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Consider the probability $p$ of an event in the full population, and the probability $p_0$ of the same event for a subset of the population. In other words, $p_0$ is a conditional probability (conditioned on belonging to that subset).

As an example, $p$ may be the probability of having a disease, and $p_0$ may be the probability of having that desease for people of a certain ethnicity.

To clarify, $p_0/p$ is akin to relative risk, but not the same. Relative risk would be $p_0/p_1$, where $p_1$ is the probability of having a disease for people that are not of the considered ethnicity. At least that's how I've always seen relative risk defined.

Does the ratio $p_0/p$ have a name? Is there an application field or a specific setting where $p_0/p$ is typically used?

Luis Mendo
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  • Loosely related question – Luis Mendo Apr 28 '23 at 18:45
  • By the law ot total probability, $p_0/p$ in the example is equivalent to the probability of being of that ethnicity conditioned on having the disease, divided by the unconditional probability of being of that ethnicity. If the latter is a known fraction $f$, then $p_0/p$ is just the probability of the ethnicity conditioned on the disease, divided by the known $f$. – Luis Mendo Apr 29 '23 at 16:51

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