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.
Am I correct that this is a bias for the long-term customer?
Is this called left-censoring/left-truncation/missing?
Is there a way to deal with this bias? Some papers, for example.
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.