Center for Primary Care and Public Health, University of Lausanne, Lausanne, Switzerland.
Stat Med. 2021 Jun 30;40(14):3286-3298. doi: 10.1002/sim.8950. Epub 2021 Apr 11.
We consider the non-trivial problem of estimating a health cost repartition among diseases from patients' hospital stays' global costs in the presence of multimorbidity, that is, when the patients may suffer from more than one disease. The problem is even harder in the presence of interactions among the disease costs, that is, when the costs of having, for example, two diseases simultaneously do not match the sum of the basic costs of having each disease alone, generating an extra cost which might be either positive or negative. In such a situation, there might be no "true solution" and the choice of the method to be used to solve the problem will depend on how one wishes to allocate the extra costs among the diseases. In this article, we study mathematically how different methods proceed in this regard, namely ordinary least squares (OLS), generalized linear models (GLM), and an iterative proportional repartition (IPR) algorithm, in a simple case with only two diseases. It turned out that only IPR allowed to retrieve the total costs and the unambiguous solution that one would have in a setting without interaction, that is, when no extra cost has to be allocated, while OLS and GLM may produce some negative health costs. Also, contrary to OLS, IPR is taking into account the basic costs of the diseases for the allocation of the extra cost. We conclude that IPR seems to be the most natural method to solve the problem, at least among those considered.
我们考虑了一个非平凡的问题，即在存在多种疾病（即患者可能患有多种疾病）的情况下，从患者住院的总费用中估算疾病的医疗费用分配。如果疾病成本之间存在相互作用，问题会更加复杂，也就是说，同时患有两种疾病的成本之和并不等于单独患有每种疾病的基本成本之和，而是会产生额外的成本，这些成本可能是正的也可能是负的。在这种情况下，可能没有“真正的解决方案”，并且选择用于解决问题的方法将取决于如何在疾病之间分配这些额外成本。在本文中，我们在只有两种疾病的简单情况下，从数学上研究了不同方法在这方面的处理方式，即普通最小二乘法（OLS）、广义线性模型（GLM）和迭代比例分配（IPR）算法。结果表明，只有 IPR 允许我们恢复总费用和在没有相互作用的情况下（即无需分配额外费用）会得到的明确解决方案，而 OLS 和 GLM 可能会产生一些负的健康费用。此外，与 OLS 不同，IPR 考虑了疾病的基本成本来分配额外成本。我们得出结论，至少在考虑的方法中，IPR 似乎是解决该问题最自然的方法。
