What is “collapsing”? (for epidemiologists) Picture a 2x2 tables from Intro Epi: (This is a collapsed table; there are no strata) DiseasedUndiseasedTotal Exposed Unexposed Total Odds Ratio: Relative Risk:

What is “collapsing”? (for epidemiologists) Now add a stratifying variable which would be considered a “precision variable”: Notice the disease proportions are different across the stratifying variable, but the exposure proportions are the same. Also we have effect modification, but whatever. Unrelated. Odds Ratio: Relative Risk: Odds Ratio: Relative Risk: Stratum 1Stratum 2 DiseasedUndiseasedTotalDiseasedUndiseasedTotal Exposed101525Exposed32225 Unexposed106575Unexposed76875 Total Total

What is “collapsing”? (for epidemiologists) If we adjust for that “precision variable,” we are creating weighted averages: Adj. Odds Ratio: Adj. Relative Risk: Stratum 1Stratum 2 DiseasedUndiseasedTotalDiseasedUndiseasedTotal Exposed101525Exposed32225 Unexposed106575Unexposed76875 Total Total Adjustment Method (Mantel Haenszel or regression)

What is “collapsing”? (for epidemiologists) Remember originally, we had them “collapsed,” where each of the cells were just added together Stratum 1 DiseasedUndiseasedTotal Exposed Unexposed Total Stratum 2 DiseasedUndiseasedTotal Exposed32225 Unexposed76875 Total Collapsed DiseasedUndiseasedTotal Exposed Unexposed Total

 Because there is no confounding, the RR was collapsible. The two RRs are identical!  The OR was NOT collapsible, because collapsing is a linear process (adding) on a nonlinear measure (odds)  This is the same concept as the L’Abbe plots, but in table form, rather than visual form Adj. Odds Ratio: Adj. Relative Risk: Original Odds Ratio: Original Relative Risk: What is “collapsing”? (for epidemiologists)