Odds Ratios: Do most people get them wrong?

Odds ratios show up everywhere in medical research—but do readers, journalists, and even researchers always know what they mean? In this episode, we tackle one of the most common statistical misunderstandings in science: treating odds ratios like risk ratios. Along the way, we explore puppy photos, fish photos, first-date hookups, sugary drinks, cardiac care, and a listener challenge that started with an informal study of five medical residents and a box of chocolate truffles. We explain why logistic regression produces odds ratios, when odds ratios can wildly exaggerate effects, and why some famous headlines turned out to be much less dramatic than they sounded.

Statistical topics

• binary outcomes
• case-control studies
• logistic regression
• odds ratios
• risk ratios
• odds vs risk

Methodological morals

• “Just because logistic regression gives you an odds ratio does not mean you have to report it.”
• “A lot of bad science communication starts long before the journalist even enters the story.”

References

• Bleich SN, Herring BJ, Flagg DD, et al. Reduction in purchases of sugar-sweetened beverages among low-income Black adolescents after exposure to caloric information. Am J Public Health. 2012;102:329–35.
• Sainani KL. How Statistics Can Mislead. Am J Public Health. 2012. 2012;102:e3–e4.
• Bleich SN, Herring BJ, Flagg DD, et al. Bleich et al. respond. Am J Public Health. 2012;102:e4.
• Press video: https://www.youtube.com/watch?v=IFyrqbf1XWs
• Sainani KL, Schmajuk G, Liu V. A Caution on Interpreting Odds Ratios. Sleep. 2009;32:976.
• Schulman KA, Berlin JA, Harless W, et al. The Effect of Race and Sex on Physicians' Recommendations for Cardiac Catheterization. NEJM. 1999;340:618–26.
• Schwartz LM, Woloshin S, Welch HG. Misunderstandings about the Effects of Race and Sex on Physicians' Referrals for Cardiac Catheterization. NEJM. 1999;341:279–83.
• Associated Press. Study Finds Bias in Doctors' Care of Women and Blacks. The New York Times. February 25, 1999.
• Knol MJ, Duijnhoven RG, Grobbee DE, et al. Potential Misinterpretation of Treatment Effects Due to Use of Odds Ratios and Logistic Regression in Randomized Controlled Trials. PLoS ONE. 2011;6:e21248.

More information on logistic regression and odds ratios:

• Sainani KL. Logistic Regression. PM&R. 2014;6:1157–62.
• Sainani KL. Understanding Odds Ratios. PM&R. 2011;3:263–67.
• Nuzzo RL. Communicating measures of relative risk in plain English. PM&R. 2022;14:283-287.

When outcomes are common, odds ratios can exaggerate effect sizes. Alternatives include:

• Presenting raw percentages (absolute risks)
• Presenting adjusted percentages from logistic regression (these may be calculated by plugging in means for the covariates)
• Converting odds ratios to risk ratios
• Reporting risk ratios directly when appropriate

Converting Odds Ratios to Risk Ratios:

• Zhang J, Yu KF. What's the Relative Risk? A Method of Correcting the Odds Ratio in Cohort Studies of Common Outcomes. JAMA. 1998;280:1690–91.
• ClinCalc. Odds Ratio to Relative Risk Calculator.
• https://clincalc.com/stats/convertor.aspx
• RR = OR / [(1 − P0) + (P0 × OR)]

Example:

OR=0.51, baseline risk=93.3%

RR = 0.51 / [(1 − 0.933) + (0.933 × 0.51)]

= 0.51 / (0.067 + 0.476)

= 0.51 / 0.543

= 0.94

Thus, an odds ratio of 0.51 corresponds to a risk ratio of 0.94 when the baseline risk is 93.3%.

The corresponding unadjusted risk ratio is 86%/93.3%=0.92

Correction: In the episode, we stated that the adjusted risk ratio was 0.92. In fact, it is 0.94, as shown above. 0.92 is the unadjusted risk ratio.

Kristin and Regina’s online courses:

Demystifying Data: A Modern Approach to Statistical Understanding

Clinical Trials: Design, Strategy, and Analysis

Medical Statistics Certificate Program

Writing in the Sciences

Epidemiology and Clinical Research Graduate Certificate Program

Programs that we teach in:

Epidemiology and Clinical Research Graduate Certificate Program

Find us on:

Kristin - LinkedIn & Twitter/X

Regina - LinkedIn & ReginaNuzzo.com

• (00:00) - Introduction
• (02:54) - What Are Odds Ratios?
• (04:02) - Puppy Photos and First Dates
• (06:09) - Risk Ratio Explained
• (08:10) - Calculating Odds Ratios
• (11:09) - Fish Photos and Reversed Numbers
• (16:01) - Real-Life Example: Sugary Beverages
• (22:08) - How Logistic Regression Works
• (31:53) - The Video: Researchers Made the Mistake Themselves
• (36:30) - The Cardiac Catheterization Study
• (39:24) - The New York Times Printed a Correction
• (46:10) - Using OR and RR Interchangeably for Case Control
• (47:00) - Reye Syndrome and Aspirin
• (49:37) - Rating the Claim and Methodological Morals