in a parametric time-to-event analysis would be minimal. Likewise, the amount of missing data to be imputed for a binary regression would be minimal, unless there are other sources of missing/censored data.

Here is a related thread on estimands, confounding, and missing data.

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  • $\begingroup$ All loans in the dataset started/have funding dates at most two years ago. Each row describes the current state after a monthly payment is made, or an update on the loan given the event of a prepayment). If I understand correctly, that would be the former scenario right? $\endgroup$
    – Brian Barry
    Commented Dec 6, 2021 at 16:02
  • $\begingroup$ Yes, it sounds like the former scenario I mentioned. You seem to have experience with loan repayments from other sources. You could make an assumption that historical data you have (with more follow-up per subject) is representative of the target population you are interested in (that has only 2 years of follow-up) and combine these data sources. This would have an effect similar to positing a missing data model and imputing the censoring times. Of course the data you choose to borrow from will impact the results and conclusions. $\endgroup$
    – Geoffrey Johnson
    Commented Dec 6, 2021 at 16:23
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Without access to your data (or a lot of expertise knowledge on this particular data) I don't think anyone can really answer your questions. In such a scenario its best to visualize your data and see if you can see any trends and patterns.

2 years seems like a very limited amount of time to fit a model for when loan prepayment would occur. In that scenario you are essentially extrapolating your model fit out potentially 28 years past your actual data.

My gut feeling (based on my personal experiences) is that the variables you listed will probably have little explanatory power for loan prepayment, even if you had all 30 years. I would think it would have a lot more to do with each individual's financial state.

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