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Odds Ratio & Relative Risk

Odds Ratio (OR) and Relative Risk (RR) both quantify the association between an exposure and a binary outcome — but they are not interchangeable. Licklider detects the study design, selects the appropriate effect measure, and enforces the disclosure of whether OR or RR was used and why, along with the Absolute Risk Reduction (ARR) and Number Needed to Treat (NNT).

STEP 1 — The Scenario

Researcher Profile — Two Parallel Scenarios

This use case covers two researchers with the same 2×2 table data but different study designs, to illustrate when OR vs. RR is appropriate:

  • Scenario A (Case-Control): An epidemiologist studying whether smoking is associated with bladder cancer. Cases (n=100 bladder cancer) and controls (n=200 cancer-free) are recruited retrospectively. Smoking status is ascertained for both groups.
  • Scenario B (Prospective Cohort / RCT): A clinical researcher following 300 patients prospectively over 5 years. Half received a statin (n=150), half did not (n=150). Outcome: cardiovascular event (Yes/No).

Research Questions

  • Scenario A: "What is the odds of bladder cancer associated with smoking vs. non-smoking?" (OR)
  • Scenario B: "What is the risk of cardiovascular events in statin users vs. non-users, and what is the absolute risk reduction?" (RR, ARR, NNT)

STEP 2 — Licklider Analysis Path

1. Study Design Declaration

Licklider asks: "What is the study design?" Options: Prospective cohort / RCT → RR is appropriate. Case-control (retrospective sampling by outcome) → OR is the only valid measure. Cross-sectional → Prevalence Ratio or OR depending on the outcome prevalence.

2. 2×2 Table Construction

From individual-level data or a pre-formatted table: a, b, c, d cells are constructed. Licklider verifies the table orientation (rows=exposure, columns=outcome).

3. Scenario A — Odds Ratio

OR = (a/c) / (b/d) = ad/bc. 95% CI via Woolf method (ln(OR) ± 1.96×SE, where SE=√(1/a+1/b+1/c+1/d)). If any cell = 0, Haldane correction (add 0.5 to all cells) is applied and disclosed.

4. Scenario B — Relative Risk & ARR

RR = [a/(a+b)] / [c/(c+d)]. 95% CI via log method. Additionally: ARR = Risk in exposed − Risk in unexposed = a/(a+b) − c/(c+d). NNT = 1/ARR. All three (RR, ARR, NNT) are calculated and reported together.

5. Figure Generation

A forest-style plot showing the OR or RR with 95% CI. A vertical reference line at OR/RR=1 (null). For Scenario B, a separate panel shows the ARR and NNT with their 95% CIs.

STEP 3 — Guards & Disclosures Activated

OR vs. RR Enforcement

If a prospective cohort or RCT design is declared and the outcome is common (>10%), Licklider blocks the use of OR as the primary effect measure and requires RR or Risk Difference instead. The guard message: "Odds Ratio overestimates Relative Risk when the outcome is common. For prospective designs with a common outcome, use RR or ARR."

Causal Language Detection (3.1.5)

For case-control data, causal language ("smoking causes bladder cancer") is blocked. The guard requires "smoking was associated with increased odds of bladder cancer (OR=[value])." For RCTs, where causal inference is more defensible, the guard allows "statin treatment was associated with a reduced risk" but flags "statin treatment prevented cardiovascular events" as potentially causal.

Effect Size + CI + N Mandatory (3.1.2)

OR or RR without 95% CI cannot be exported. For Scenario B, ARR and NNT without CIs are also blocked (NNT 95% CI is calculated from ARR CI boundaries).

N Disclosure (1.2.1)

Both the total n and the n per group are required. For case-control designs, the case-to-control ratio is disclosed. For prospective designs, the follow-up duration and censoring summary are required.

STEP 4 — Export Package

  • Scenario A Figure: Forest plot — OR (95% CI) — 300 dpi TIFF/PDF
  • Scenario B Figure: Forest plot + ARR/NNT panel — 300 dpi TIFF/PDF
  • Statistical Report (Scenario A): 2×2 table with OR (95% CI, Woolf method); p-value (chi-square or Fisher's); Cramér's V; case-to-control ratio; exposure rates per group
  • Statistical Report (Scenario B): 2×2 table with RR, ARR, NNT (all with 95% CI); event rates per arm; follow-up duration; study design declaration
  • Methods Text (Scenario A): "The association between smoking and bladder cancer was assessed in a case-control design. Odds Ratio and 95% CI were calculated using the Woolf method. Results are expressed as associations; causal inference is not implied. Cases: n=100; Controls: n=200."
  • Methods Text (Scenario B): "Cardiovascular event rates were compared between statin and non-statin groups in a prospective cohort. Relative Risk, Absolute Risk Reduction, and Number Needed to Treat are reported with 95% CIs. n=300; follow-up: 5 years."
  • Preprocessing Audit Log: Study design declaration; OR vs. RR selection rationale; Haldane correction applied (if any cell = 0)