1. What is “collapsing”? (for epidemiologists) Picture a 2x2 tables from Intro Epi: (This is a collapsed table; there are no strata) DiseasedUndiseasedTotal Exposed133750 Unexposed17133150 Total30170200 Odds Ratio: 2.748808 Relative Risk: 2.294118

2. 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: 4.333333 Relative Risk: 3.0000 Odds Ratio: 1.324675 Relative Risk: 1.285714 Stratum 1Stratum 2 DiseasedUndiseasedTotalDiseasedUndiseasedTotal Exposed101525Exposed32225 Unexposed106575Unexposed76875 Total2080100Total1090100

3. What is “collapsing”? (for epidemiologists) If we adjust for that “precision variable,” we are creating weighted averages: Adj. Odds Ratio: 2.809211 Adj. Relative Risk: 2.294118 Stratum 1Stratum 2 DiseasedUndiseasedTotalDiseasedUndiseasedTotal Exposed101525Exposed32225 Unexposed106575Unexposed76875 Total2080100Total1090100 Adjustment Method (Mantel Haenszel or regression)

4. What is “collapsing”? (for epidemiologists) Remember originally, we had them “collapsed,” where each of the cells were just added together Stratum 1 DiseasedUndiseasedTotal Exposed101525 Unexposed106575 Total2080100 Stratum 2 DiseasedUndiseasedTotal Exposed32225 Unexposed76875 Total1090100 Collapsed DiseasedUndiseasedTotal Exposed133750 Unexposed17133150 Total30170200

5.  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: 2.809211 Adj. Relative Risk: 2.294118 Original Odds Ratio: 2.748808 Original Relative Risk: 2.294118 What is “collapsing”? (for epidemiologists)