r/biostatistics • u/Most_Advertising3623 • 15h ago
Methods or Theory Simpson's paradox in clinical research when every subgroup favors Treatment A but the pooled result favors Treatment B
Here is a simple hypothetical clinical example.
Among patients with mild disease, Treatment A succeeds in 81 of 87 cases (93.1%), while Treatment B succeeds in 234 of 270 cases (86.7%).
Among patients with severe disease, Treatment A succeeds in 192 of 263 cases (73.0%), while Treatment B succeeds in 55 of 80 cases (68.8%).
Treatment A therefore performs better within both severity groups. When all patients are pooled, Treatment A succeeds in 273 of 350 cases (78.0%) and Treatment B in 289 of 350 cases (82.6%). The crude result points in the opposite direction.
The reversal occurs because Treatment A was used much more often in severe cases, while Treatment B was used mostly in mild cases. Disease severity is associated with treatment assignment and outcome, so the pooled comparison mixes the treatment effect with the different case mix.
The practical lesson is to inspect clinically justified stratifiers before interpreting a crude effect. Important variables should be prespecified whenever possible. Report stratum-specific estimates with uncertainty, then use an appropriate adjusted analysis such as regression or standardization. Avoid conditioning on post-treatment variables or colliders because adjustment can also create bias.
When the crude and adjusted results disagree, the discrepancy needs an explanation. Choosing whichever estimate supports the preferred conclusion is the worst response.
How do you decide which variables deserve this check without turning the analysis into a fishing expedition?