I have been trying with some difficulty to follow your discussion @sander, @s_doi and @AndersHuitfeldt about collapsibility of the proportions in @s_doi’s tables.
It is my understanding that RR is collapsible when r is constant under the following circumstances: p(Y=1∩X=0|Z=1∩X=0)/p(Y=1∩X=1|Z=1∩X=1) = r, p(Y=1∩X=0|Z=0∩X=0)/p(Y=1∩X=1|Z=0∩X=1) = r and the marginal p(Y=1∩X=0|X=0)/p(Y=1∩X=1|X=1) = r. This situation will arise in the special case when p(Z=1∩X=1|Y=1∩X=1)=p(Z=1∩X=0|Y=1∩X=0) and also if p(Z=1∩X=1|X=1)= p(Z=1∩X=0|X=0). It follows that the ratios of ‘survival from Y=0’ (i.e. Y=1) will also be collapsible. These special cases will be met rarely in a precise manner for observed proportions that are subject to stochastic variation and can only be postulated for ‘true’ parametric values.
It is also my understanding is that the OR will be collapsible when r’ is constant under the following circumstances odds(Y=1∩X=0|Z=1∩X=0)/odds(Y=1∩X=1|Z=1∩X=1) = r’, odds(Y=1∩X=0|Z=0∩X=0)/odds(Y=1∩X=1|Z=0∩X=1) = r’ and the marginal odds(Y=1∩X=0|X=0)/odds(Y=1∩X=1|X=1) = r’. It follows that the odds ratios for Y=0 will also be collapsible. This collapsibility of odds will arise in the special case when p(Z=1∩X=1|Y=1∩X=1)= p(Z=1∩X=0|Y=1∩X=0) and p(Z=1∩X=1|Y=0∩X=1)= p(Z=1∩X=0|Y=0∩X=0).
In the special conditions for OR collapsibility, p(Z=1|X=1)≠p(Z=1|X=0) so that when the OR is collapsible, it does not model exchangeability at baseline between {X=0} the set of control subjects and {X=1} the set of treated subjects. Therefore p(Z=1|X=1)≠p(Z=1|X=0) implies that p(Z=0|X=0) is a pre-treatment baseline probability of the covariate Z=1 and p(Z=1|X=1) is a post treatment probability. However, the RR and SRR models do model exchangeability between the sets {X=0} and {X=1}. Again these special cases will be met rarely for observed proportions subject to stochastic variation and can only be postulated for ‘true’ parametric values.
In my limited experience of analysing data for diagnostic and prognostic tests, the observed proportions remain different to the above special cases but often not too different so that it possible to assume that the data is compatible with parameters that satisfy either of the conditions for collapsibility of OR and RR.
So in conclusion I can follow your reasoning that the RD is collapsible (0.2-0.1 = 0.1, 0.9-0.8- =0.1 and marginal 0.55-0.45 = 0.1. I follow that the OR are not collapsible (2.25, 2.25 and marginal 1.5) and especially as the data do not satisfy the special case of paragraph 3 above. Regarding RRs, I find them to be 90/80= 1.125, 20/10=2 and marginal 110/90 = 1.22. In this context, what do you mean @sander by “the causal RR is collapsible but not constant”?