Estimating Health Cost Repartition Among Diseases in the Presence of Multimorbidity

We consider the nontrivial problem of estimating the health cost repartition among different diseases in the common case where the patients may have multiple diseases. To tackle this problem, we propose to use an iterative proportional repartition (IPR) algorithm, a nonparametric method which is simple to understand and to implement, allowing (among other) to avoid negative cost estimates and to retrieve the total health cost by summing up the estimated costs of the different diseases. This method is illustrated with health costs data from Switzerland and is compared in a simulation study with other methods such as linear regression and general linear models. In the case of an additive model without interactions between disease costs, a situation where the truth is clearly defined such that the methods can be compared on an objective basis, the IPR algorithm clearly outperformed the other methods with respect to efficiency of estimation in all the settings considered. In the presence of interactions, the situation is more complex and will deserve further investigation.