From the aDepartment of Epidemiology, Biostatistics, and Occupational Health, McGill University, Montreal, QC, Canada; and bInstitut national de santé publique du Québec, and Research Centre of the University of Montreal Hospital Centre, Montreal, QC, Canada.
Epidemiology. 2014 Mar;25(2):292-9. doi: 10.1097/EDE.0000000000000053.
Inverse probability-weighted marginal structural models with binary exposures are common in epidemiology. Constructing inverse probability weights for a continuous exposure can be complicated by the presence of outliers, and the need to identify a parametric form for the exposure and account for nonconstant exposure variance. We explored the performance of various methods to construct inverse probability weights for continuous exposures using Monte Carlo simulation. We generated two continuous exposures and binary outcomes using data sampled from a large empirical cohort. The first exposure followed a normal distribution with homoscedastic variance. The second exposure followed a contaminated Poisson distribution, with heteroscedastic variance equal to the conditional mean. We assessed six methods to construct inverse probability weights using: a normal distribution, a normal distribution with heteroscedastic variance, a truncated normal distribution with heteroscedastic variance, a gamma distribution, a t distribution (1, 3, and 5 degrees of freedom), and a quantile binning approach (based on 10, 15, and 20 exposure categories). We estimated the marginal odds ratio for a single-unit increase in each simulated exposure in a regression model weighted by the inverse probability weights constructed using each approach, and then computed the bias and mean squared error for each method. For the homoscedastic exposure, the standard normal, gamma, and quantile binning approaches performed best. For the heteroscedastic exposure, the quantile binning, gamma, and heteroscedastic normal approaches performed best. Our results suggest that the quantile binning approach is a simple and versatile way to construct inverse probability weights for continuous exposures.
反向概率加权边际结构模型在医学领域应用广泛，可用于研究二分类暴露因素。但构建连续型暴露的逆概率权重时，由于存在异常值，需要确定暴露的参数形式，并考虑非恒定的暴露方差，因此较为复杂。本研究通过蒙特卡罗模拟，探讨了不同连续型暴露逆概率权重构建方法的性能。采用来自大型经验队列的数据，模拟两种连续型暴露和二分类结局。第一种暴露符合正态分布，方差齐性；第二种暴露符合污染泊松分布，异方差等于条件均值。使用六种方法构建逆概率权重：正态分布、正态分布加异方差、截断正态分布加异方差、伽马分布、t 分布（1、3 和 5 自由度）和分位数分箱法（基于 10、15 和 20 个暴露类别）。在回归模型中，对每个模拟暴露的单位增加量进行加权，权重为每种方法构建的逆概率权重，估计边际优势比，并计算每种方法的偏倚和均方误差。对于同方差暴露，标准正态、伽马和分位数分箱方法表现最佳；对于异方差暴露，分位数分箱、伽马和异方差正态方法表现最佳。研究结果表明，分位数分箱法是一种构建连续型暴露逆概率权重的简单、通用方法。
