Dose-response and trend
What question does this help answer?
Whether the relationship behaves as a causal one usually does, and where along the exposure range the risk actually changes, which matters for any threshold or guideline that follows.
Why the gradient matters
A monotonic gradient is one of the classic considerations in causal reasoning, because a chance association or a crude bias is less likely to produce an orderly progression across levels. It is supportive evidence, not proof, and its absence is not disproof either: threshold effects, saturation and competing mechanisms all produce non-monotonic true relationships.
How to model it
- Prefer keeping the exposure continuous and modelling its shape with splines, rather than categorising it at all.
- If categories are used, report the estimate for each level against a common reference, with the reference chosen for interpretability and stated.
- For a formal trend test, assign scores that reflect the actual exposure values (a median within category, say) rather than 1, 2, 3, and say which was used.
- Report the exposure distribution alongside the estimates, so a dramatic top-category effect resting on few people is visible.
- Test departure from linearity as well as the trend itself.
Cumulative exposure needs a time model
Pack-years, cumulative dose and years of employment all fold intensity and duration into one number, which assumes they act interchangeably. Twenty cigarettes for ten years and ten cigarettes for twenty years are the same pack-years and are not necessarily the same risk. Where the data allow, model intensity and duration separately and check.
Why Mallard may recommend it
Mallard may propose a trend analysis when the exposure is graded and the causal question would be strengthened by showing the gradient, and it will prefer a spline over categories where the data support one.
What to watch out for
A trend test assumes a shape, and the usual one assumes the effect is linear in whatever scale the categories were coded on, which is rarely defensible when the categories are quartiles of a skewed exposure. Assigning the category midpoint as a score builds in an assumption about spacing that the data may contradict. And a dose-response gradient strengthens a causal argument but does not establish it: confounders that themselves increase with exposure produce the same gradient.
Clinical example
Question: Does risk rise with cumulative occupational exposure? Analysis: Model exposure continuously with a restricted cubic spline, plot the fitted curve with a confidence band, and report a formal trend test using median within-category exposures alongside a test for departure from linearity.
- Methods for trend estimation from summarized dose-response data, with applications to meta-analysis (opens in a new tab) · Am J Epidemiol · doi 10.1093/oxfordjournals.aje.a116237
- Cubic splines to model relationships between continuous variables and outcomes: a guide for clinicians (opens in a new tab) · Bone Marrow Transplant · doi 10.1038/s41409-019-0679-x