Questions: Dose-Response Analysis and Exposure-Outcome Curves

Question 1

A cohort study finds that people who consume 1 serving of red meat per week have an RR of 1.1 for colorectal cancer, 2 servings/week = RR 1.2, and 3+ servings/week = RR 1.35 — a clear stepwise gradient. A researcher concludes this dose-response pattern proves red meat causes colorectal cancer. What is wrong with this conclusion?

• A. Nothing — a dose-response gradient is the strongest possible evidence for causation in epidemiology
• B. The gradient could still reflect confounding (e.g., higher meat consumers may also smoke more or exercise less), reverse causation, or exposure measurement error — all of which can produce apparent gradients without a causal relationship
• C. The study is invalid because it used relative risks instead of odds ratios
• D. Dose-response analysis only applies to toxicological studies, not nutritional epidemiology

Answer: (B)

A dose-response gradient is one of Bradford Hill's criteria that strengthens causal inference — but it is not proof of causation. Confounders that co-vary with the exposure at every level of the dose can produce a gradient. Reverse causation (sick people changing their diet) can produce a gradient. Differential measurement error across exposure levels can create artifactual gradients. The dose-response pattern shifts the evidentiary bar because a confounder would need to track exposure quantity precisely across the distribution — but this is possible, especially for lifestyle exposures that cluster. Causal inference requires considering the full evidence, not just the gradient.

Question 2

A researcher studying alcohol and cardiovascular disease fits a linear regression model to the dose-response relationship. The model estimates a constant reduction in risk per standard drink per day. Why might restricted cubic splines be a better choice for this analysis?

• A. Because splines always produce better statistical fit than linear regression
• B. Because the true relationship may be non-linear — for example, showing a J-shaped curve where low doses are protective and high doses are harmful — and imposing linearity would miss or mischaracterize this shape
• C. Because splines provide lower p-values, making the dose-response more statistically significant
• D. Because Bradford Hill's biological gradient criterion requires a non-linear functional form

Answer: (B)

The functional form of a dose-response relationship carries biological meaning. A linear model assumes constant effect per unit of exposure across the entire range — sometimes true, often not. For alcohol, the relationship is debated but may show J-shaped or threshold patterns. A threshold model would show no effect at low doses. A supralinear model would show disproportionate risk at the lowest doses. Restricted cubic splines let the data determine the shape by fitting flexible polynomial segments through knot points without imposing a predetermined functional form. Mischaracterizing the shape (e.g., imposing linearity on a threshold relationship) can lead to incorrect policy or clinical conclusions.

Question 3

Evidence of a dose-response gradient strengthens causal inference in part because it is harder for a confounding variable to produce a precisely graded relationship across the full exposure distribution than to produce a simple exposed-versus-unexposed association.

• T. True
• F. False

Answer: True

This is the core epidemiological logic behind using dose-response as evidence for causality. For a confounder to produce a gradient mimicking a true dose-response, it would have to be positively and monotonically associated with the exposure at every quantile of exposure, not just on average. While possible — lifestyle confounders like socioeconomic status can do this — it is a more demanding coincidence than simple confounding of an exposed/unexposed comparison. The gradient doesn't rule out confounding but raises the evidentiary threshold for explaining away the association.

Question 4

Observing a dose-response relationship between an exposure and an outcome is sufficient evidence to conclude that the exposure causes the outcome.

• T. True
• F. False

Answer: False

Dose-response is one of several causal considerations (Bradford Hill criteria), not a definitive proof. Three threats to causal interpretation can produce apparent dose-response gradients: reverse causation (sicker individuals change their behavior in a dose-related way), confounding (a third variable that tracks exposure quantity), and exposure measurement error (differential misclassification across the distribution). A dose-response gradient must be evaluated alongside study design quality, biological plausibility, consistency across studies, and other considerations. Interpreting a gradient as proof of causation is a common error in nutritional and environmental epidemiology.

Question 5

Explain why reverse causation is a particular threat to the validity of dose-response analyses, and give an example of how it could produce a spurious gradient.

Model answer: Reverse causation occurs when the outcome (or its precursor) influences the exposure rather than the reverse. In dose-response analysis, this can produce a gradient if the severity of disease systematically changes how much of the exposure a person consumes. For example: a study might find that people who drink more alcohol have lower cardiovascular disease risk at low doses — a classic J-curve. But reverse causation could explain this: people who already have cardiovascular disease (or are at high risk) may reduce or stop drinking on medical advice, making abstainers look sicker than light drinkers. The apparent protective gradient at low doses reflects sick people avoiding alcohol, not alcohol protecting health. The gradient is real in the data but causally reversed.

Reverse causation is particularly insidious in dose-response analysis because it can mimic biologically plausible gradients. Unlike simple confounding (where you might identify the confounder and adjust), reverse causation is a structural problem — the temporal ordering of cause and effect is wrong. The solution is prospective study design (measuring exposure before disease onset), restriction to healthy participants at baseline, and lagged analysis (excluding early follow-up where disease may already be influencing behavior). Without these design elements, apparent protective dose-response relationships for common lifestyle exposures should be interpreted with caution.