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

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Table 5 Small sample efficiencies for evaluating the AR(1) correlation structure for varying values of \(\alpha \) and sample size per group

m	\(\alpha \)	R*	\({\hat{\beta }}_0\)	\({\hat{\beta }}_1^{[1]}\)	\({\hat{\beta }}_2^{[2]}\)	\({\hat{\beta }}_3^{[2]}\)	\({\hat{\alpha }}^{[1]}\)
Mean squared error using ML
60	0.2	1000	0.056	0.355	0.297	0.291	0.609
	0.4	1000	0.088	0.503	0.427	0.445	0.505
	0.6	1000	0.127	0.803	0.642	0.619	0.308
	0.7	998	0.132	0.908	0.716	0.656	0.171
120	0.2	1000	0.029	0.176	0.138	0.137	0.305
	0.4	1000	0.040	0.254	0.203	0.194	0.236
	0.6	1000	0.054	0.381	0.291	0.294	0.124
	0.7	1000	0.067	0.489	0.349	0.325	0.067
300	0.2	1000	0.010	0.071	0.057	0.054	0.111
	0.4	1000	0.016	0.101	0.084	0.078	0.080
	0.6	1000	0.025	0.153	0.121	0.118	0.047
	0.7	1000	0.029	0.174	0.144	0.140	0.023
Mean squared error using GEE
60	0.2	1000	0.057	0.355	0.300	0.290	0.668
	0.4	1000	0.089	0.516	0.427	0.450	0.701
	0.6	1000	0.137	0.852	0.703	0.653	0.571
	0.7	1000	0.160	1.133	0.883	0.795	0.424
120	0.2	1000	0.029	0.176	0.139	0.138	0.340
	0.4	1000	0.040	0.260	0.204	0.198	0.334
	0.6	1000	0.062	0.415	0.327	0.325	0.240
	0.7	1000	0.083	0.595	0.435	0.402	0.178
300	0.2	1000	0.010	0.072	0.058	0.054	0.128
	0.4	1000	0.017	0.103	0.085	0.079	0.124
	0.6	1000	0.027	0.162	0.132	0.129	0.093
	0.7	1000	0.036	0.211	0.182	0.176	0.066

The true correlation structure is AR(1)
There are equal sample sizes of \(\frac{m}{2}\) per group and \(\beta = (\beta _0, \beta _{drug}, \beta _{baseline}, \beta _{age})' = (0.4467, -0.1659, 0.0232, 0.0258)'\); [1] True value by a factor of \(10^2\); [2] True value by a factor of \(10^4\)