# How to compare right-censored discrete data?

I have 2 groups of 24 members, let's call the groups x and y. In some sense, x is "untreated" and y is "treated". For each member of x and y, there is a discrete value which refers to a time (1-10 days) at which an event occurred (a binary state change). The data is right-censored, meaning there is no data after 10 days. Each member of x has a value, something like [2, 4, 3, 3, 2, 2, 4, 2, 3, 5, etc.]. On the other hand, y is incomplete, looking something like: [9, 6, 5, NA, NA, 8, NA, 9, NA, 5, NA, NA, NA, etc.]

The NA value may mean to "the event might have occurred on some day after day 10" or "the event will never occur".

Two questions:

1. What test can I use to assess a difference in time-to-event for groups x and y, where time is a discrete variable?
2. How can I address the right-censored nature of group y?

This is a lot like survival analysis, but it's slightly different because in survival analysis everyone dies at some point (even if the death was right-censored). We hypothesized that the "treatment" would result in a group that looks a lot like y: time-to-event is much longer than x or does not occur at all.

The differences between the 2 groups are as extreme as presented here, but I still need to put a p-value on this to please the scientific reviewers. Also, in some cases, only 2-3 members of y have a value, and the other 21-22 members are NA.

I would appreciate some guidance on this one, thanks!

• Is you goal to model time-to-event or are you really interested in Pr(event ever occurs) and your just aware that some events happen after data collection is censored?
– Joe
Commented Mar 15, 2023 at 16:43