Modelling well being care price is commonly problematic as a result of are distributed in a non-normal method. Usually, 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 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 way to estimate prices with illness mannequin states utilizing generalized linear fashions. The tutorial incorporates for most important steps.
Step 1: Getting ready the dataset:
- The dataset usually requires calculating price for discrete time durations. As an illustration, when you’ve got claims knowledge, you could have info on price by date, however for analytic functions might need to have a dataset with price info by individual (rows) with the columns being the price by 12 months (or month). Alternatively, you could possibly create the unit of remark to be the person-year (or person-month) and every row can be a separate person-year file.
- Subsequent, one should specify the illness states. In every time interval, the individual is assigned to a illness state. Challenges embody figuring out how granular to make the states (e.g. simply MI vs timing since MI) and the 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 price knowledge are lacking (however the affected person is just not 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 doubtlessly remodeling knowledge.
- A pattern knowledge set is proven under.
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 under. You might be required to estimate each a hyperlink operate and the distribution of the error time period. “The preferred ones (combos of hyperlink operate and distribution) for healthcare prices are linear regression (id 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: Deciding on the ultimate mannequin.
- Mannequin choice first should contemplate 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 embody bootstrapping stepwise choice and penalized methods (e.g. least angle choice and shrinkage operator, LASSO). Interactions between covariates is also thought of.
- 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 influence of illness state on price is extra complicated. The authors advocate the next:
For a one-part non-linear mannequin or a two-part mannequin, marginal results may be derived utilizing recycled prediction. It consists of 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.
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