Prediction models for clustered data with informative priors for the random effects: a simulation study

Table 1 An example of using posterior samples from model development data analysis for prediction in a new cluster

Posterior from model development data					Prediction for new cluster c
Iteration					Subject 1		…	Subject n_c
k	\( {\overset{\sim }{\beta}}_0^{(k)} \)	\( {\overset{\sim }{\beta}}_1^{(k)} \)	\( {{\overset{\sim }{\sigma}}_u^2}^{(k)} \)	\( {\widehat{u}}_c^{(k)} \) ^a	x _{1 c}	\( {\widehat{p}}_{1c}^{(k)} \) ^b	…	\( {x}_{n_cc} \)	\( {\widehat{p}}_{n_cc}^{(k)} \) ^b
.	.	.	.	.	.	.	.	.	.
.	.	.	.	.	.	.	.	.	.
5001	−1.35	1.07	1.17	.50	1.11	.58	…	−.46	.21
5011	−1.24	1.08	.88	−1.89	1.11	.13	…	−.46	.03
5021	−1.36	1.18	1.28	−.06	1.11	.47	…	−.46	.12
5031	−1.31	1.05	.98	−.64	1.11	.31	…	−.46	.08
5041	−.94	.98	1.37	.26	1.11	.60	…	−.46	.24
.	.	.	.	.	.	.	.	.	.
.	.	.	.	.	.	.	.	.	.
Median						.52			.15

^arandom effect sampled from the normal distribution \( N\left(0,{{\overset{\sim }{\sigma}}_u^2}^{(k)}\right) \)
^bpredicted risk calculated by \( {\widehat{p}}_{\mathrm{sc}}^{(k)}=\frac{1}{1+\exp \left(-{\overset{\sim }{\beta}}_0^{(k)}+{\overset{\sim }{\beta}}_1^{(k)}{x}_{sc}+{\widehat{u}}_c^{(k)}\right)} \)

ISSN: 1471-2288