  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.

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