I was rereading some sections from the Breslow and Day IARC publication and noted the following:
Clayton (1982) has shown that [the Mantel Haenszel] estimate arises at the first stage of iteration of one of the computational methods used to find the maximum likelihood estimate.
I cannot find this citation and am curious how one shows this to be the case.
As far as I know, Mantel Haenszel estimation requires that the statistician designate a primary exposure and a (set of) stratifying variable(s) and these cannot be exchanged whereas logistic regression arrives at the same estimates regardless of covariate order in the model matrix. Is that not necessarily the case during the intermediate iterations of Newton Raphson?