I have data from an experiment where we looked at the time-to-death of pseudoscorpions under three treatment conditions: control, heat, and submersion underwater. Both the control and heat groups were checked daily and those that survived were right-censored. However, the pseudoscorpions in the underwater group were unresponsive while submerged and would only become active again when they were removed from the water and allowed to dry. Therefore, we removed 10 individuals per day and checked how many of the 10 were dead. All individuals removed from the water on a given day were also removed from the study on that day i.e. we did not re-submerge individuals that were observed to be alive after they were removed from the water the first time. The underwater group is therefore left-censored. We have run Kaplan-Meier curves for all three groups and the underwater group has a much steeper curve and non-overlapping 95% confidence intervals compared to the control and heat groups.
Is there a way to further analyze all three groups in one model given that one level of the treatment is left-censored and the other two levels are both right-censored? Can a Cox regression be run on the left-censored group by itself to produce a hazard rate with 95% CI for the rate? I am a biologist so try to make your answer intelligible to a statistical novice.
Yes, there is a large literature, Here is a start: https://www.researchgate.net/search.Search.html?type=publication&query=random%20censoring%20in%20cox%20regression
Best, D. Booth
If you have Stata, the answer is yes. It even analyses data with both and interval censoring.
You do have to make assumptions about the distribution, of course!
In Stata you can perform a simultaneous right and left censoring.
For Poisson regression:
cpoisson outcome independent1 independent2 independent3, ll(?) ul(?)
For Linear regression:
tobit outcome independent1 independent2 independent3, ll(?) ul(?)
ll --> is the lower limit for left censor (in number)
ul --> is the upper for right censor (in number)
For cox regression I have never used, please check:
https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=rja&uact=8&ved=2ahUKEwiG3fXslJbsAhWjURUIHeBQA84QFjAAegQIAxAC&url=https%3A%2F%2Fwww.stata.com%2Fmanuals13%2Fststcox.pdf&usg=AOvVaw0A-01-pTCSCWOeRVWF37l1 (page 6)
https://www.stata.com/stata-news/news33-1/spotlight-stintreg/
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