An observational study of smoking and lung cancer risk enrolls 600 smokers and 600 matched non-smokers, balanced on 12 measured confounders (age, SES, air pollution, diet, alcohol use, occupational exposures, etc.). The matched analysis yields:
Conditional odds ratio: 2.4 (smokers have 2.4× higher odds of lung cancer)
A Rosenbaum sensitivity analysis assesses robustness to an unmeasured confounder. The analysis finds:
"If a hidden binary confounder increased both smoking odds and lung cancer odds by a factor of Γ ≥ 2.8, it could entirely explain the observed association under the null hypothesis of no true smoking effect."
Which statement correctly interprets this finding?
A) The unmeasured confounder definitely exists; the smoking effect is spurious
B) The observed effect is robust to unmeasured confounding only if no such confounder with Γ ≥ 2.8 in both directions exists
C) An unmeasured confounder of size Γ = 2.8 is implausibly large; the smoking–cancer association is causal
D) Sensitivity analysis proves that smoking causes lung cancer in matched data
An observational study of smoking and lung cancer risk enrolls 600 smokers and 600 matched non-smokers, balanced on 12 measured confounders (age, SES, air pollution, diet, alcohol use, occupational exposures, etc.). The matched analysis yields:
Conditional odds ratio: 2.4 (smokers have 2.4× higher odds of lung cancer)
A Rosenbaum sensitivity analysis assesses robustness to an unmeasured confounder. The analysis finds:
"If a hidden binary confounder increased both smoking odds and lung cancer odds by a factor of Γ ≥ 2.8, it could entirely explain the observed association under the null hypothesis of no true smoking effect."
Which statement correctly interprets this finding?
A) The unmeasured confounder definitely exists; the smoking effect is spurious
B) The observed effect is robust to unmeasured confounding only if no such confounder with Γ ≥ 2.8 in both directions exists
C) An unmeasured confounder of size Γ = 2.8 is implausibly large; the smoking–cancer association is causal
D) Sensitivity analysis proves that smoking causes lung cancer in matched data