regression models are developed using statistical techniques to measure the response of outcomes of interest to predictor variables . in general , model development begins by employing a combination of literature search and expert panel knowledge to select factors believed to influence outcome variables of interest such as cost , complications , readmissions , or mortality . once selected , candidate predictor variables must be further specified so that they can be identified within available data sources . thus , a decision to test the effect of chronic obstructive pulmonary disease ( copd ) on patient cost first requires the creation of a variable to identify patients with copd . the creation of the candidate predictor variables is a design decision affecting all subsequent results and may vary by developer . for example , developers must decide which international classification of diseases , tenth revision , codes constitute copd , the sites of service from which reported data are utilized to identify copd ( eg , inpatient data only or both inpatient and outpatient data ) and the time frame of the reported data used to identify copd ( eg , inpatient data only or inpatient data and data preceding the inpatient admission ) . after making these design decisions , the candidate predictor variables are tested within the framework of the statistical model . the statistical framework is another design decision and can vary by both developer and the outcome being measured . for example , the hierarchical condition category ( hcc ) capitation risk - adjustment model is built from a multiple linear regression that treats the relationship between observed enrollee costs and the predictor variables as primarily additive ( pope et al . , 2004 ) . thus , with a few exceptions , the presence of a predictor variable adds a fixed amount to the prediction of enrollee cost . by contrast , the regression model developed for the hospital readmission reduction program ( hrrp ) is based upon the logistic ( odds ratio ) variant of the hierarchical generalized linear model , which is primarily multiplicative ( yale new haven health services corporation / center for outcomes research & evaluation , 2014 ) . thus , the presence of a predictor variable increases the predicted risk of readmission by a fixed percentage . the percentage increase is multiplicative to all other predictor variables , resulting in a compounding effect . these design decisions are often made after testing the regression model to see which regression model offers superior fit ( better prediction of the outcome ) . there is however a tendency for outcomes that are binary ( yes / no ) to be fitted with logistic regression models because of the possibility that standard regression models might predict an outcome with likelihood greater than 1 or less than 0 ( asymptotically constrained ) . because probabilities outside the range 0,1 are not meaningful , regression models for binary variables are first constrained within the probability range before optimizing data fit . after specifying variables of interest and the statistical framework , the developer must specify other requirements , such as whether there will be any patient - level exclusions , service carve - outs , outlier trims or caps , etc . this entails using a development dataset complete with subsequent testing on a calibration , or validation dataset . resulting coefficients and the overall fit of the model are subsequently reviewed for statistical significance . in summary , regression models hypothesize variables that will predict an outcome , define how those variables are to be constructed , specify a statistical framework within which the predictor variables interact , compute fixed coefficient values for each predictor variable , and test whether there is sufficient association between each predictor variable and outcome for it to be retained within the regression model . the final model provides a formula from which the likelihood or magnitude of an outcome variable can be estimated given the presence of selected predictor variables ( risk factors ) . once developed , the regression formula can be used to predict the outcome in other databases , following the same approaches in terms of patient exclusions , service carve - outs , and outliers . as with regression models , clinical categorical models utilize predictor variables to estimate the value of an outcome . the process used in the development of a clinical categorical model is an iterative process of formulating clinical hypotheses regarding the relationship between the outcome of interest and predictor variables and then testing the hypotheses with historical data . the historical data are used to confirm or refine the clinical hypotheses identified by clinicians . when there are discrepancies between clinical expectations and the data results from the historical data , the clinical expectations are refined to form the basis of the clinical categorical model . typically , a clinical categorical model will be expressed as an exhaustive and mutually exclusive set of categories defined on the basis of the predictor variables with each category having a distinct predicted value of the outcome . the prediction of the outcome is based on the clinical category assigned and is typically computed as the average value of outcome for all patients assigned to the category . the most prominent example of a categorical model is diagnosis - related groups ( drgs ) . unlike regression models , categorical models require expert clinical opinion to hypothesize the likely effects ( eg , large steps in cost or the presence of attenuating circumstances ) of the predictor variables interaction with each other and the outcome of interest . how predictor variables interact is generally hypothesized to vary across health conditions ; hence , a categorical model is hierarchically structured with layers of rules governing interactions among predictor variables . the hcc regression model contains 111 distinct condition categories to predict enrollee cost within the medicare advantage risk - adjustment algorithm . each variable carries with it a coefficient