The effects of treatments on continuous outcomes can be estimated by the mean difference (i.e. by measurement units) and the relative effect scales (i.e. by percentages), both of which provide only a single effect size estimate over the study population. Quantile treatment effect (QTE) analysis is more informative as it describes the effect of the treatment across the whole population. A drawback of QTE has been that it is usually presented over the quantiles of the control group distribution, whereas presentation over the measurement units is often more informative. We developed a method to estimate back-transformed QTE (BQTE), that presents QTE as a function of the outcome value in the control group, using piecewise linear interpolation and bootstrapping. We further applied the BQTE function to provide informative bounds on the treatment effect at the upper and lower tails of the population. To illustrate the approach, we used 3 data sets of treatment for the common cold: zinc gluconate lozenges, zinc acetate lozenges, and nasal carrageenan. In all data sets, the relative scale provided a better summary of the BQTE distribution than the mean difference. The BQTE approach is particularly useful for describing the variability of effects on the duration of illnesses, length of hospital stay and other continuous outcomes that can vary greatly in the population. Using this method, it is possible to present the QTE by the measurement units, which provides an informative addition to the standard presentation by quantiles.

翻译：连续型结果变量的处理效应可通过均值差异（即测量单位）和相对效应尺度（即百分比）进行估计，但二者仅提供研究人群中的单一效应量估计。分位数处理效应（QTE）分析更具信息价值，因其描述了处理在整个群体中的效应。传统QTE的局限在于通常基于对照组分布的分位数呈现，而基于测量单位的呈现往往更具信息性。我们开发了一种方法用于估计反向转换分位数处理效应（BQTE），该方法通过分段线性插值与自助法，将QTE呈现为对照组结果值的函数。进一步地，我们应用BQTE函数为人群上下尾部的处理效应提供了信息性边界。为演示该方法，我们采用了三个普通感冒治疗数据集：葡萄糖酸锌含片、醋酸锌含片和鼻用卡拉胶。在所有数据集中，相对尺度对BQTE分布的概括优于均值差异。BQTE方法尤其适用于描述疾病持续时间、住院时长等群体变异较大的连续型结果变量的效应变异性。通过该方法，可按测量单位呈现QTE，为标准的基于分位数呈现提供了具有信息量的补充。