R help - Jun 2003 - COX PH models for event histories?

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).

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