Wikipedia:Reference desk/Archives/Mathematics/2015 September 9

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September 9

Apples/Oranges Problem in Statistical Analysis?

I am a third-party editor of research papers and while this question is beyond the scope of what is expected of me, I am currently having trouble understanding the following: Among a total of 1000 patients taking a specific drug, 250 of them reported experiencing one or more adverse drug reactions (ADR). Specifically, a total of 350 reactions were reported by those 250 patients. The authors are trying to report a prevalence rate of 35 %. First they wrote that "a total of 250 (25%) patients reported 350 (35%) ADRs" and later they write, "the prevalence of ADRs to [drug X] was 35% in this study." It seems to me that these are two different statistical expressions; one compares total ADRs to total patients, the other compares ADRs to the drug in question. Is there another relationship available, like a ratio of ADRs to patients? Or do I just suck so badly at math, as was reflected in my grades as a student? Thank you for your time. Wolfgangerl (talk) 16:52, 9 September 2015 (UTC)

• To me the word "prevalence" applies better to the likelihood of a patient's having any incidents, i.e. the fraction of the population that is susceptible to ADRs (which is 1/4 here). If we're counting incidents rather than affected patients, the appropriate ratio imho is incidents to doses or to patient-years. The "35%" may also be useful to actuaries, but ought to be more transparently labeled, and not expressed as %. —Tamfang (talk) 20:18, 9 September 2015 (UTC)

Yes, that is the normal formal definition of prevalence in epidemiology. I agree a more clear way of stating this would be better. As it stands the use of "prevalence" and 35% is wrong, even if there happened to be exactly 1000 total ADRs as well - prevalence is measured over the population of the studied objects, not the number of different types of reported responses. SemanticMantis (talk) 22:57, 9 September 2015 (UTC)

OK, I follow. Thank you both very much for taking your time to answer. Wolfgangerl (talk) 01:37, 10 September 2015 (UTC)