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

["Seed, Paul" <paul.seed@kcl.ac.uk>]

Dear all, 

Thank you for your responses to my query.

Austin Nichols <austinnichols@gmail.com> suggested:
"Why not just include all RHS variables in logs rather than forming a
ratio on the RHS?  If the "exposure" is supposed to have a coef of
one, that will be estimated; if the numerator and denominator of your
ratio are supposed to have coefs of equal size and opposite sign, they
will be estimated so. I would lean toward -xtpoisson, fe- myself. You
might also look for "Granger causality" by hand, i.e. see if a higher
outcome value predicts later higher treatment.  I would guess that
endogeneity is a pervasive problem here--what is the setting in which
these practices are getting patients and making decisions about
prescriptions?"

Taking logs is a very useful suggestion.  It should separate drug effects from 
exposure effects. I will try that next.

We have looked for "Granger causality", but there is 
very little change over time.  The uptake of the new drug was just before the 
period of the data.

I do not fully follow the point about endogenicity.  There are inner London 
National Health Service (NHS) primary care practices, of different sizes, but fairly similar 
disease rates.  Decisions are made primarily on the basis of perceived medical 
need, possibly with some effect of NHS and practice policy.  All costs are borne 
centrally by the taxpayer. Patients' ability to pay (wealth or medical insurance 
status) is not directly relevant; except that the burden of disease is generally 
higher in deprived areas.

Peter Lachenbruch <Peter.Lachenbruch@oregonstate.edu> said 
"Did I miss something?  Wouldn't patients having more prescriptions likely be sicker and 
more likely to be admitted to hospital.  If we had an oncology center or a dialysis center 
those patients will have a high number of prescriptions and a lot of admissions (possibly 
outpatient for chemotherapy)."

We are using prescriptions for other disease-relevant drugs as a surrogate for disease severity.

If we had individual patient data, the severity of disease for each patient would be very 
relevant. However, the data is entirely at the practice level (mean list size 6697 patients per practice),
 so there is considerable averaging out. We are looking at entire practice lists, including people who 
are too young to have this particular disease, who are completely healthy, or who are being treasted for 
other conditons.  It is not clear how many patients have the disease, much less how severe it is.
 
None of the practices specialise in the disease in question; all are in the caschement area for the same hospitals; 
patients referred to the hospital for outpatient treatment will be referred back to the same practice.

Carlo Lazzaro" <carlo.lazzaro@tin.it> said 
"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."

I hope so, but I feel obliged to check carefully.
With this in mind, we have decided to seek a further, larger data set, at the PCT 
(primary care trust) level.  There are some 152 PCTs in England, with an average 
population of just under 330,000 per trust. This may give tighter confidence intervals 
for the key estimates, but averaging over such large numbers will reduce diferences in 
the predictors.

Thank you all again.
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