Smooth quantile ratio estimation with regression: estimating medical expenditures for smoking-attributable diseases.
Smooth quantile ratio estimation with regression: estimating medical expenditures for smoking-attributable diseases.
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通过回归进行平滑分位数比估计：估计吸烟引起的疾病的医疗支出。
DOI：
10.1093/biostatistics/kxi031
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
Zeger,ScottL
中科院分区：
文献类型：
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作者：
Dominici,Francesca;Zeger,ScottL
本文的方法学发展是由计量经济学中的一个常见问题引起的，我们对估计两个人群之间的平均支出差异感兴趣，比如有疾病和没有疾病，作为协变量的函数。例如，设y1和y2为两个非负随机变量，表示病例和对照的卫生支出。平滑分位数比估计（Smooth Quantile Ratio Estimation， SQUARE）是一种估计Δ =E[Y1]−E[Y2]的新方法，它通过平滑两个分位数函数的对数变换比的跨百分位数来估计Δ =E[Y1]−E[Y2]。Dominiciet al.（2005）已经表明，SQUARE定义了大量的Δ估计量，比Δ的普通参数和非参数估计量更有效，并且是一致的和渐近正态的。然而，在应用中，通常需要估计Δ(x) =E[Y1|x]−E[Y2|x]，即均值差作为x的函数。在本文中，我们将SQUARE扩展为一个回归模型，并引入一个两部分回归的SQUARE来估计Δ(x)作为x的函数。我们使用模型的第一部分来估计产生任何成本的概率，模型的第二部分来估计医疗支出的平均差异，假设观察到非零成本。在模型的第二部分，我们将SQUARE的基本定义应用于正成本，以比较具有“相似”协变量概况的情况和控制的支出。我们通过使用倾向得分匹配来确定具有“相似”协变量概况的病例和对照的分层。然后，我们对1987年全国医疗保险支出调查应用两部分回归平方来估计患有吸烟归因疾病的人和没有这些疾病的人之间的差异Δ(x)作为患病倾向的函数。通过模拟研究，我们比较了对数转换支出的两部分回归平方与最大似然估计的频率特性。
The methodological development of this paper is motivated by a common problem in econometrics where we are interested in estimating the difference in the average expenditures between two populations, say with and without a disease, as a function of the covariates. For example, letY1andY2be two nonnegative random variables denoting the health expenditures for cases and controls. Smooth Quantile Ratio Estimation (SQUARE) is a novel approach for estimating Δ =E[Y1] −E[Y2] by smoothing across percentiles the log-transformed ratio of the two quantile functions. Dominiciet al.(2005) have shown that SQUARE defines a large class of estimators of Δ, is more efficient than common parametric and nonparametric estimators of Δ, and is consistent and asymptotically normal. However, in applications it is often desirable to estimate Δ(x) =E[Y1|x] −E[Y2|x], that is, the difference in means as a function ofx. In this paper we extend SQUARE to a regression model and we introduce a two-part regression SQUARE for estimating Δ(x) as a function ofx. We use the first part of the model to estimate the probability of incurring any costs and the second part of the model to estimate the mean difference in health expenditures, given that a nonzero cost is observed. In the second part of the model, we apply the basic definition of SQUARE for positive costs to compare expenditures for the cases and controls having ‘similar’ covariate profiles. We determine strata of cases and control with ‘similar’ covariate profiles by the use of propensity score matching. We then apply two-part regression SQUARE to the 1987 National Medicare Expenditure Survey to estimate the difference Δ(x) between persons suffering from smoking-attributable diseases and persons without these diseases as a function of the propensity of getting the disease. Using a simulation study, we compare frequentist properties of two-part regression SQUARE with maximum likelihood estimators for the log-transformed expenditures.