- Published
- Updated
Transforming a variable to a logarithmic or other scale can help modelling. The meaning of a difference on that scale still needs explanation on the clinical scale. Units and interpretation should not change silently when estimates are returned to their original presentation.
Define the question and assumptions
Define the transformation rationale, treatment of zero or negative values and back-transformation method. Back-transforming a transformed mean does not necessarily recover an arithmetic mean. Name the effect measure correctly and avoid interchanging ratios with differences. Review assumptions, clinical meaning and table units together rather than treating transformation as a purely technical programming step.
Hypothetical study example
In a hypothetical study, a difference on the log scale is labelled as an arithmetic mean difference in original units. The team corrects the derivation and heading, explaining which quantity is produced. It does not choose the more impressive-looking number or change underlying group definitions to support a preferred interpretation.
Design review checks
- Record the transformation and rules for special or out-of-domain values.
- Confirm whether the returned estimate represents a ratio, difference or another quantity.
- Check that interval limits receive the corresponding appropriate transformation.
Record the decision and its limits
Accepted outputs include headings and footnotes understandable to clinical readers. Check numerical and interpretive correctness separately. Identify planned or supportive roles for alternative scales rather than changing the main scale for a smaller p-value. Report measurement and source-quality limitations that the transformation does not resolve, even when the model fits successfully.
Frequently asked questions
- Is a back-transformed mean an arithmetic mean?
- Not for every transformation. State which quantity was calculated.
- Are units alone enough?
- No. Define the effect measure and the back-transformation approach.