The study objective is to compare the effect of 4 level discrete Exposure(A : 1,2,3,4) on outcome(Y) adjusted for confounders X1, X2, X3, X4. This main model y~A +x1 + x2 + x3 + x4 works fine. When i run this model, I get 3 estimates for my exposure(A) , beta_a=2, beta_a=3, beta_a=4 (beta_a=1 is the reference level).
As a part of sensitivity analysis I am interested in estimating the effect of subsets of exposure on outcome Y. For example the effect of a=1 on y , effect of a=2 on y, effect of a=3 on y and effect of a=4 on y, 4 different models. The problem is, all the X variables (x1,x2,x3, x4) that worked well with the main model does not work with the subset model. For example:
model with only a=1 works when i only include x1,x2,
y~A(a=1)+x1 + x2 *
model with only a=2 works when i only include x3,x4, so on…
y~A(a=2)+x3 + x4
y~A(a=3)+x1 + x3
y~A(a=4)+x2 + x4*
So my question is, when comparing the effect of A on y, Can I compare the point estimates from main model y~A +x1 + x2 + x3 + x4 for example: beta_a=2, with the point estimates from the subset model y~A(a=2)+x3 + x4 when the confounder are different ? Would this not be a an apples to oranges comparisons ? Please advise.