A Tutorial on Estimating Prices Related to Illness Mannequin States Utilizing GLM – Healthcare Economist

Modelling well being care value is usually problematic as a result of are distributed in a non-normal method. Sometimes, there are numerous $0 observations (i.e., people who don’t use any well being care) and value distribution that’s strongly proper skewed amongst well being care customers due a disproportionate variety of people with very excessive well being care prices. This commentary is well-known by well being economists however a complicating issue for modelers is mapping illness value to particular well being care states. As an example, whereas the price of most cancers care might fluctuate based mostly on illness stage and whether or not the most cancers has progressed; the price of heart problems will differ if the affected person has a myocardial infarction.

A paper by Zhou et al. (2023) offers a pleasant tutorial on the right way to estimate prices with illness mannequin states utilizing generalized linear fashions. The tutorial incorporates for major steps.

Step 1: Getting ready the dataset:

• The dataset usually requires calculating value for discrete time durations. As an example, when you have claims knowledge, you might have data on value by date, however for analytic functions might need to have a dataset with value data by particular person (rows) with the columns being the associated fee by yr (or month). Alternatively, you would create the unit of commentary to be the person-year (or person-month) and every row could be a separate person-year document.
• Subsequent, one should specify the illness states. In every time interval, the particular person is assigned to a illness state. Challenges embrace figuring out how granular to make the states (e.g. simply MI vs timing since MI) and the right way to deal with multi-state situations.
• When knowledge are censored one can (i) add a covariate to point knowledge are censored or (ii) exclude observations with partial knowledge. If value knowledge are lacking (however the affected person will not be in any other case censored), a number of imputation strategies could also be used. Forming the time durations of research requires mapping to the choice mannequin’s cycle size, dealing with censoring appropriately, and probably remodeling knowledge.
• A pattern knowledge set is proven beneath.

Step 2: Mannequin choice:

• The paper recommends utilizing a two-part mannequin with a generalized linear mannequin (GLM) framework, since OLS assumptions round normality and homoscedasticity within the residuals are sometimes violated.
• With the GLM, the anticipated worth of value is remodeled non-linearly, as proven within the system beneath. You might be required to estimate each a hyperlink operate and the distribution of the error time period. “The preferred ones (mixtures of hyperlink operate and distribution) for healthcare prices are linear regression (identification hyperlink with Gaussian distribution) and Gamma regression with a pure logarithm hyperlink.)

• To mix the GLM with a two-part mannequin, one merely estimate the equation above on all optimistic values after which calculates a logit or probit mannequin for the chance a person has optimistic value.

Step 3: Deciding on the ultimate mannequin.

• Mannequin choice first should contemplate which covariates are included within the regression which might be obtained by stepwise choice utilizing a pre-specified statistical significance. Nonetheless this can lead to over becoming. Various covariate choice methods embrace bootstrapping stepwise choice and penalized methods (e.g. least angle choice and shrinkage operator, LASSO). Interactions between covariates may be thought of.
• Total match might be evaluated utilizing the imply error, imply absolute error and root imply squared error (the final is mostly used). Higher becoming fashions have smaller errors.

Step 4: Mannequin prediction

• Whereas predicted value are simple to do, the impression of illness state on value is extra complicated. The authors advocate the next:

For a one-part non-linear mannequin or a two-part mannequin, marginal results might be derived utilizing recycled prediction. It contains the next two steps: (1) run two situations throughout the goal inhabitants by setting the illness state of curiosity to be (a) current (e.g. recurrent most cancers) or (b) absent (e.g. no most cancers recurrence); (2) calculate the distinction in imply prices between the 2 situations. Customary errors of the imply distinction might be estimated utilizing bootstrapping.

The authors additionally present an illustrative instance making use of this method to modeling hospital value related to cardiovascular occasions within the UK. The authors additionally present the pattern code in R as properly and you may obtain that right here.