# How to analyse categorical data (0/1) with structural zeros?

I have a categorical dependent variable (emerged/not emerged) and two predictors 1) treatment (continuous time, 28 to 35h) and 2) group (test/control). I want to know if test group emerges earlier than control group. I have a n=20 in each group+treatment, but I get structural zeros as control group never emerges before 32h (see data below). Thus I apparently cant use a simple logistic regression directly to compare my two groups.

Here is the data, values are %emergence (calculated) :

Treatment(h)___28___29___30___31___32___33___34___35 Control________0____0____0____0___59___70___100__100 Test__________50___70___90__100__100__100___100__100

Anybody can suggest a method to make this work? Note that I'm prety green in stats, I would appreciate a few details with the suggestions! :)

• I don't understand. What is the problem you face? I do not see why the zeroes are an issue in a logistic regression framework.
– mkt
Commented Jul 5, 2017 at 13:47
• Well, I read that one of the conditions for the logistic regression to produce correct estimates is that it shouldn't have cells with 0 events. I may be wrong though...? Commented Jul 5, 2017 at 13:58
• I don't really understand that objection. The logistic regression will estimate the probability of emergence as a function of time here. That probability will be close to zero till the 31-32 hour time period. Try it out.
– mkt
Commented Jul 5, 2017 at 14:07
• You don't need to calculate an odds ratio at all, since you have a continuous variable here. You can simply calculate the probability of emergence as a function of time in control and in test groups.
– mkt
Commented Jul 5, 2017 at 14:22
• If your only question is did group A emerge before group B, then it shouldn't be too difficult to construct a randomisation test for this.
– mkt
Commented Jul 5, 2017 at 14:38