I have got an extensive dataset of customers in a certain industry. I will build a survival model of churn on the customers. Some customers data back to 1990 and are still, as of 2020, customers in the dataset. The dataset was constructed in 2012. I have data on the date customers signed their contract, but I have only the data on those who are still in the dataset after 2012.

Hence my problem: The dataset doesn't contain data on customers who churned before 2012. This means, as I see it, that there is a bias in the data set for customers who stay in for a long time.


  1. Am I correct that this is a bias for the long-term customer?

  2. Is this called left-censoring/left-truncation/missing?

  3. Is there a way to deal with this bias? Some papers, for example.

  4. If there isn't an effect, can you covince me there isn't?

My question is similar (i.e. conceptually the same) as Kaplan-Meier estimates with missing data on non-survivors.

  • $\begingroup$ 1) I don't necessarily think it'd bias your model. They're a part of population. 2) Left - censoring occurs when a subject experiences your event of interest before the observation window starts. For that reason, observations prior to 2012 would be left - censored. 3) Refer to 1). $\endgroup$
    – ralph
    Jan 25 '20 at 12:10
  • $\begingroup$ @ralph Isn't this a sort of survivorship bias? The dataset will contain only long-term customers who didn't churn. You are missing a whole population of customers from 1990 to 2012 who left the population due to censoring or some event? $\endgroup$
    – epp
    Jan 27 '20 at 12:09
  • $\begingroup$ Exactly, I miss the whole population of customers between 1990 and 2012 who churned in that time. $\endgroup$
    – Cardinal
    Jan 27 '20 at 12:59
  • $\begingroup$ You don't even know how many customers ever signed up or cannot infer it from other records? If you know that, you could see if there would be reasonable ways of imputing data if rough estimates are OK. If you have not such data, I see no solution but removing all costumers that signed up before the dataset was constructed, and only estimate dropouts from then. $\endgroup$ Jan 30 '20 at 9:24
  • $\begingroup$ Ah ah. I agree with @StatsPlease. Your edits made your issue clear. $\endgroup$
    – ralph
    Jan 31 '20 at 8:35

Yes, you are correct that is survivor-ship bias in this data. This data is left truncated data because you only are observing customers who have made it to at least 2012, and hence you need to adjust for this.

Check out this paper https://www.tandfonline.com/doi/abs/10.1080/10485250500393222

or try to get this paper: A Note on the Product-Limit Estimator Under Right Censoring and Left Truncation Wei-Yann Tsai, Nicholas P. Jewell and Mei-Cheng Wang, Biometrika


Good luck!

  • $\begingroup$ This is helpful, but it borders on a link-only answer. Can you post full citations & summaries of these papers? $\endgroup$ Jan 31 '20 at 20:53
  • $\begingroup$ Yes, I can do this. I was just trying to answer the question about whether or not it was left truncation, and then also provide links as requested. I need to read these closer to succinctly summarize. Thanks for the feedback! $\endgroup$
    – ma83
    Feb 2 '20 at 2:05

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