[R] R Kaplan-Meier plotting quirks?

[Michael Rentz]

Hello. I apologize in advance for the VERY lengthy e-mail. I endeavor to 
include enough detail.

I have a question about survival curves I have been battling off and on for 
a few months. No one local seems to be able to help, so I turn here. The 
issue seems to either be how R calculates Kaplan-Meier Plots, or something 
with the underlying statistic itself that I am misunderstanding. Basically, 
longer survival times are yielding steeper drops in survival than a set of 
shorter survival times but with the same number of loss and retention 
events.

As a minor part of my research I have been comparing tag survival in marked 
wild rodents. I am comparing a standard ear tag with a relatively new 
technique. The newer tag clearly “wins” using survival tests, but the 
resultant Kaplan-Meier plot does not seem to make sense. Since I am dealing 
with a wild animal and only trapped a few days out of a month the data is 
fairly messy, with gaps in capture history that require assumptions of tag 
survival. An animal that is tagged and recaptured 2 days later with a tag 
and 30 days later without one could have an assumed tag retention of 2 days 
(minimum confirmed) or 30 days (maximum possible).

Both are significant with a survtest, but the K-M plots differ. A plot of 
minimum confirmed (overall harsher data, lots of 0 days and 1 or 2 days) 
yields a curve with a steep initial drop in “survival”, but then a 
leveling off and straight line thereafter at about 80% survival. Plotting 
the maximum possible dates (same number of losses/retention, but retention 
times are longer, the length to the next capture without a tag, typically 
25-30 days or more) does not show as steep of a drop in the first few days, 
but at about the point the minimum estimate levels off this one begins 
dropping steeply. 400 days out the plot with minimum possible estimates has 
tag survival of about 80%, whereas the plot with the same loss rate but 
longer assumed survival times shows only a 20% assumed survival at 400 
days. Complicating this of course is the fact that the great majority of 
the animals die before the tag is lost, survival of the rodents is on the 
order of months.

I really am not sure what is going on, unless somehow the high number of 
events in the first few days followed by few events thereafter leads to the 
assumption that after the initial few days survival of the tag is high. The 
plotting of maximum lengths has a more even distribution of events, rather 
than a clumping in the first few days, so I guess the model assumes 
relatively constant hazards? As an aside, a plot of the mean between the 
minimum and maximum almost mirrors the maximum plot. Adding five days to 
the minimum when the minimum plus 5 is less than the maximum returns a plot 
with a steeper initial drop, but then constant thereafter, mimicking the 
minimum plot, but at a lower final survival rate.

Basically, I am at a loss why surviving longer would *decrease* the 
survival rate???

My co-author wants to drop the K-M graph given the confusion, but I think 
it would be odd to publish a survival paper without one. I am not sure 
which graph to use? They say very different things, while the actual 
statistics do not differ that greatly.

I am more than happy to provide the data and code for anyone who would like 
to help if the above is not explanation enough. Thank you in advance.

Mike.


-- 
Michael S. Rentz
PhD Candidate, Conservation Biology
University of Minnesota
5122 Idlewild Street
Duluth, MN 55804
(218) 525-3299
rent0009 at umn.edu