. Determine the normal skeptical prior and compute the posterior distribution assuming that the log odds ratio has a normal likelihood.
Holzer et al. (2006) analyzed a retrospective cohort study for the efficacy and safety of endovascular cooling in unselected survivors of cardiac arrest compared to controls. The authors found that the patients in the endovascular cooling had a 2-fold increased odds of survival (67/97 patients versus 466/941 patients; odds ratio 2.28, 95% CI, 1.45 to 3.57) compared to the control group. After adjustment for baseline imbalances, the odds ratio was 1.96 (95% CI = [1.19, 3.23]). In the final step, the authors took account of the fact that their study was nonrandomized and wished to discount their results for the study design. More specifically, they discounted their cohort study data by assuming that the observed effect on the logarithmic scale (log odds ratio) was actually 0 and the probability of exceeding the observed effect was 5% (skeptical prior). Determine the normal skeptical prior and compute the posterior distribution assuming that the log odds ratio has a normal likelihood.
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