Berkson's Paradox

Berkson's original argument

Berkson (1946) pointed out that analyzing the association between two diseases using hospital inpatient data can lead to false conclusions. Because having either disease is enough to be admitted, among hospitalized patients those without one disease are more likely to have the other. As a result, two diseases that are independent in the general population show a negative correlation in a hospital sample. Roberts and colleagues (1978) confirmed the bias empirically by comparing community and hospital samples, and Sackett (1979) included it in his catalog of biases arising from study design.

Colliders and causal graphs

In Pearl's (2009) causal graph framework, the phenomenon is explained as conditioning on a collider. If you hold fixed, or select your sample by, a variable that two causes both affect, where the arrows collide, a spurious association appears between causes that were originally independent. Greenland, Pearl and Robins (1999) brought these graphical tools into study design, and Hernán, Hernández-Díaz and Robins (2004) unified selection bias in general under this structure. Elwert and Winship (2014) systematically cataloged cases of endogenous selection bias in sociological research. In economics, Heckman (1979) formalized the sample selection bias that arises when a wage equation is estimated using only employed workers whose wages are observed, a problem of the same family. Where Simpson's paradox is an illusion created by splitting or pooling groups, Berkson's paradox is an illusion created by how cases enter the sample.

Examples from everyday life and data science

Pearl and Mackenzie (2018) and Ellenberg (2014) illustrated it with everyday examples. If someone only dates people who clear a bar on either looks or personality, then among the people they date, better looks may seem to go with a worse personality. Similar patterns appear among students admitted on either grades or another strength, and in film criticism where only hits are remembered. Munafò and colleagues (2018) warned that in data where participation itself is selected, such as large biobanks, this bias can substantially change research conclusions, and Griffith and colleagues (2020) showed that in infectious disease studies analyzing only people who were tested, collider bias can distort estimates of risk factors. Along with survivorship bias, it is one of the most common pitfalls in analyzing observational data.

FAQ

What is Berkson's paradox in simple terms?

Even when two traits have nothing to do with each other, if you only look at a group where people get in by having at least one of them, the stronger one trait is, the weaker the other seems.

How is it different from Simpson's paradox?

Simpson's paradox is when the direction of a relationship flips depending on whether data are split into subgroups or pooled. Berkson's paradox is when a correlation that doesn't exist appears because of how the sample was selected.

Sources reviewed: 2026-10-26

References

1. Berkson, J. (1946). Limitations of the application of fourfold table analysis to hospital data. Biometrics Bulletin, 2(3), 47–53.
2. Roberts, R. S., Spitzer, W. O., Delmore, T., & Sackett, D. L. (1978). An empirical demonstration of Berkson's bias. Journal of Chronic Diseases, 31(2), 119–128.
3. Sackett, D. L. (1979). Bias in analytic research. Journal of Chronic Diseases, 32(1–2), 51–63.
4. Pearl, J. (2009). Causality: Models, Reasoning, and Inference (2nd ed.). Cambridge: Cambridge University Press.
5. Pearl, J., & Mackenzie, D. (2018). The Book of Why: The New Science of Cause and Effect. New York: Basic Books.
6. Hernán, M. A., Hernández-Díaz, S., & Robins, J. M. (2004). A structural approach to selection bias. Epidemiology, 15(5), 615–625.
7. Greenland, S., Pearl, J., & Robins, J. M. (1999). Causal diagrams for epidemiologic research. Epidemiology, 10(1), 37–48.
8. Elwert, F., & Winship, C. (2014). Endogenous selection bias: The problem of conditioning on a collider variable. Annual Review of Sociology, 40, 31–53.
9. Heckman, J. J. (1979). Sample selection bias as a specification error. Econometrica, 47(1), 153–161.
10. Griffith, G. J., et al. (2020). Collider bias undermines our understanding of COVID-19 disease risk and severity. Nature Communications, 11, 5749.
11. Munafò, M. R., Tilling, K., Taylor, A. E., Evans, D. M., & Davey Smith, G. (2018). Collider scope: When selection bias can substantially influence observed associations. International Journal of Epidemiology, 47(1), 226–235.
12. Ellenberg, J. (2014). How Not to Be Wrong: The Power of Mathematical Thinking. New York: Penguin Press.
13. Snoep, J. D., Morabito, M., Bernardi, M., et al. (2014). Commentary: A structural approach to Berkson's fallacy and a guide to a history of opinions about it. International Journal of Epidemiology, 43(2), 515–521.