@Lidya1888 good question. It depends on the context, but probably, no. Generally in epidemiology, risk means the probability of something bad happening during some time interval. Here's a definition in Modern Epi 4e (p57):

(see also https://en.wikipedia.org/wiki/Risk).

In a cross-sectional study, there's usually no time interval, and you can't measure incidence/risk, only prevalence, unless you're making some strong assumptions and/or using data fusion. Do you have a particular use case in mind?

Thank you! In the note, it mentions that if a cross-sectional study is a probability sample of a population (which it rarely is), then we can estimate risks. So, is the note specifically referring to acute and short-lived diseases, and not all types of diseases even if the sampling is probabilistic?

@Lidya1888 are you referring to https://d-morrison.github.io/rme/logistic-regression.html#odds-ratios-in-cross-sectional-studies ?

Using the word "risk" in that section was probably not ideal. I'll change it to "prevalence": https://github.com/d-morrison/rme/pull/229/files.

"Risk" sometimes gets used to mean the probability of having an ongoing infection at a given time point (in other words, prevalence), but usually it refers to the probability of a new infection during a given time period (i.e., the cumulative incidence proportion).

Under some assumptions, there is a relationship between incidence, prevalence, and duration of disease, as you alluded to (see section "Prevalence, Incidence, and Mean Duration" in Modern Epi 4, p. 73-74, for more details), but generally, when analyzing cross-sectional studies, I would recommend avoiding the term "risk".

Does that help at all?