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Estimating quantile treatment effect on the original scale of the outcome variable: a case study of common cold
1Department of Public Health, University of Helsinki, POB 20, Helsinki, FI-00014, Finland. harri.hemila@helsinki.fi.
Background:
Effects of treatments on continuous outcomes are commonly estimated using the mean difference (in units of measurement) or the ratio of means (percentages), each providing a single average effect across the study population. Quantile treatment effect (QTE) analysis is more informative as it estimates the effect of treatment across the whole population. A limitation of the standard QTE is its presentation over control group quantiles, which can hinder interpretability. Presentation of the effect over the measurement units would often be more informative.
Methods:
We introduce a method to estimate back-transformed QTE (BQTE), which presents QTEs as a function of the original outcome values in the control group. This approach uses a bootstrap algorithm to estimate both the BQTE curve and its uncertainty. We further derive informative bounds for the average treatment effect at the upper and lower tails of the distribution. The method was applied to 3 datasets on the treatment of the common cold: zinc gluconate lozenges, zinc acetate lozenges, and nasal carrageenan.
Results:
Across all 3 datasets, BQTE revealed substantial heterogeneity in treatment effects on the units of measurement scale (days). Specifically, shorter colds showed smaller average effects than longer colds, indicating that the assumption of a constant mean difference across the distribution may be inappropriate. In all cases, the relative scale provided a better summary of the BQTE distribution than the mean difference.
Conclusions:
The BQTE method enhances the interpretability of QTEs by presenting results on the outcome's original scale. It provides a nuanced understanding of how the average treatment effect varies across the distribution. BQTE is particularly suited for analyzing continuous clinical outcomes such as illness duration or hospital stay and offers a valuable complement to the standard effect size measures in individual-patient data meta-analysis and clinical trial reporting.
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