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

Estimating quantile treatment effect on the original scale of the outcome variable: a case study of common cold treatments