Extended Data Fig. 2: Bias that occurs when using the odds ratio to approximate the relative risk.
From: Childhood vaccines and antibiotic use in low- and middle-income countries
a–d, We illustrate the degree of bias that occurs in attributable fraction estimates (indicated by the departure of the estimated proportion from the 1:1 diagonal) under differing parameterizations with respect to the true aetiological fraction and vaccine efficacy against the targeted infection. Values correspond to our meta-analytic estimates of PCV efficacy against vaccine-serotype invasive pneumococcal disease (a), PCV efficacy against vaccine-serotype acute otitis media (b), rotavirus vaccine efficacy against rotavirus gastroenteritis in middle-income countries (c) and rotavirus vaccine efficacy against rotavirus gastroenteritis in low-income countries (d). The range of 15–30% is highlighted in grey as plausible values for the proportion of disease attributable to vaccine-serotype pneumococci for children aged 24–59 months and rotavirus for children aged 0–23 months, based on previously published studies6, 7. Values are plotted on a blue-to-red ramp corresponding to increases in symptom prevalence (ρ + ω); values of 0.01, 0.02, 0.03, 0.05 and 0.1 correspond to incidence rates of 52, 104, 156, 261 and 521 episodes per 100 children annually (roughly the range of our all-cause ARI and diarrhoea incidence rate estimates); under the assumption of a 3-day duration of symptoms, the same prevalence values correspond to incidence rates of 122 to 1,217 episodes per 100 children annually. These outcomes suggest negligible bias in aetiological fractions over the range of plausible values for our analysis.