that can be added so as to predict enrollee cost . a categorical model developed using the same number of condition categories needs to account for 2 possible interactions among these variables within its rules . to place a limit upon the number of rules employed by the categorical model , for example , medicare severity ( ms)-drgs are currently restricted to 749 payable ms - drgs . within these 749 categories , the impact of a particular predictor variable is neither assumed equal to its impact in another ms - drg nor assumed to have a uniform impact when combined with other predictor variables within the ms - drg . instead , the combined impact from risk factors for cases within same drg cells is hypothesized to have a similar impact upon the outcome variable . by allowing more cells , the categorical model allows a greater range of different interactions to be recognized . at the other end of the spectrum from using 749 drgs to describe risk factor interaction for the medicare inpatient prospective payment system ( ipps ) , the diagnosis treatment combinations used for payment in holland have 29 000 distinct categories ( fleur , 2011 ) . although there is no magic number determining the number of cells that a categorical model should contain , the final model needs to be understandable to health professionals affected by the model . in addition , the final model needs to have sufficient volume distributed within cells so that the developers can assess the stability of the hypothesized relationships ( without overfitting ) . in summary , categorical models hypothesize variables that will predict outcomes , define how those variables are to be constructed , specify a clinical model with extensive rules that determine how the variables interact , and utilize data to test the clinical model at each stage as part of a process to confirm or revise the clinical rules . an in - depth description of the process of forming clinical categorical models can be found in the original article describing the formation of the drgs ( thompson et al . the end result is a clinical model that can be applied to many different population datasets from which weights or rates can be separately calculated . for the clinical model to be broadly applicable to different populations , it is essential that the dataset used for testing include a full cross - section of the population , including less common but serious conditions . users work from the same model , but are free to calculate weights or rates differently in terms of exclusions , carve - outs , outliers , etc . unlike the coefficients in a regression model , the weights and rates used in a clinical model are independent of the underlying clinical model , allowing a uniform and stable clinical model to be maintained . for example , different payers , ( eg , medicare and medicaid ) can use different prices in payment applications of drgs while calculating payment using the same drgs . in terms of similarities and differences , both models start by identifying variables of interest and operationalizing the definition of these variables from an available data source . the regression model specifies a statistical framework within which the variables interact , and computes a mathematical formula with coefficient values for the predictor variables , which are held constant across the model . the coefficients of the model are specific to a population dataset used to develop the regression formula . in contrast , the categorical model develops a clinical model with an extensive set of rules that specify the predictor variables and their varying interactions with each other and the outcome of interest . the final model is a clinical model that is separate from and can be applied to many different population datasets , from which weights and rates can then be calculated . in practice , the decision to enforce the uniformity of effect on an outcome within a category ( categorical ) or to enforce uniformity of an effect by a variable across all interactions ( regression ) leads to significant differences in the measurement of risk factors . a general statement can be made that , in regression models , if the level of risk when 2 factors are present is greater than the sum of their individual risk then the calculated coefficients for individual risk factors will be overstated . conversely , if the level of risk when the 2 factors are present is less than the sum of their individual risk , then the individual coefficients will be understated . a simplification of this difference is shown in table 1 . in table 1 , we hypothesize 2 risk factors a and b that influence cost . in isolation , risk factor a is observed to increase cost by $ 100 and risk factor b by $ 300 . when found together , cost is observed to increase by $ 1000 because of the interaction of the 2 variables . in the example we restrict the categorical model to 2 cells ( high and low ) and the regression to single terms only ( no interactions ) . furthermore , we assume that there are equal amounts of cases with risk factors a , b , and a / b . in this example , we assume the developers would be sufficiently proficient to structure the categorical model so as to keep the lower cost cases a and b ( low ) together , whereas the higher cost cases a / b ( high ) would form its own cell . the regression model will calculate coefficients for a ( $ 300 ) and b ( $ 500 ) , with the results summed to provide an estimate for cases with both a and b ( $ 800 ) . if it were this simple , a very accurate solution could easily be implemented . in the categorical model , a third cell could be added , and it would not be necessary to average the difference between just a and just b. in the regression model , an interactive term could be added to produce a distinct coefficient for cases that have both risk factors . in actuality , outcomes of interest are a lot more complex and difficult to predict , and it is not a matter of simply adding additional interaction terms or categorical cells until prediction power is added . there are many reasons why developers restrict the number of terms or cells in a risk - adjustment model . first , by including a wider array of complex variables to capture interactions , one runs the risk of introducing more instability in the measured relationships between variables and predicted outcomes . this can be the result of  underpowered  cells ( too few individuals with the matching array of conditions upon which to base a firm conclusion ) , colinearity across predictor variables ( interaction effects between the predictors ) , clustering effects ( with fewer observations exhibiting the characteristics of interest , there is a higher likelihood that they come from a single source , ie , hospital or region , thus embedding the performance of the source within the estimate of the effect ) , or simply random variation . second and related to the first reason , it is important to not overfit a risk - adjustment model to the development database . it is key that predictor variables have a clear clinical rationale and will hold up across datasets and over time ( though periodically all models need to be reviewed and updated ) . to be successful , the model needs to capture the essential predictors , not omit any key predictors ( omitted variable bias may give a false sense of precision to the coefficient or category estimates ) , and not include overlapping or redundant variables ( which would allow for double - counting of risk variables and make the model very vulnerable to variations in coding and  code creep  ) . a third reason for restricting the number of predictor variables is that risk - adjustment models often need to avoid adjusting for unwanted and/or unnecessary variation . for example , increases in cost can be explained by the unnecessary use of expensive resources or complications from treatment . it is therefore reasonable to exclude those conditions that are predictive of cost but signal low - quality care from a risk - adjustment algorithm used for payment . simply stated , a model that buries harm or poor performance within the algorithm , although it might improve explanatory power , provides no foundation for improvement . fourth , overly large unwieldy models with large numbers of interaction terms or multiple small volume cells confuse interpretation . overall , those seeking to understand and redress cost and quality failings require objective , transparent , and understandable comparative information to move forward . developers therefore attempt to deliver parsimonious models to achieve the optimal tradeoff between maximizing predictive accuracy ( consistent with policy objectives ) and using the fewest predictors . the streamlining of models is not merely about the number of categories or variables but also the degree to which clinically meaningful distinctions can be drawn across them . this is particularly true of categorical - clinical models as they are inherently conceived as management tools , but is likewise important for the integrity of regression models . in simpler situations where there are fewer interacting variables , regression and categorical models can yield similar results . that is , they can be used to predict similar amounts or rates of an outcome using the same predictor variables . this is not necessarily the case when interactions become more complex and the measurement of predictive accuracy also becomes more complex . in addressing regression and categorical risk - adjustment models , it is important to understand risk and carefully evaluate predictive accuracy but it is also very important to evaluate a number of other attributes for system use and policy . table 2 provides a comparison of design characteristics that should be considered and in the context of the 5 objectives of risk adjustment . table 2 begins by considering how differences in the method of model development affect the presentation of the model to users . a byproduct of creating a rule - based classification algorithm is that the rules used to classify patients and enrollees are available for review . moreover , hierarchical classification results in discrete categories of patients ( or enrollees ) within understandable disease groupings . this differs from regression models that permit a review of risk factor coefficients but only limited insight into why the interaction of patient risk factors manifests in a particular outcome . independent review of payment and performance measures is important for credibility , but transparency has an even greater role in letting clinicians know how their relative performance impacts both patient outcome and their own finances and areas in need of improvement . update , response to change , and accommodating policy variation ( carve - outs ) highlight how differences in the structure of the models affect their stability . categorical clinical models are more robust in these circumstances as , after the initial extensive development , they are designed to tolerate changes within subsections of the model . as described previously , regression models are built with the requirement that risk factors have a common effect across all patient and disease subtypes , hence they require re - estimation and often respecification of the model in the face of change . regression models , such as hccs , are not fully defined without the use of some categorical rules . variables from the same family or those related by hierarchical severity require definition to avoid double counting  and a subsequent unwanted mix of  paying for coding  and misestimation of their effect size . moreover , the creation of the model usually identifies some interactions across variables that warrant an additional adjustment requiring definition . the issues of transparency , communication , and stability can be understood using the hrrp risk - adjustment model as an example . the centers for medicare and medicaid services ( cms ) segments performance measurement within the hrrp by admission type so that congestive heart failure ( chf ) is modeled separately from pneumonia and acute myocardial infarction ( ami ) . individual risk factor coefficients are permitted to vary across the models , thereby giving dissimilar signals , depending upon the admission type while holding the effect