I'm trying to use some form of survival analysis (e.g. accelerated failure time or proportional hazards) to study seed germination time. My data is interval censored (also called "grouped-time") and has a random effect (also called "frailty"). How can I do this, ideally in SAS?

My seeds were on petri dishes that were censused on day 1, 3, 5, 8, and 14. These are interval censored, with a seed that germinated on d8 really germinated between day 6 and day 8. PROC LIFEREG can handle interval censoring, but as far as i know, it doesn't handle random effects. Seeds on the same petri dish are not independent, so I need to be able to include the dish as a random effect.

Is there an approach that allows interval censoring as well as random effects? If so , how should I modify the SAS code below to include random effects? Can I do this in PROC NLMIXED? What is the best/easiest software to do this?

PROC LIFEREG DATA=survGeno2 plots=probplot;
TITLE "Interval censored AFT";
CLASS geno;
MODEL (start,fin)=geno;