Modelling well being care price 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 statement 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 example, whereas the price of most cancers care might 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 tips on how to estimate prices with illness mannequin states utilizing generalized linear fashions. The tutorial comprises for major steps.
Step 1: Making ready the dataset:
- The dataset usually requires calculating price for discrete time durations. As an example, if in case you have claims knowledge, you’ll have info on price by date, however for analytic functions might need to have a dataset with price info by particular person (rows) with the columns being the associated fee by 12 months (or month). Alternatively, you possibly can create the unit of statement to be the person-year (or person-month) and every row could be a separate person-year report.
- 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 tips on how 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 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’re required to estimate each a hyperlink operate and the distribution of the error time period. “The most well-liked 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 price.
Step 3: Choosing the ultimate mannequin.
- Mannequin choice first should think about which covariates are included within the regression which will be obtained by stepwise choice utilizing a pre-specified statistical significance. Nevertheless 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.
- Total match will 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 simple to do, the influence of illness state on price is extra advanced. The authors advocate the next:
For a one-part non-linear mannequin or a two-part mannequin, marginal results will be derived utilizing recycled prediction. It consists of 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 will 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 nicely and you’ll obtain that right here.
