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# Table 3 Association structures for joint model

From: Bayesian joint modelling of longitudinal and time to event data: a methodological review

Parameterisation | Latent association |
Number of articles (%)^{a}
| Reference | |
---|---|---|---|---|

Random effect | Univariate |
W_{i}(t) = αb_{i}
| 31(41%) | [13, 15, 17, 19, 22, 23, 25, 27, 31, 33, 35, 37, 38, 44, 48, 51, 53, 54, 56, 59,60,61, 66, 69, 70, 75, 77,78,79,80, 82] |

Multivariate | \( {W}_i(t)={\sum}_{k=1}^K{\alpha}_k{b}_{ik} \) | 8(10.7%) | [20, 30, 36, 41, 50, 82, 85,86,87] | |

Current Value parameterisation | Univariate |
W_{i}(t) = αm_{i}(t)
| 14(18.7%) | [13, 24, 39, 40, 43, 46, 47, 52, 65, 67, 71,72,73, 76] |

Multivariate | \( {W}_i(t)={\sum}_{k=1}^K{\alpha}_k{m}_{ik}(t) \) | 13(17.3%) | [14, 21, 26, 28, 32, 34, 45, 49, 57, 63, 83, 84, 87] | |

Correlated random effect | Univariate |
W_{i}(t) = φwith ϐ _{i} = {b_{i}, φ_{i}}~H
| 2(2.7%) | [16, 18] |

Multivariate |
W_{i}(t) = φwith \( {\mathrm{\ss}}_i=\left\{{b}_i,{\varphi}_i\right\}\sim {H}_{\alpha_k} \) | 1(1.3%) | [57] | |

Random effect with fixed effect | Multivariate | \( {W}_i(t)={\sum}_{k=1}^K{\alpha}_k\left({\beta}_k+{b}_{ik}\right) \) | 2(2.7%) | [29, 57] |

Time-dependent slope | Univariate | \( {W}_i(t)={\alpha}^{(1)}{m}_i(t)+{\alpha}^{(2)}\ \frac{d\ }{dt}{m}_i(t) \) | 1(1.3%) | [87] |

Multivariate | \( {W}_i(t)={\sum}_{k=1}^K\left\{{\alpha_k}^{(1)}\ {m}_{ik}(t)+{\alpha_k}^{(2)}\ \frac{d\ }{dt}{m}_{ik}(t)\right\} \) | 2(2.7%) | [45, 81] | |

Cumulative effect | Univariate | \( {W}_i(t)=\alpha {\int}_0^t{m}_i(s) ds \) | 1(1.3%) | [45] |