Modelling well being care value is usually 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 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 might 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) supplies a pleasant tutorial on learn how to estimate prices with illness mannequin states utilizing generalized linear fashions. The tutorial accommodates for major steps.
Step 1: Getting ready the dataset:
- The dataset sometimes requires calculating value for discrete time intervals. As an illustration, when you have claims information, you will have info on value by date, however for analytic functions might wish to have a dataset with value info by particular person (rows) with the columns being the price by 12 months (or month). Alternatively, you can 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 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 learn how to 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 doubtlessly remodeling information.
- A pattern information 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 value is remodeled non-linearly, as proven within the system under. 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 chance a person has optimistic value.
Step 3: Deciding on the ultimate mannequin.
- Mannequin choice first should think about which covariates are included within the regression which could be obtained by stepwise choice utilizing a pre-specified statistical significance. Nonetheless this can lead to over becoming. Different covariate choice methods embrace bootstrapping stepwise choice and penalized methods (e.g. least angle choice and shrinkage operator, LASSO). Interactions between covariates is also thought-about.
- General match could 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 advocate the next:
For a one-part non-linear mannequin or a two-part mannequin, marginal results could 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. Normal errors of the imply distinction could 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 effectively and you may obtain that right here.
A Tutorial on Estimating Costs Associated with Disease Model States Using GLM
