On the logic of collapsibility for causal effect measures

• Published in: Biometrical Journal
• Main Authors: Didelez, Vanessa, Stensrud, Mats Julius
• Language: English
• Published: 2021
• Subjects: Causal inference; Survival analysis; Collapsibility; Confounding; Greenland
• Online Access: https://repository.publisso.de/resource/frl:6433311; https://doi.org/10.1002/bimj.202000305

Liu et al. (2020) discuss the relation between efficacy measures within subgroups and efficacy measures on the population level, which can be obtained by merging the subgroups. They come to the conclusion that neither odds ratios (for binary endpoints) nor hazard ratios (for time-to-event endpoints) are suitable measures of efficacy in this context. This insight is not new, and more general settings have been considered previously (Daniel, Zhang, & Farewell, 2020; Greenland & Pearl, 2011; Greenland, Robins, & Pearl, 1999; Huitfeldt, Stensrud, & Suzuki, 2019; Martinussen & Vansteelandt, 2013; Pang, Kaufman, & Platt, 2013; Sjölander, Dahlqwist, & Zetterqvist, 2016). While we largely agree with their conclusion, we do so for different reasons and would like to point out a number of important subtleties that have perhaps not been appreciated by Liu et al. (2020). These should be carefully understood to avoid any further misleading interpretations. In particular, we want to emphasise, like many before, that confounding and non-collapsibility are separate issues (Didelez et al., 2010; Greenland, 1996; Greenland & Pearl, 2011; Greenland et al., 1999; Pand, Kaufman, & Platt, 2013; Pang et al., 2013; Shrier & Pang, 2015); to cite Greenland (2011): ‘confounding may occur with or without non-collapsibility, and non-collapsibility may occur with or without confounding’. Moreover, in view of patients and investigators preferring contrasts in terms of absolute risks (Murray, Caniglia, Swanson, Hernández-Díaz, & Hernán, 2018), we are sceptical about the emphasis on relative median survival time proposed in Liu et al. (2020).