. 2019 Jul 13;106(3):567–585. doi: 10.1093/biomet/asz030

Table 3.

Robustness of generalized meta-analysis estimation: results for the genmeta estimates using the study covariance estimators in the setting of logistic regression. In setting (I), data are simulated in the ideal setting where the covariate distribution, characterized by the mean, standard deviation and correlation of normal variates, is the same across all populations. In settings (II)–(IV), the assumption is violated by creating variations in means and/or standard deviations, correlations, and selection criteria across the studies and the reference sample. The vectors of covariate means, variances and correlations are denoted by , and for , where , , , , , , , and . Estimated standard deviation is obtained from the asymptotic formula (1) and used to construct confidence intervals

Setting	Bias	SD (ESD)	RMSE	CR	AL
I	0.001	0.111 (0.112)	0.111	0.947	0.437
	0.002	0.098 (0.099)	0.098	0.956	0.389
	0.005	0.096 (0.098)	0.096	0.954	0.382
	0.010	0.103 (0.104)	0.103	0.952	0.405
	0.006	0.083 (0.083)	0.083	0.954	0.324
	0.005	0.085 (0.088)	0.085	0.956	0.343
II	0.003	0.139 (0.136)	0.139	0.939	0.529
	0.003	0.084 (0.086)	0.084	0.956	0.335
	0.003	0.112 (0.111)	0.112	0.949	0.431
	0.013	0.124 (0.126)	0.125	0.946	0.493
	0.006	0.073 (0.075)	0.073	0.958	0.291
	0.005	0.097 (0.100)	0.097	0.949	0.391
	0.092	0.142 (0.151)	0.169	0.958	0.579
	0.019	0.105 (0.109)	0.107	0.963	0.423
	0.053	0.120 (0.129)	0.131	0.971	0.495
	0.035	0.099 (0.099)	0.106	0.917	0.385
	0.002	0.096 (0.096)	0.096	0.954	0.377
	0.012	0.087 (0.087)	0.088	0.944	0.343
III	0.060	0.113 (0.113)	0.128	0.916	0.443
	0.001	0.096 (0.097)	0.096	0.955	0.379
	0.006	0.103 (0.102)	0.104	0.944	0.398
	0.039	0.130 (0.132)	0.135	0.939	0.515
	0.006	0.097 (0.100)	0.097	0.958	0.392
	0.027	0.116 (0.118)	0.119	0.944	0.461
	0.036	0.165 (0.173)	0.169	0.957	0.671
	0.013	0.103 (0.109)	0.104	0.962	0.424
	0.003	0.143 (0.153)	0.143	0.959	0.591
IV	0.014	0.123 (0.127)	0.124	0.961	0.494
	0.008	0.105 (0.109)	0.105	0.965	0.428
	0.001	0.094 (0.093)	0.093	0.958	0.366

SD, standard deviation; ESD, estimated standard deviation; RMSE, square root of mean square error; CR, coverage rate of 95% confidence intervals; AL, average length of 95% confidence intervals.