[R] Nesting in Cox proportional hazards survivorship analysis

From: Jessica M Pearce <j.pearce_at_utah.edu>
Date: Thu 01 Jun 2006 - 01:40:10 EST


My advisor and I have been working on some survivorship analyses in R and we are hoping to get some feedback on a particular issue involving nesting.  

We are interested in patterns of food discovery by ant species. Our observations consist of time to discovery by an ant for three different food types, each of two different sizes. These data were collected at 6 plots located in each of two states. Every plot is divided into 25 stations, at which the observations were made. In a repeated measures style design, all stations received all levels of food type and size over the course of 6 sampling periods. So multiple measurements are drawn from each station and site; however, each individual bait item is only discovered once. We also have vapor pressure deficit measurements (a measure that combines temperature and relative humidity) for each discovery time. Each state is being analyzed separately and we are using the Cox proportional hazards approach.  

It is clear from preliminary analysis that there is a strong influence of spatial heterogenity as evidenced by significant contributions of stations and plots to discovery. However, we are not necessarily interested in the details of this heterogenity and simply wish to control for it in examining the other factors of the model. Thus we employed what we think to be the appropriate nesting syntax in the model we are running (as gleaned from Venables and Ripley 1999, 3rd edition), with stations being nested within sites.  

To provide an example of the syntax, the full model with which we began is:  

TXa <- coxph(Surv(dt, status)~site/station+foodtype*foodsize+vpd, data=TXbait)  

This obviously generates a large number of terms, even as we work down to the reduced model.  

Is this syntax testing what we think it is testing, i.e. are we controlling for station effects in our results? Are there potential problems with our approach to the analysis of which we should be aware in our interpretation? We have looked at many sources of survivorship analysis literature and havenít seen this nesting issue discussed, besides briefly in Venables and Ripley. We recognize that this is an unusual use of survivorship analysis and would appreciate any insight provided.  

Jessica Pearce
Biology Department
University of Utah
Salt Lake City, UT

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