Beyond Berkson: Further Light on the Selection Bias

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Abstract

The Berkson effect shows that two independent diseases, A and B, become negatively correlated if they are confined within the walls of a hospital. We explain that, simply by adding a third disease, C, the negative correlation may flip into a positive one, and we identify the point where this happens. That leads to a necessary and sufficient condition for a positive as well as a negative correlation between A and B. We further explain that a flip from negative to positive is impossible if C is independent of A, of B, and of the disjunction of A and B: with these three independences in place, the Berkson effect remains in force. However, if only two of the three independences hold, the effect is not guaranteed.
Original languageEnglish
JournalNotre Dame Journal of Formal Logic
Publication statusAccepted/In press - Nov-2024

Keywords

  • Berkson Effect, probability, independence, selection bias

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