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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.

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First, with your experimental design for the underwater group you are estimating the cumulative survival from the beginning of the study up to the time of capture. That insight might give you a different, potentially simpler way to describe the survival of that group.

You can, however, accommodate left censoring in survival models. The Surv() function in the R survival package allows for specifying a censoring type of "left" for your underwater captures found to be dead, along with the default "right" for right censoring.

There is a potential problem with this approach, as censoring is assumed to be uninformative. In your situation, the censoring pattern is completely different for the underwater group and the other groups, which might violate that assumption. I haven't thought that through carefully.

Also, you might want to consider whether your time scale is sufficiently granular for a continuous-time survival analysis. If you checked once a day and the experiment lasted only a few days, you might need to consider interval censoring or discrete-time survival models. Interval censoring is tricky, and the survival package only supports it for parametric models (based on a particular functional form over time). There is an icenReg package available in R that was designed to handle interval censoring in other models like Cox models, but I have no personal experience with it.

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  • $\begingroup$ Thank you, I will look into this $\endgroup$ – DNelsen Oct 6 '20 at 17:51

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