Abstract:
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This presentation explains why relative risk/response and ratio of time are logic respecting (a condition stronger than strict collapsibility), while odds ratio and hazard ratio are not. Then, following the discussions paper Liu et al (2021 Biometrical Journal), this presentation shows that mixing odds ratios and hazard ratios in subgroups dilutes them. A real life immunotherapy example in oncology then illustrates this dilution can lead to incorrect targeting of patients. In contrast, for logic respecting efficacy measures, we show that following the Subgroup Mixable Estimation (SME) principle ensures marginal and conditional analyses will agree (resolving the apples versus oranges controversy). For efficacy measured as a ratio of time, SME has been implemented in an app.
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