[R] COX PH models for event histories?

[Frank E Harrell Jr]

On Wed, 11 Jun 2003 19:54:11 +0200
Derek Eder <Derek.Eder at neuro.gu.se> wrote:

> This is a question about the use of the Cox proportional hazards model to analyze event histories.
> 
> I am looking at the responses of sympathetic nervous system activity to a stimulus.  The activity I observe is a burst that can only occur once per heart beat cycle (e.g., a binary count).  Typically bursts occur in 60-80% of the heart cycles * sensory stimuli can modify these burst probabilities.
> 
> I give 48 stimuli-trials at random intervals and count the number of bursts associated with the stimuli.  For example, a person with 75% burst probability at rest (e.g., 36/48) may have an stimulation induced increase to 87.5% (42 bursts in 48 trials).  There are 14 subjects in each of 3 different patient groups.  Simple enough.
> 
> But what if the stimulus reactions are modified over time?  The surprise of the stimulus (electric shock) soon wears off and the responses (e.g., increased burst probability) diminish over the trials.
> 
> Intuition tells me that the Cox proportional hazard model cast as in Anderson-Gill counting formulation is a useful tool too look for possible changes in burst occurrence probability across time (48 trials).  Can one assume that non-uniform burst probabilities would manifest in the cox.zph tests of proportionality of hazards?  I also plotted the Cox model along with a Cox model of a surrogate data set, formulated by randomizing the trial times (e.g., removing any temporal dependencies) Am I on the right track?   
> 
> 
> 
> Thank you
> 	
> 
> Derek Eder
> 
> 
> Oh yes, the relevance of this question to R ... ummmm.  Yes, what is the assignment operator in R? (Just kidding).
> 
Derek- This avoids answering your question but in problems like this I have found pooled logistic regression can be easier to use and provide more easily interpretable predictions and their confidence intervals.  I have used cluster bootstrap variance estimators in this context to adjust for intra-subject correlations.  See 

@ARTICLE{dag90rel,
  author = {{D'Agostino}, Ralph B. and Lee, M. L. and Belanger, A. J. and
           Cupples, L. A.},
  year = 1990,
  title = {Relation of pooled logistic regression to time dependent {Cox}
          regression analysis: {The} {Framingham} {Heart} {Study}},
  journal = Statistics in Medicine,
  volume = 9,
  pages = {1501-1515},
  annote = {time-dependent covariable; repeated measures logistic
  model; person-years logistic model}
}



---
Frank E Harrell Jr              Prof. of Biostatistics & Statistics
Div. of Biostatistics & Epidem. Dept. of Health Evaluation Sciences
U. Virginia School of Medicine  http://hesweb1.med.virginia.edu/biostat