Modeling perinatal mortality in twins via generalized additive mixed models: a comparison of estimation approaches

Table 3 Estimate, 95% confidence/credible interval (CI), mean average squared distance (MASE), mean average 95% coverage probability (MACP), and mean average coverage length (MACL) for model parameters estimated via various approaches when number of clusters m = 1000, cluster size n_i = 2, and \( {\rho}_{x_1.{x}_2}=0.7 \)

Method	\( {\sigma}_{int}^2=0.75 \)			β_trt = 0.7			f₁(x₁)			f₂(x₂)
Method	\( {\hat{\sigma}}_{int}^2 \)	PRB	95% CI	\( {\hat{\beta}}_{trt} \)	PRB	95% CI	MASE	MACP	MACL	MASE	MACP	MACL
Event probability = 0.05
DPQL (ML)	15.83	2010.60	(4.56, 27.10)	1.24	76.44	(0.23, 2.24)	7.510	0.32	1.71	11.784	0.33	1.72
DPQL (REML)	30.45	3959.66	(16.39, 44.56)	1.07	52.38	(0.01, 2.13)	6.472	0.34	1.79	12.584	0.34	1.70
Laplace ML	56.02	7369.66	(5.71, 106.34)	0.79	13.21	(0.07, 1.51)	0.763	0.70	1.76	0.907	0.73	1.82
Bayesian (Uniform Prior)	0.96	27.42	(0.06, 2.88)	0.75	6.54	(0.28, 1.25)	0.148	0.94	1.39	0.112	0.94	1.24
Bayesian (Half-Cauchy Prior)	0.87	15.40	(0.06, 2.71)	0.72	3.25	(0.29, 1.22)	0.142	0.94	1.27	0.103	0.94	1.15
Bayesian (IG Prior)	0.39	−48.40	(0.01, 2.20)	0.71	1.71	(0.27, 1.18)	0.149	0.93	1.25	0.103	0.93	1.13
Event Probability = 0.5
DPQL (ML)	0.87	15.70	(0.40, 1.34)	0.64	−8.55	(0.42, 0.86)	0.032	0.89	0.57	0.023	0.88	0.48
DPQL (REML)	0.98	30.92	(0.52, 1.44)	0.66	−5.86	(0.42, 0.90)	0.028	0.91	0.58	0.024	0.90	0.47
Laplace ML	0.36	−52.49	(0.12, 0.60)	0.66	−5.77	(0.43, 0.89)	0.037	0.87	0.58	0.024	0.87	0.49
Bayesian (Uniform Prior)	0.82	8.99	(0.33, 1.40)	0.71	1.35	(0.47, 0.97)	0.032	0.95	0.70	0.024	0.95	0.61
Bayesian (Half-Cauchy Prior)	0.80	6.04	(0.34, 1.36)	0.71	0.76	(0.47, 0.96)	0.032	0.95	0.67	0.023	0.95	0.58
Bayesian (IG Prior)	0.72	−6.50	(0.19, 1.30)	0.69	−0.92	(0.47, 0.95)	0.033	0.94	0.68	0.023	0.95	0.58

For the Bayesian method, the three alternative priors used for the variance components were: uniform (0, 100), half-Cauchy (25), and inverse gamma, IG(0.001, 0.001)

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