st: R: Negative binomial regression with exposure and predictors correlated

["Carlo Lazzaro" <carlo.lazzaro@tin.it>]

Paul wrote:

"If correct, it would appear the drug is doing harm!"

For sure Paul has already ruled out a possible explanation (out of
statistical technicalities)for this strange "more prescribing, more hospital
admissions" result, that is the new treatment-induced adverse effects
requiring hospitalization. 

Kind Regards,
Carlo
-----Messaggio originale-----
Da: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] Per conto di Seed, Paul
Inviato: martedì 31 agosto 2010 13.42
A: statalist@hsphsun2.harvard.edu
Oggetto: st: Negative binomial regression with exposure and predictors
correlated 

Dear Statalist, 

I am struggling with a rather tricky modelling problem & would greatly
appreciate any thoughts.

I wish to know whether the introduction of a new treatment in Primary Care
can be linked to a fall in Hospital admissions.  However, all my data is at
the level of the practice, not the patient or patient group.  I therefore
use negative binomial regression, with the number of patients as the
exposure.

The main predictor is the rate of prescribing, estimated as the total cost
of prescriptions for the drug of interest, divided by number of patients in
each practice.  After correcting for age, gender & other drugs used, I find
a strong paradoxical effect of more prescribing associated with more
hospital admissions.  If correct, it would appear the drug is doing harm!

However, the number of patients with the condition per practice appears
twice in the model (as divisor and as exposure), so the effect may be an
artefact.

As a sensitivity analysis, I can use a variety of different exposures and
divisors:
E_diag - the number of patients with the diagnosis recorded 
E_50y - The total number of patients over 50 (the condition is rarely seen
below this age)
E_Pred - The predicted number of patients affected, based on the age &
gender profile of the practice (typically 10 patients affected for 1
diagnosed).

This gives 9 possible combinations of exposure and divisor.  When the
exposure and the divisor are both the same do I get the significant result.
But I also get a significant result when using E_50y and E_pred together.  (
A total of 5 results significant out of 9)

One further complication:  I actually have data repeated for 3 years. The
results above generally hold when looking at one year at a time.  When I
combine the data & use -xtpoisson, fe-, instead of -nbreg-, only one
comparison (matching E_diag with E_diag) remains significant.

2 questions (for those of you have read this far)
*	Is there a better model to use than -nbreg- or -xtpoisson, fe-?
(NOTE: xtnbreg does not generally converge, but when it does the answers are
similar)
*	Is it safe to ignore the anomalous result and conclude that there is
no evidence of an effect ? 
 
I can of course supply code and output if required, but I think I have taken
up enough bandwidth.

Best Wishes, 


Paul Seed

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