Modelling well being care value is commonly problematic as a result of are distributed in a non-normal method. Usually, 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 remark is well-known by well being economists however a complicating issue for modelers is mapping illness value to particular well being care states. For example, whereas the price of most cancers care could differ 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) gives a pleasant tutorial on the best way to estimate prices with illness mannequin states utilizing generalized linear fashions. The tutorial incorporates for essential steps.
Step 1: Making ready the dataset:
- The dataset sometimes requires calculating value for discrete time durations. For example, you probably have claims knowledge, you might have data on value by date, however for analytic functions could need to have a dataset with value data by individual (rows) with the columns being the price by 12 months (or month). Alternatively, you possibly can 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 best way to deal with multi-state eventualities.
- 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 isn’t 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’re 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 (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 chance a person has optimistic value.
Step 3: Deciding on the ultimate mannequin.
- Mannequin choice first should take into account which covariates are included within the regression which might be obtained by stepwise choice utilizing a pre-specified statistical significance. Nevertheless this can lead to over becoming. Different covariate choice strategies embody bootstrapping stepwise choice and penalized strategies (e.g. least angle choice and shrinkage operator, LASSO). Interactions between covariates may be thought-about.
- 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 affect of illness state on value is extra advanced. 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 eventualities 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 eventualities. 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.