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@statsepi @ashtroid22 @Epi_D_Nique @healthstatsdude @stephensenn (1/n) The problem Senn is referring to here, was solved by Mindel C. Sheps in NEJM in 1958. I proposed a counterfactual causal model that formalizes the intuition behind her argument in this paper: degruyter.com/view/j/em.2018…
@statsepi @ashtroid22 @Epi_D_Nique @healthstatsdude @stephensenn (2/n) Consider this example: If people both Russia and Norway are randomized to play Russian Roulette at the end of every year, and the baseline risk of death in a year i 0.5% in Norway and 1.0% in Russia: Calculate how many people will die in the active arm in each country.
@statsepi @ashtroid22 @Epi_D_Nique @healthstatsdude @stephensenn (3/n) If you do the maths, you will find that 17.5% die in the active arm in Russia, and 17.1% die in the active arm in Norway. This means risk ratio is 17.5 in Russia and 35 in Norway. Odds ratio is 21 in Russia and 41 in Norawy, and survival ratio is 5/6 in both countries
@statsepi @ashtroid22 @Epi_D_Nique @healthstatsdude @stephensenn The fact that the survival ratio is the only effect measure which is equal between that is equal between the two countries is NOT A COINCIDENCE. I can give you a complete formal model that tells you why this happens and when it happens.
@statsepi @ashtroid22 @Epi_D_Nique @healthstatsdude @stephensenn (4/n) There is NO POSSIBLE similar logic that results in stability of the odds ratio between countries (other than models that result in stability of the risk ratio, but which also lead to stability of odds ratio because the disease is rare)
@statsepi @ashtroid22 @Epi_D_Nique @healthstatsdude @stephensenn (5/n) My suggestion is to use risk ratio for exposures which reduce incidence, and survival ratio for exposures that increase incidence. This suggestion coheres with a lot of earlier work, including Sheps brilliant 1958 NEJM paper "Shall we count the living or the dead".
@statsepi @ashtroid22 @Epi_D_Nique @healthstatsdude @stephensenn (6/n) When the disease is rare, it also results in essentially the same analysis as the earlier suggestion to consider "relative benefits and additive harms" (Glasziou and Irwig, BMJ, 1995) bmj.com/content/311/70…
@statsepi @ashtroid22 @Epi_D_Nique @healthstatsdude @stephensenn (7/n) On a personal note, I am a graduate from the methods concentration in Epidemiology at Harvard School of Public Health and I literally gambled my academic career on this framework as a principled solution to the problem that Senn discusses above.
@statsepi @ashtroid22 @Epi_D_Nique @healthstatsdude @stephensenn (8/n) It now appears that I have lost that gamble, not because anybody has found any errors in my reasoning, but because nobody bothered to read it.
@statsepi @ashtroid22 @Epi_D_Nique @healthstatsdude @stephensenn (9/9) If anybody in #epitwitter or #statstwitter is willing to just read the paper and try their best to find an error, I would consider it the biggest favor I could hope for from anyone. Thank you.
