# Current status data with range for exposure time

I am analyzing a dataset with current status data, meaning I know the total time of exposure for each patient and whether or not they had the event of interest during that exposure. I know the typical approach to dealing with this sort of data is interval censoring -- a patient with 5 months of exposure and an event would have interval $$[0,5]$$ for their event time, while a patient with 5 months of exposure and no event would have interval $$(5, \infty)$$.

A complication in my dataset is that I don't know the exposure times exactly. In particular, patients reported that they fell into a particular range of exposure lengths: 0-2 months, 2-4 months, 4-6 months, etc. So a few examples:

• If a patient reports 3-4 months of exposure and "yes" for having the outcome, their event time could have been 0.5 months or 3.5 months but not 4.5 months. Any event time in the range of $$[0,4]$$ months could have occurred.
• If a patient report 3-4 months of exposure and "no" for having the outcome, their event time could have been 4.5 months or 3.5 months but not 0.5 months. Any event time in the range of $$(3,\infty)$$ months could have occurred.

My question is how to perform survival analysis (e.g. estimate the survival function) in this setting. I was thinking of a few different approaches:

1. Assign the middle of the time interval as the exposure time and proceed with standard interval censoring analysis, or
2. For a patient selecting 3-4 months of exposure who had the event, use interval $$[0,4]$$, and for a patient selecting 3-4 months of exposure who did not have the event, use interval $$(3,\infty)$$.

While both seem like reasonable approaches, I wanted to check if there are standard ways to deal with this scenario.