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Difficulty: HardMeasures of Disease Frequency and Association

A clinical investigator is presenting findings from a retrospective cohort study at a surgical conference. The study aimed to evaluate whether a newly implemented anesthetic protocol reduces the incidence of postoperative nausea and vomiting (PONV) in patients undergoing laparoscopic cholecystectomy. The investigator presents the following data collected from electronic health records:

GroupTotal PatientsPatients Developing PONV
Standard Protocol400200
Modified Protocol400100

During the presentation, the investigator concludes: "Our statistical analysis demonstrates an odds ratio of 0.330.33 for the modified protocol. This indicates that patients receiving the new protocol have a 67%67\% lower risk of developing PONV compared to those receiving the standard protocol."

Which of the following is the most accurate critique of the investigator's conclusion?

  1. The odds ratio overestimates the actual risk reduction because the outcome is common.Answer
  2. B
    Relative risk cannot be directly calculated because the data was collected retrospectively.
  3. C
    The odds ratio represents the positive predictive value of the protocol rather than the reduction in risk.
  4. D
    The observed reduction in postoperative nausea and vomiting is due to effect modification rather than a true association.
  5. E
    The efficacy of the new protocol should have been evaluated using a root cause analysis instead of a cohort design.

Answer

The odds ratio overestimates the actual risk reduction because the outcome is common.
The rare disease assumption states that the odds ratio (OR) provides a valid mathematical approximation of the relative risk (RR) only when the outcome is infrequent (typically defined as <10%< 10\% incidence). In this retrospective cohort study, the incidence of the outcome (PONV) is very high (50%50\% in the standard group and 25%25\% in the modified group). The true relative risk is 0.500.50, corresponding to a 50%50\% relative risk reduction. By utilizing an odds ratio of 0.330.33, the investigator inappropriately claims a 67%67\% risk reduction. When an outcome is common, an odds ratio that is further from 1.01.0 will always exaggerate the magnitude of the clinical association compared to the true relative risk. Consequently, a protective exposure appears significantly more protective than it actually is.

Step-by-Step Solution

1
Calculate the true Relative Risk (RR) and Relative Risk Reduction (RRR) based on the cohort data.
Standard protocol risk = 200/400=0.50200/400 = 0.50 (50%50\%). Modified protocol risk = 100/400=0.25100/400 = 0.25 (25%25\%). True RR = 0.25/0.50=0.500.25 / 0.50 = 0.50. True RRR = 1−0.50=0.501 - 0.50 = 0.50 (50%50\%).
To determine the actual mathematical reduction in risk afforded by the new protocol.
2
Calculate the Odds Ratio (OR) to verify the investigator's claim.
Standard odds = 200/200=1200 / 200 = 1. Modified odds = 100/300=0.33100 / 300 = 0.33. OR = 0.33/1=0.330.33 / 1 = 0.33. Claimed reduction = 1−0.33=0.671 - 0.33 = 0.67 (67%67\%).
To understand how the investigator derived the 67%67\% risk reduction statement from the raw data.
3
Compare the OR to the true RR using the rare disease assumption.
The OR (0.330.33) makes the intervention appear more effective than the true RR (0.500.50). Because the baseline risk is high (50%50\%), the OR significantly overestimates the true protective effect.
The odds ratio only approximates relative risk when the outcome incidence is low (typically <10%< 10\%).

Key Concept

Rare Disease Assumption (Odds Ratio vs. Relative Risk)
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Topics

Measures of Disease Frequency and Association

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