The primary question is whether a licorice gargle, compared with a sugar-water gargle, lowers the odds of any sore throat at rest thirty minutes after arrival in the recovery room. “Any” means a score above zero on the zero-to-ten scale (D-001). Every comparison below is licorice against sugar water, in the patients observed at thirty minutes.
The simplest answer
Thirty minutes after arrival in the recovery room, 42 of 116 (36%) patients in the sugar-water arm had a sore throat at rest, compared with 22 of 117 (19%) in the licorice arm. The risk difference is -17.4 percentage points (95% CI -28.7 to -6.2).
Primary model: the marginal odds ratio
The pre-specified primary model is an unadjusted logistic regression of any sore throat on treatment (Chapter 3; D-007). With treatment as its only term, its odds ratio is the population-averaged (marginal) odds ratio. It compares the odds of sore throat had every patient gargled licorice with the odds had every patient gargled sugar water.
The marginal odds ratio is OR 0.41, 95% CI 0.22 to 0.74 (p = 0.003, 233 patients). The ratio of the two proportions (the relative risk) is 0.52. The odds ratio is further from one than that, as it always is when the outcome is not rare, so the risk difference above is the easier number to read (D-006).
The missing outcomes of patients in the file cannot change this conclusion: the best- and worst-case bounds both keep the confidence interval below one (Chapter 2). Those bounds do not cover the 1 enrolled patient absent from the file. A post hoc worst case that also counts that patient as a licorice patient with a sore throat still keeps the interval below one, at OR 0.45, 95% CI 0.25 to 0.81 (D-021).
Sensitivity analysis: adjusted for baseline covariates
The plan adjusts for baseline covariates as a sensitivity analysis only (D-009, D-011). The covariates are listed below. Age and BMI enter as linear terms, and the rest as factors.
Covariates in the model: age, BMI, sex, ASA physical status, smoking, surgery size. The covariate-adjusted odds ratio is OR 0.37, 95% CI 0.19 to 0.71 (p = 0.003, 233 patients).
This is a conditional odds ratio. It compares patients with the same covariate values, not the whole population. Odds ratios are non-collapsible, so the adjusted odds ratio differs from the unadjusted one even when the arms are perfectly balanced. A difference between the two is not evidence of confounding (D-009). The unadjusted odds ratio is OR 0.41, 95% CI 0.22 to 0.74. The two estimates point the same way, and neither confidence interval includes one.
No warnings from the model fits in this chapter.