Table 4 Results obtained by fitting the proposed combined model, in which routine and clinical data are considered while taking into account ODS: Posterior estimates of model parameters from a converged MCMC chain for outcome process and observation time process models: posterior median and 95% highest posterior density (HPD) credible intervals

Outcome process model

Infection status at previous visit\(^{*}\)

 Negative+AL use

\(\beta _1\)

0.201 (− 0.279, 0.680)

− 0.303 (− 0.586, − 0.002)

− 0.419 (− 0.635, − 0.212)

 Symptomatic

\(\beta _2\)

− 0.577 (− 1.489, 0.265)

− 0.942 (− 1.275, − 0.620)

− 1.042 (− 1.283, − 0.808)

 Asymptomatic

\(\beta _3\)

1.513 (1.023, 1.997)

0.882 (0.527, 1.222)

0.416 (0.181, 0.643)

Shifted year of birth

\(\beta _4\)

− 0.059 (− 0.143, 0.025)

0.501 (0.372, 0.637)

0.277 (0.186, 0.367)

Age (Gompertz model)

\(\theta _1\)

0.061 (0.014, 0.123)

3.0e−4 (1.9e−5, 6.8e−4)

0.012 (0.002, 0.025)

\(\theta _2\)

− 0.568 (− 0.966, − 0.211)

0.561 (0.410, 0.709)

0.224 (0.093, 0.355)

Observational time process model

 Shifted year of birth

\(\zeta\)

0.173 (0.084, 0.258)

0.125 (0.073, 0.179)

0.501 (0.408, 0.598)

 Age (Gompertz model)

\(\vartheta _1\)

0.573 (0.188, 0.952)

0.753 (0.397, 1.126)

0.065 (0.011, 0.143)

\(\vartheta _2\)

0.064 (− 0.022, 0.153)

0.202 (0.149, 0.257)

0.542 (0.440, 0.640)

Variance components

 Random intercept for households

\(\sigma ^2_{b0}\)

1.258 (0.653, 1.943)

1.198 (0.795, 1.620)

0.615 (0.401, 0.859)

 Random intercept for subjects

\(\sigma ^2_{b1}\)

0.095 (0.002, 0.317)

0.233 (0.003, 0.656)

0.110 (0.002, 0.303)