Dose-response meta-analysis of differences in means

Table 4 Study-specific dose-response coefficients and corresponding covariances for different dose-response models considered in the analysis

Model	id	\(\hat \theta _{1}\)	\(\hat \theta _{2}\)	\(\text {Var} \left (\hat \theta _{1} \right)\)	\(\text {Cov} \left (\hat \theta _{1},\hat \theta _{2} \right)\)	\(\text {Var} \left (\hat \theta _{2} \right)\)
Restricted cubic splines	1	0.55	0.55	0.065	0.065	0.065
	2	0.59	0.59	0.031	0.031	0.031
	3	0.84	−1.69	0.054	−0.12	0.38
	4	0.47	−0.54	0.021	−0.043	0.15
	5	0.78	−1.25	0.23	−0.62	1.8
Fractional Polynomials	1	17.47	−7.84	2.9e+02	−2.2e+02	1.8e+02
	2	29.59	−12.42	2.5e+02	−1.6e+02	1e+02
	3	32.12	−13.47	1.4e+02	−70	37
	4	18.48	−6.42	1.8e+02	−93	49
	5	21.97	−7.00	2.3e+02	−1.1e+02	55
Emax	1	8.13	3.13	27	24	36
	2	11.39	0.00	38	35	42
	3	10.54	0.00	37	53	1e+02
	4	9.20	0.00	60	1.4e+02	3.6e+02
	5	13.28	0.94	23	2.7	2.7
Quadratic	1	1.54	−0.09	0.96	−0.086	0.0083
	2	1.54	−0.05	0.35	−0.017	0.00089
	3	1.40	−0.04	0.18	−0.0055	0.00018
	4	0.83	−0.02	0.14	−0.0047	0.00017
	5	1.08	−0.02	0.51	−0.016	0.00051
Piecewise linear	1	0.55		0.065
	2	0.59		0.031
	3	0.84	−1.69	0.054	−0.12	0.38
	4	0.47	−0.54	0.021	−0.043	0.15
	5	0.78	−1.25	0.23	−0.62	1.8

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