Table 1.

Average and standard deviation (in parentheses) of the confidence interval width of the Q‐profile method, GENQ method with variance weights ( $a_i=1/{\widehat{\sigma }}_i^2$), and GENQ method with standard error weights (SE; $a_i=1/{\widehat{\sigma }}_i$)

		${\pi }_i^C=0.5$
		τ = 0	τ = 0.1	τ = 0.2	τ = 0.3	τ = 0.4	τ = 0.5
k = 5	Q‐profile	0.830 (0.392)	0.870 (0.398)	0.980 (0.405)	1.121 (0.433)	1.280 (0.454)	1.449 (0.501)
	GENQ (variance)	0.747 (0.308)	0.797 (0.321)	0.934 (0.355)	1.103 (0.402)	1.290 (0.450)	1.478 (0.512)
	GENQ (SE)	0.775 (0.332)	0.817 (0.340)	0.942 (0.359)	1.097 (0.393)	1.267 (0.416)	1.438 (0.460)
k = 10	Q‐profile	0.461 (0.188)	0.490 (0.186)	0.564 (0.175)	0.641 (0.161)	0.710 (0.155)	0.786 (0.166)
	GENQ (variance)	0.404 (0.141)	0.440 (0.144)	0.531 (0.142)	0.623 (0.134)	0.709 (0.139)	0.802 (0.167)
	GENQ (SE)	0.435 (0.156)	0.465 (0.156)	0.546 (0.152)	0.636 (0.136)	0.709 (0.120)	0.783 (0.127)
k = 40	Q‐profile	0.221 (0.075)	0.251 (0.068)	0.285 (0.040)	0.282 (0.029)	0.299 (0.030)	0.327 (0.034)
	GENQ (variance)	0.199 (0.059)	0.230 (0.054)	0.267 (0.027)	0.269 (0.015)	0.294 (0.026)	0.332 (0.035)
	GENQ (SE)	0.227 (0.069)	0.255 (0.064)	0.3 (0.041)	0.295 (0.023)	0.295 (0.015)	0.318 (0.024)
k = 80	Q‐profile	0.167 (0.052)	0.198 (0.043)	0.201 (0.022)	0.191 (0.014)	0.205 (0.015)	0.225 (0.017)
	GENQ (variance)	0.154 (0.043)	0.185 (0.036)	0.187 (0.019)	0.181 (0.007)	0.201 (0.013)	0.228 (0.017)
	GENQ (SE)	0.180 (0.051)	0.207 (0.045)	0.226 (0.029)	0.196 (0.011)	0.200 (0.007)	0.218 (0.012)
k = 160	Q‐profile	0.130 (0.039)	0.161 (0.027)	0.137 (0.011)	0.133 (0.007)	0.143 (0.007)	0.157 (0.008)
	GENQ (variance)	0.122 (0.034)	0.153 (0.024)	0.126 (0.010)	0.125 (0.003)	0.140 (0.006)	0.159 (0.009)
	GENQ (SE)	0.145 (0.040)	0.174 (0.032)	0.158 (0.024)	0.134 (0.002)	0.139 (0.004)	0.152 (0.006)

		${\pi }_i^C=0.1$
		τ = 0	τ = 0.1	τ = 0.2	τ = 0.3	τ = 0.4	τ = 0.5
k = 5	Q‐profile	1.399 (0.712)	1.412 (0.714)	1.488 (0.728)	1.587 (0.751)	1.732 (0.759)	1.889 (0.793)
	GENQ (variance)	1.201 (0.500)	1.233 (0.518)	1.315 (0.537)	1.449 (0.589)	1.614 (0.627)	1.791 (0.682)
	GENQ (SE)	1.276 (0.559)	1.297 (0.569)	1.372 (0.581)	1.486 (0.618)	1.639 (0.641)	1.807 (0.682)
k = 10	Q‐profile	0.734 (0.311)	0.760 (0.314)	0.814 (0.317)	0.899 (0.316)	0.981 (0.306)	1.067 (0.306)
	GENQ (variance)	0.626 (0.223)	0.655 (0.23)	0.718 (0.239)	0.814 (0.247)	0.912 (0.243)	1.005 (0.241)
	GENQ (SE)	0.696 (0.256)	0.722 (0.259)	0.774 (0.264)	0.862 (0.272)	0.955 (0.266)	1.051 (0.262)
k = 40	Q‐profile	0.317 (0.113)	0.337 (0.114)	0.395 (0.11)	0.455 (0.087)	0.474 (0.065)	0.477 (0.055)
	GENQ (variance)	0.289 (0.094)	0.310 (0.096)	0.37 (0.093)	0.429 (0.069)	0.447 (0.042)	0.448 (0.028)
	GENQ (SE)	0.348 (0.111)	0.365 (0.111)	0.417 (0.109)	0.485 (0.094)	0.526 (0.071)	0.525 (0.053)
k = 80	Q‐profile	0.223 (0.082)	0.246 (0.082)	0.307 (0.075)	0.347 (0.047)	0.330 (0.035)	0.321 (0.026)
	GENQ (variance)	0.210 (0.073)	0.233 (0.072)	0.295 (0.066)	0.332 (0.041)	0.309 (0.028)	0.299 (0.013)
	GENQ (SE)	0.263 (0.085)	0.282 (0.084)	0.336 (0.08)	0.396 (0.059)	0.395 (0.049)	0.354 (0.036)
k = 160	Q‐profile	0.160 (0.060)	0.183 (0.061)	0.249 (0.050)	0.256 (0.032)	0.223 (0.016)	0.221 (0.012)
	GENQ (variance)	0.154 (0.055)	0.178 (0.056)	0.243 (0.046)	0.245 (0.034)	0.207 (0.012)	0.205 (0.005)
	GENQ (SE)	0.199 (0.067)	0.219 (0.067)	0.279 (0.059)	0.322 (0.042)	0.271 (0.039)	0.237 (0.012)

Abbreviation: GENQ, generalized Q‐statistic.

The probability of having the outcome of interest in the control group is denoted by ${\pi }_i^C$, the number of primary studies in a meta‐analysis with k, and the amount of between‐study heterogeneity with τ.