Case-mix adjustment versus risk adjustment, what are their differences in practice and objective? I have encountered in swathes of medical literature the use of the terms "case-mix" and "risk" adjustment without any citations or explanations of their exact usage and motivation from a modeling perspective. I understand the principles of covariate adjustment in multiple regression modeling to address confounding (bias) and stratification (efficiency). However, I can't seem to find a reference with discussion on the definition of these terms, their impact on analyses, and the objectives of their use.
Can someone explain generally how and why case-mix and risk adjustment would be used in practice?
 A: I've seen the two terms are sometimes used synonymously, and they're both an attempt to control for a particular type of confounding, namely that some patients have a set of covariate risk factors the predispose them to the outcome.
Generally speaking, I've found "case-mix" most often used in studies where the unit of comparison is the study site. For example, when comparing the incidence of surgical errors at Hospital A versus Hospital B, one might wish to control for the fact that Hospital A is a major regional teaching hospital that gets very complex cases. If you were exposed to any of the controversy regarding the Consumer Reports rating of hospitals based on their infection rates, and rating some very prestigious hospitals poorly while giving high marks to obscure local hospitals, this is essentially a working example of having failed to adjust for case mix.
"Risk adjustment", in contrast, I find most often used when the unit of comparison is the patient. For example, if you want to compare the risk of death for patients given Drug A versus Drug B, there's the possibility that, because you aren't randomly assigning the drugs in this example, those on Drug A are somehow different. Say Drug B is known to be hard on the kidneys - you wouldn't give Drug B to patients on kidney dialysis. Which means the study subjects using Drug A are worse off generally, beyond the efficacy of the drug itself.
In both cases, there are a number of ways to adjust for them. You can stratify with small numbers, match using something like a propensity score, include some measure of case-mix or risk (I prefer particular covariates, some people favor composite risk scores like APACHE II) as a covariate in a regression model, or ever more sophisticated techniques to try to arrive at an unbiased estimate.
But what it comes down to is "Some people are sicker than others, and that may not be random".
A: I do not think there is any real difference between "case-mix adjustment" and "risk adjustment" in this context. I would say the terms are used interchangeably.
They refer to adjusting for confounding due to patient ("case") mix, or the patients' risks of the outcome being examined.
Funders often want to compare hospitals based on indicators such as 30-day mortality (proportion of patients who die within 30 days of discharge from the hospital). But the hospitals can have quite different types of patients. One hospital may have a nursing home down the road, and treat many older patients with multiple chronic conditions. Another may be located near a major highway and treat many emergency trauma patients from motor vehicle accidents. Any comparison of the hospitals needs to somehow adjust for these differences in case mix.
In practice adjustment is usually through some form of logistic regression (generally hierarchical to account for clustering within hospitals), either directly including patient characteristics, or calculating and using a propensity score for how likely a patient is to be treated at a particular hospital.
A: http://www.rti.org/files/HHS-HCC_Risk_Adjustment_Model.pdf
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.
A: In the specific context of hospital financial reporting, such as
 
** average cost per admission, or 
 
** average revenue per admission
"case-mix adjusted" is a term of art that means "DRG-adjusted".
In other words, sum[of whatever] / sum[of DRG weights] for the group of patients being reported.
And 99% of the time, unless specifically noted otherwise, the DRG weights used will be the Medicare weights for the appropriate time period, even if the patients aren't all Medicare. 
It's a simplistic adjustment, but ubiquitous in the industry. (It's been said that accountants express everything in dollars, because they can only think in one dimension. I'm not here to opine on that.) 
In other contexts, I agree with timbp that the terms "case-mix adjusted" and "risk adjusted" are used interchangeably, without clear distinctions. You have to look at the methodology detail to understand what's been done.
A: http://www.nber.org/MedicareAdvtgSpecRateStats/risk-adjustment/2011/Evaluation2011/Evaluation_Risk_Adj_Model_2011.pdf
This link explains risk adjustment scores and risk adjustment transfers in the CMS-HCC (hierarchical condition categories) methodology. HHS, the parent to CMS, has its own methodology, which is applied to Medicare Advantage plans under the Affordable Care Act of 2010. I can provide a link to the SAS v9 code and associated data (regression coefficients) which implements the HHS-HCC methodology. The SAS code is really (!) simple, as HHS has done all the heavy lifting in terms of analysis.
