A note on obtaining correct marginal predictions from a random intercepts model for binary outcomes

Table 1 Calibration results from the simulation study with 20 centres

Method	ICC	Calibration Intercept (se)	Calibration Slope (se)
No clustering	0.05	−0.022 (0.130)	0.974 (0.077)
RE-zero	0.05	−0.008 (0.132)	0.948 (0.076)
RE-integ	0.05	−0.026 (0.129)	0.970 (0.075)
RE-approx	0.05	−0.024 (0.129)	0.968 (0.075)
GEE	0.05	−0.023 (0.131)	0.970 (0.076)
No clustering	0.10	−0.019 (0.174)	0.981 (0.073)
RE-zero	0.10	0.031 (0.182)	0.922 (0.069)
RE-integ	0.10	−0.014 (0.173)	0.984 (0.069)
RE-approx	0.10	−0.009 (0.173)	0.979 (0.068)
GEE	0.10	−0.026 (0.175)	0.983 (0.071)
No clustering	0.15	−0.016 (0.208)	0.971 (0.080)
RE-zero	0.15	0.049 (0.225)	0.884 (0.071)
RE-integ	0.15	−0.009 (0.207)	0.972 (0.073)
RE-approx	0.15	−0.004 (0.209)	0.964 (0.071)
GEE	0.15	−0.026 (0.211)	0.971 (0.076)
No clustering	0.30	0.004 (0.282)	0.963 (0.100)
RE-zero	0.30	0.142 (0.333)	0.788 (0.070)
RE-integ	0.30	−0.020 (0.280)	0.977 (0.090)
RE-approx	0.30	−0.009 (0.283)	0.956 (0.084)
GEE	0.30	−0.018 (0.285)	0.982 (0.097)

Calibration intercept and calibration slope using different forms of marginal risk calculation for varying degrees of clustering (median calibration and empirical standard errors over 100 simulated datasets)

ISSN: 1471-2288