Modelling well being care price is commonly problematic as a result of are distributed in a non-normal method. Sometimes, there are a lot of $0 observations (i.e., people who don’t use any well being care) and price 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 remark is well-known by well being economists however a complicating issue for modelers is mapping illness price to particular well being care states. As an illustration, whereas the price of most cancers care might range primarily based 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) supplies a pleasant tutorial on estimate prices with illness mannequin states utilizing generalized linear fashions. The tutorial incorporates for predominant steps.
Step 1: Getting ready the dataset:
- The dataset usually requires calculating price for discrete time durations. As an illustration, you probably have claims information, you will have data on price by date, however for analytic functions might need to have a dataset with price data by individual (rows) with the columns being the price by yr (or month). Alternatively, you could possibly create the unit of remark 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 individual 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 deal with multi-state situations.
- When information are censored one can (i) add a covariate to point information are censored or (ii) exclude observations with partial information. If price information 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 information.
- A pattern information 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 price is remodeled non-linearly, as proven within the method beneath. You might be required to estimate each a hyperlink operate and the distribution of the error time period. “The most well-liked ones (combos 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 probability a person has optimistic price.
Step 3: Choosing the ultimate mannequin.
- Mannequin choice first should think about which covariates are included within the regression which may 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-about.
- General match may 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 price are straightforward to do, the affect of illness state on price is extra complicated. The authors suggest the next:
For a one-part non-linear mannequin or a two-part mannequin, marginal results may 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 may be estimated utilizing bootstrapping.
The authors additionally present an illustrative instance making use of this strategy to modeling hospital price related to cardiovascular occasions within the UK. The authors additionally present the pattern code in R as properly and you’ll obtain that right here.
