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

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Table 7 Coverage probabilities for the ML and GEE approaches with the AR(1) correlation structure for varying values of \(\alpha \) and sample size per group

m	\(\alpha \)	Method	R	Coverage Probability
m	\(\alpha \)	Method	R	\({\hat{\beta }}_0\)	\({\hat{\beta }}_1\)	\({\hat{\beta }}_2\)	\({\hat{\beta }}_3\)	\({\hat{\alpha }}\)
60	0.2	ML	1000	94.7	95.2	95.5	95.5	93.8
	0.2	GEE	1000	94.4	95.0	94.8	95.1	91.1
	0.4	ML	1000	93.8	94.6	95.9	93.0	94.6
	0.4	GEE	1000	93.2	94.3	95.5	92.7	86.1
	0.6	ML	1000	93.8	93.9	94.3	94.0	93.4
	0.6	GEE	1000	94.1	93.6	95.1	93.1	83.2
	0.7	ML	998	95.4	95.3	95.4	95.5	92.3
	0.7	GEE	1000	95.0	94.9	94.0	95.7	84.6
120	0.2	ML	1000	94.7	95.2	95.2	94.8	92.9
	0.2	GEE	1000	94.2	95.1	94.9	94.5	91.3
	0.4	ML	1000	95.1	96.1	95.6	94.7	95.1
	0.4	GEE	1000	95.2	96.0	95.5	94.5	85.4
	0.6	ML	1000	95.9	94.5	95.3	94.9	95.5
	0.6	GEE	1000	95.5	95.5	95.5	94.9	84.5
	0.7	ML	1000	95.3	94.2	94.7	96.2	92.9
	0.7	GEE	1000	95.3	94.2	95.0	95.9	87.2
300	0.2	ML	1000	95.2	95.0	94.7	94.7	94.5
	0.2	GEE	1000	95.6	95.3	94.8	94.6	91.5
	0.4	ML	1000	93.5	95.4	94.2	93.9	96.5
	0.4	GEE	1000	93.7	96.0	94.9	94.3	86.2
	0.6	ML	1000	93.2	95.4	94.9	94.0	95.2
	0.6	GEE	1000	93.8	95.6	94.6	94.9	85.9
	0.7	ML	1000	94.5	95.1	94.1	94.4	92.4
	0.7	GEE	1000	94.8	95.9	94.6	94.8	88.0

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