Maximum likelihood based analysis of equally spaced longitudinal count data with first-order antedependence and overdispersion

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Table 6 Percent bias for evaluating the AR(1) correlation structure for varying values of \(\alpha \) and sample size per group

m	\(\alpha \)	R*	\({\hat{\beta }}_0\)	\({\hat{\beta }}_1\)	\({\hat{\beta }}_2\)	\({\hat{\beta }}_3\)	\({\hat{\alpha }}\)
Percent bias using ML
60	0.2	1000	2.57	0.53	−0.61	−0.53	9.41
	0.4	1000	6.33	−0.42	−1.15	−2.31	5.15
	0.6	1000	1.95	0.05	−0.95	0.27	2.65
	0.7	998	−2.21	2.71	0.72	1.21	0.69
120	0.2	1000	−0.04	0.14	0.07	0.20	5.30
	0.4	1000	2.25	−0.52	−0.57	−0.65	2.74
	0.6	1000	0.43	−0.79	0.08	−0.13	1.39
	0.7	1000	2.00	0.15	−0.01	−1.04	0.17
300	0.2	1000	0.68	−0.18	−0.57	0.22	2.83
	0.4	1000	0.85	−0.29	−0.16	−0.25	1.31
	0.6	1000	1.91	−0.38	−0.30	−0.75	0.53
	0.7	1000	1.47	−0.29	−0.14	−0.63	−0.03
Percent bias using GEE
60	0.2	1000	2.48	0.54	−0.60	−0.49	10.94
	0.4	1000	6.26	−0.34	−1.10	−2.29	6.06
	0.6	1000	1.88	0.64	−0.90	0.45	4.86
	0.7	1000	0.60	1.87	−0.28	0.84	4.60
120	0.2	1000	−0.22	0.07	0.13	0.24	6.19
	0.4	1000	1.95	−0.51	−0.40	−0.64	2.89
	0.6	1000	0.16	−1.05	0.34	−0.21	2.18
	0.7	1000	1.74	−0.22	0.14	−0.83	2.55
300	0.2	1000	0.65	−0.23	−0.57	0.23	2.87
	0.4	1000	0.72	−0.32	−0.15	−0.18	0.98
	0.6	1000	2.03	−0.33	−0.23	−0.88	0.86
	0.7	1000	2.83	−0.20	−0.58	−0.91	1.64

The true correlation structure is AR(1)
There are equal sample sizes of \(\frac{m}{2}\) per group and \(\beta \) = \((\beta _0, \beta _{drug}, \beta _{baseline}, \beta _{age})' = (0.4467, -0.1659, 0.0232, 0.0258)'\)