| Assessment | Sugar water | Licorice | Risk difference (95% CI) | Odds ratio (95% CI) | p-value |
|---|---|---|---|---|---|
| PACU 30 min | 42 of 116 (36%) | 22 of 117 (19%) | -17.4 (-28.7 to -6.2) | 0.41 (0.22 to 0.74) | p = 0.003 |
| PACU 90 min | 41 of 116 (35%) | 12 of 117 (10%) | -25.1 (-35.4 to -14.8) | 0.21 (0.10 to 0.42) | p < 0.001 |
| 4 h after surgery | 52 of 116 (45%) | 24 of 117 (21%) | -24.3 (-36.0 to -12.7) | 0.32 (0.18 to 0.57) | p < 0.001 |
| First postoperative morning | 46 of 116 (40%) | 24 of 117 (21%) | -19.1 (-30.7 to -7.6) | 0.39 (0.22 to 0.70) | p = 0.002 |
7 Does it last?
The PI asked whether the effect lasts past the recovery room (Chapter 1). The plan answers this from the estimate at each assessment, read together with its confidence interval. There is no formal test across assessments (D-002, D-003, D-013). A later assessment whose interval included one would not show that the effect had worn off; it would show only that the data could not rule out no effect at that time.
7.1 The effect at each assessment
Each row is a separate unadjusted logistic regression in the patients observed at that assessment, so each odds ratio is marginal (D-007). Risk differences are licorice minus sugar water, in percentage points.
At ninety minutes the odds ratio is OR 0.21, 95% CI 0.10 to 0.42; at four hours it is OR 0.32, 95% CI 0.18 to 0.57; and on the first postoperative morning it is OR 0.39, 95% CI 0.22 to 0.70. Across the assessments, between 35% and 45% of the sugar-water arm had a sore throat, and the risk difference on the first postoperative morning is -19.1 percentage points (95% CI -30.7 to -7.6). At every assessment, through to the first postoperative morning, the confidence interval for the odds ratio lies below one and the interval for the risk difference lies below zero. The data are consistent with a benefit that lasts beyond the recovery room. These are descriptive estimates at secondary time points, with no adjustment for multiplicity (D-003).
7.2 Common odds ratios across the four assessments
The two models below summarise all four assessments with one odds ratio. Each assumes that the effect is the same at every assessment. Neither answers whether the effect lasts; the table above does (D-014). They estimate different things and should not be compared as if they were the same quantity.
7.2.1 Marginal (population-averaged): the GEE
A generalized estimating equation with treatment and assessment as terms, an exchangeable working correlation within patient, and robust standard errors (D-007). Its odds ratio is on the same population-averaged scale as the table above.
The common marginal odds ratio is OR 0.34, 95% CI 0.22 to 0.53 (p < 0.001; 233 patients, 932 observations). The estimated within-patient working correlation is 0.45. The robust standard errors allow for this correlation between a patient’s assessments.
7.2.2 Conditional (patient-level): the mixed model
A logistic mixed model with the same terms and a random intercept for patient, fitted by adaptive quadrature (D-008, D-020). Its odds ratio compares the odds for the same patient under licorice and under sugar water. It is a supporting estimate only, labeled conditional wherever it appears.
The common conditional (patient-level) odds ratio is OR 0.14, 95% CI 0.06 to 0.35 (p < 0.001). The estimated standard deviation of the patient random intercept is 2.76 on the log-odds scale.
The conditional odds ratio is further from one than the marginal one. That is expected whenever patients differ in their underlying risk, which the random-intercept SD of 2.76 indicates. It does not mean the treatment effect is larger. Odds ratios are non-collapsible, so averaging patient-level effects over patients with different baseline risks pulls the population-averaged odds ratio toward one (D-008). The PI’s question is about patients as a population, and the marginal estimates answer it.
No warnings from the model fits in this chapter.