Dose-Response Analysis — Quantifying How Exposure Level Relates to Outcome Risk

A linear trend test collapses the dose-response relationship into a single slope coefficient and tests whether that slope differs from zero. It is concise but assumes linearity and cannot detect threshold or U-shaped patterns. A full dose-response model — using splines or polynomials — estimates the entire exposure-risk curve, revealing whether the relationship is linear, non-linear, or threshold-dependent. Both approaches are complementary and should usually be reported together.

Yes. In a case-control study, exposure categories are defined for both cases and controls, and odds ratios for each exposure level relative to the reference category are estimated using conditional or unconditional logistic regression. The ordinal exposure score is then entered as a continuous variable in the model to test for trend. The interpretation is analogous to cohort study analysis, but the odds ratio approximates the relative risk only when the outcome is rare.

The Greenland and Longnecker (1992) method is the standard approach. It reconstructs the covariance matrix of the log relative risks across exposure categories from each study and then uses generalized least squares to fit a common dose-response trend. This requires that individual studies report the number of cases and person-time (or controls) per exposure category along with the adjusted effect estimate — information that is sometimes missing from published reports.

Restricted cubic splines (also called natural splines) are generally preferred over polynomials because they fit flexibly in the interior of the exposure range while being constrained to be linear in the tails, which avoids erratic extrapolation beyond the data. Polynomials can produce implausible curves at the extremes. For most epidemiological dose-response analyses, three to five knots placed at quantiles of the exposure distribution provide a good balance between flexibility and parsimony.

No. A dose-response gradient is one of Bradford Hill's criteria that strengthens a causal argument, but it is neither necessary nor sufficient on its own. Confounding, reverse causation, and exposure misclassification can all produce or mask a gradient. The dose-response evidence must be interpreted alongside temporality, consistency across studies, biological plausibility, and other causal criteria.