Modelling well being care value is commonly 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 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 value to particular well being care states. As an illustration, whereas the price of most cancers care could fluctuate 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) gives a pleasant tutorial on how you can estimate prices with illness mannequin states utilizing generalized linear fashions. The tutorial incorporates for important steps.
Step 1: Getting ready the dataset:
The dataset usually requires calculating value for discrete time intervals. As an illustration, you probably have claims information, you’ll 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 associated fee by yr (or month). Alternatively, you might create the unit of remark to be the person-year (or person-month) and every row can 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 how you can deal with multi-state eventualities.When information are censored one can (i) add a covariate to point information are censored or (ii) exclude observations with partial information. If value information 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 intervals of study requires mapping to the choice mannequin’s cycle size, dealing with censoring appropriately, and probably reworking 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 value is remodeled non-linearly, as proven within the method beneath. You’re required to estimate each a hyperlink perform and the distribution of the error time period. “The most well-liked ones (mixtures of hyperlink perform 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 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 embrace bootstrapping stepwise choice and penalized strategies (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 straightforward to do, the affect of illness state on value is extra complicated. The authors suggest the next:
For a one-part non-linear mannequin or a two-part mannequin, marginal results might 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. Commonplace 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 nicely and you may obtain that right here.