constant across all interactions within the model . for example , the presence of asthma or history of coronary artery bypass grafting is associated with reduced readmission risk for pneumonia admissions , whereas history of coronary artery bypass grafting is associated with increased readmission risk for ami admissions and decreased risk for chf admissions . the presence of asthma is associated with increased readmission risk for ami and chf admissions but not for all time periods . the variation in coefficient values across models indicates potential problems for a regression model that unifies readmission risk across admission types without first understanding or adjusting for the source of variation . stability of results over time , and thereby ability of users to identify important risk profiles , also requires interpretation . for example , dementia is associated with an increased readmission risk for ami admissions in 1 year , decreased risk in the subsequent year , and little or no effect in a third . a similar pattern is produced by the effect of being male upon hf admissions ( yale new haven health services corporation / center for outcomes research & evaluation , 2014 ) . a question posed by reviewing the hrrp model is how clinicians can use the risk - adjustment model to routinely identify those patients who are at the highest risk of readmission and are suffering from systematic failures . another arguably more important question is whether or not these findings are clinically logical or more likely an artifact of data patterns that were somewhat random , particular to a database , or resulting from how the regression model was specified . in the introduction to this article , we described 5 attributes of a risk - adjustment model upon which it should be compared and evaluated . the first 2 attributes , matching payment to patient risk and avoiding incentives to select less complex patients , are amenable to statistical measurement but require an understanding of their interrelatedness . evaluating the accuracy of a model in matching payment to cost , or risk to likelihood of an outcome , has a tendency to rely upon an r comparison of global fit . although this may work with comparing overall historical patterns , it is essential to compare how well the model fits for subsections of a population  such as those with a particular chronic condition , of a particular location , with particular challenges or other identifiable risk factor . it should be assumed that those paid to take on risk will look for ways to minimize their risk relative to their payment and will adopt strategies to do so , making this more complex analysis more important than the overall measure of global fit usually utilized to compare models . regression models require more detailed and complex interaction terms to account for instances where patients / enrollees have either greater or lesser risk in the presence of an additional risk factor than would be predicted by simply adding the risk of the separate variables . not doing so can lead to the transfer of allowance for risk across high- and low - risk case types for a given predictor variable . categorical models are reliant upon the rules derived to classify patients / enrollees and therefore can benefit from very detailed clinical review . classifying patients / enrollees within discrete cells will generally average the risk of some higher and lower risk patient types . put differently , categorical models tend to transfer allowance for risk within high- or low - risk case types . two models may appear equivalent in their ability to discriminate between outcome predictions at an aggregate level , yet conceal a bias against particular providers because of the clustering of high - risk cases in particular providers or conversely by classifying distinct patient types of varying risk within single cells . the attributes of communication , transparency , and stability are harder to quantify but easier to compare . categorical models are designed to promote comparison , enable review of the rules that are generated to differentiate risk and to be modified in the face of expert commentary and insight . categorical models separate the weighting of an outcome variable ( such as cost ) from the definition of patient complexity . the job of the model is to develop clinical rules to bring together similar patients / enrollees within a single consistent classification whereas the weight linking the model to risk adjustment ( or payment ) is computed and updated with changes in data and/or changes with regard to inclusions / exclusions , outlier policies , and other adjustment factors . as noted by the cms the separation of the methodologies for developing the clinical model and the payment weights was a critical factor in the success and widespread adoption of the drg system . the separation of the clinical and payment weight methodologies allows stable clinical methodology to be maintained while the payment weights evolve in response to changing practice patterns . but the separation of payment and classification introduced with the ipps not only  set a reasonable price for a known product ( schweiker , 1982 ) but also created a language to link the clinical and financial aspects of care , thereby improving communication between administrators and clinicians . thus , a clinical categorical model can remain relatively stable , providing a consistent and powerful communication tool , whereas weights fluctuate to reflect changing practice patterns and new technology . the same model by being structured to define differences in patients / enrollees can be employed over varying geographic areas , over time and for a variety of outcomes without being dependent upon the initial data used in its development . although clinical categorical models have many advantages in terms of communication , transparency , and stability , their initial development requires a significant effort and clinical input . regression models usually require less initial development effort but are unstable in a changing environment and fail to provide the same degree of communication value and transparency .