AdamO has asked how the terms case mix and risk adjustment are defined and used in research results posted in the medical literature, " their exact usage and motivation from a modeling perspective." My experience with case mix modeling is exclusively within health care, wherein the models seek to link patients, their diseases, and the cost of making them whole again.
These are wholly operational definitions, and depend 100% on the objective of the model and the data available to the modelers, thus making "their exact usage" arguable.
For instance, one might define one's population as all patients who billed Medicare in 2011, of which the Medicare Advantage portion might be 15M. One might define a case mix in terms of medical severity, eg SIRS, sepsis, septic shock, and septicemia in patients with neoplastic co-morbidities. One might define a unit of analysis as hospitals, with further control for trauma centers and community hospitals with <50 beds. One might then operationally define risk as money spent, in toto, by Medicare Advantage.
The model thus far provides no method for linking our patients with our risk, so let us connect them by the bills that are paid for these patient's treatment and the diagnostic disease codes (ICD) contained therein. We are likely to discover that the community hospital has zero risk because it has transferred the risk from itself to the trauma center by transferring the patient. The community hospital provided no treatment, so it cannot bill for services.
In order for our model to make more sense, let us remove the control of neoplastic co-morbidity, and focus upon blood diseases. Our patients at the trauma center are likely very different in their diagnostic code mix, their case mix, than at the community hospital. We are likely to find that the risk, the money spent, at the trauma center is less than the risk at the community hospital, mostly because the efficiencies at the trauma center far exceed the community hospital. Patients at the trauma center do not progress to more serious blood diseases, but at the community hospital, patients do get sicker, more often.
For this reason, based upon the results of our case mix modeling extrapolated to our population described by the 2011 patients, Medicare might well require an adjustment in the community hospital's case mix by mandating a risk adjustment in the form of a transfer of certain diagnostic category (DRGs) patients to the trauma center.
This simple example, although it has some obvious flaws, describes straight forward operational definitions of case mix, risk, and risk adjustment that have little to do with statistical analysis, and everything to do with "motivation from a modeling perspective." If you want a more sophisticated set of definitions, see the URL above.
Simple rules of thumb: when you read "case mix", think disease classifications and reach for the nearest ICD-10-CM manual; when you read "risk adjustment", reach for your wallet and think money.