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September 22, 2020

The underlying issue is the non-collapsibility of ORs and HRs. Non-collapsibility means that the conditional ratio is different from the marginal (unadjusted) ratio even in the complete absence of confounding (as in our example dataset below). By the way, don’t make the mistake of concluding that non-collapsibility is undesirable. Any measure that has the potential for summarizing a treatment effect with one constant for all types of patients will be non-collapsible when the outcome is categorical or represents time to event1. Collapsible measures such as absolute risk reduction and relative risk reduction must vary over risk factors (creating mathematical but not subject-matter-relevant interactions), otherwise probabilities will arise that are outside the allowable range of [0,1]. Log odds and log hazard ratios have an unlimited ranges and can possibly apply to everyone. This makes them good bases for studying heterogeneity of treatment effect. — Unadjusted Odds Ratios are Conditional.