Stephanie Chan wrote:

> I will be leading an EBM teaching session for housestaff on the Annals 
> article, "*Universal Surveillance for Methicillin-Resistant 
> /Staphylococcus aureus/ in 3 Affiliated Hospitals*"  (Ann Intern Med, 
> Mar 2008; 148: 409 - 418).  I was planning to analyze it using the 
> standard questions about therapy from the Users' Guides to the Medical 
> Literature, but I was wondering if there should be any special 
> considerations, given that therapy (MRSA screening & eradication) was 
> given at a hospital-wide level.  For example, the results are presented 
> as incidence of nosocomial MRSA infections per person-years -- can I 
> convert this to a percentage, to churn out an ARR and an NNT?  Or is 
> this statistically forbidden?  Please let me know of any journal 
> articles you're aware of that address the issue of studies taken at a 
> hospital- or population-based level.

I like the phrase "statistically forbidden". Unfortunately, I don't 
think there is a "statistics police officer" who could enforce any 
rules. I'd be glad to take on the role if I could keep 10% of the fines 
from the statistics citation violations that I write up.

I'm unaware of any methodological publications on this issue. I have 
seen a few examples of number needed to treat being calculated on rates, 
but don't have any particular citations that I can offer. The only thing 
I can offer is a bit of numeric common sense.

You need to distinguish first between proportions and rates. When you 
have a fraction where the numerator is a count and the denominator is 
another count and the numerator represents a subset of the denominator, 
then you have a proportion. A proportion is guaranteed to be between 
zero and one and it is unitless.

When you have a fraction where the numerator is a count and the 
denominator is a measure of time, area, or something in different units 
than a count, then you have a rate. A rate also occurs if the numerator 
and the denominator are counts of different units (e.g., number of 
warranty claims per automobiles sold). A rate always has units, such as 
deaths/person year of exposure. A rate has the potential of exceeding 
one, and frequently the units used in the rate are adjusted to make the 
rate more manageable.  Often you will see rates multiplied by one 
thousand, ten thousand, or a million. So instead of saying 0.0023 events 
per person years of exposure, you will see 23 events per ten thousand 
years of person exposure.

There's an implicit assumption that rates are uniform over time, area or 
whatever unit appears in the denominator. Otherwise, the rate is 
difficult to interpret. If infections, for example, occur very 
frequently on the first day of hospitalization and taper off over time 
then 24 infections across 500 patients each with a 2 day stay is not 
directly comparable to 24 infections across 50 patients, each with a 20 
day stay.

While it is possible to calculate a number needed to treat for a rate, 
it should be interpreted with caution. If, for example, a treatment 
group has an infection rate of 2.4 per thousand patient days and the 
control group has an infection rate of 2.9 per thousand patient days, 
then the NNT is two thousand patient days. That means that if you 
adopted the treatment, you would see on average one fewer event every 
two thousand patient days. If you have 10 patients on average on a 
typical day in your unit, then you would see one fewer infection every 
200 days on average if you adopted the intervention. Note that this 
interpretation assumes uniformity across time.

Another issue is that rates are often calculated from observational 
data, and interpretation of number needed to treat is tricky for 
observational data. IF you note a rate of 2.4 per thousand patient years 
in females and 2.9 per thousand patient years in males, then the number 
needed to treat say that you would see one fewer event on average in 
every 2000 patient days if you could change the sex of all your male 
patients to female patients. You can't change the sex of your patients, 
so what does this number really mean?
-- 
Steve Simon, Standard Disclaimer.
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