[mattkrause]

It's a regression model, so "accounted for" usually means that the factors were included in the models.

Ideally, we'd ask a group of male doctors and a group of female doctors to independently diagnose and treat the same set of patients. We can't actually do that--in addition to the cost, you obviously can't treat the same patient twice. However, we can try to estimate this effect statistically.

First, they build a model describing the probability of a patient dying within 30 days. They used a linear probability model, which essentially means that the probability of someone dying is the sum of the "weights" related to the patient, doctor, and hospital. These weights are estimated from the data using ordinary least squares (the same way you may have learned to fit a line to points at school).

Having built the model, they then ask what the marginal effect of the doctor's sex is. In other words, if you hold everything but that constant, how does the probability of dying change? They cite a nice Stata guide (#32 in the paper here: http://www.stata-journal.com/sjpdf.html?articlenum=st0260 ) which gives some background and examples.

The rest of the paper looks at different variations (only hospitalists, different diseases, etc), using a pretty similar approach.