Noncollapsibility, confounding, and sparse-data bias.

 Part 1:

Noncollapsibility, confounding, and sparse-data bias. Part 1: The oddities of odds - Journal of Clinical Epidemiology (jclinepi.com)

Part 2:

Noncollapsibility, confounding, and sparse-data bias. Part 2: What should researchers make of persistent controversies about the odds ratio? - Journal of Clinical Epidemiology (jclinepi.com)

generalized linear model - Is there a mathematical definition of non-collapsibility? - Cross Validated (stackexchange.com)

Estimating and contextualizing the attenuation of odds ratios due to non collapsibility: Communications in Statistics - Theory and Methods: Vol 46, No 2 (tandfonline.com)

Joint cumulative distribution of X1 and X2

 

Proving law of the unconscious statistician (LOTUS) for discrete variable