Table 3 The prior distributions for parameters used in the Bayesian multilevel multivariable binomial model
Parameter | Main analysis | Sensitivity analysis scenarios | ||
|---|---|---|---|---|
1 | 2 | 3 | ||
β 0 | N (−7.6, 0.71) | N (−5, 0.001) | N (−7.6, 0.71) | N (−7.6, 0.71) |
β 1 | \( \mathrm{logit}\left({\overset{\sim }{p}}_1\right)-{\beta}_0 \) | N (0, 0.001) | \( \mathrm{logit}\left({\overset{\sim }{p}}_1\right)-{\beta}_0 \) | \( \mathrm{logit}\left({\overset{\sim }{p}}_1\right)-{\beta}_0 \) |
β 2 | \( \mathrm{logit}\left({\overset{\sim }{p}}_2\right)-\mathrm{logit}\left({\overset{\sim }{p}}_1\right) \) | N (0, 0.001) | \( \mathrm{logit}\left({\overset{\sim }{p}}_2\right)-\mathrm{logit}\left({\overset{\sim }{p}}_1\right) \) | \( \mathrm{logit}\left({\overset{\sim }{p}}_2\right)-\mathrm{logit}\left({\overset{\sim }{p}}_1\right) \) |
β 3 | N (0, 0.001) | N (0, 0.001) | N (0, 0.001) | N (0, 0.001) |
σ U | Uniform (0, 3) | Uniform (0, 3) | Uniform (0, 5) | Uniform (0, 9) |
σ W | Uniform (0, 2) | Uniform (0, 2) | Uniform (0, 3) | Uniform (0, 2) |