. Author manuscript; available in PMC: 2009 Oct 1.

Published in final edited form as: J Am Stat Assoc. 2008 Mar 1;103(481):61–73. doi: 10.1198/016214507000000329

Table 5.

Range in relative asymptotic bias for the GRE and FM models when the true conditional dependence structure is (i) a Bahadur model with all correlations of order 3 and higher equal to 0, (ii) a log-linear model with a three-way interaction, and (iii) a beta-binomial model

True model	Estimator	GRE	FM
Bahadur model^a	SENS	−2.8–.19%	−.83–4.4%
	SPEC	−.75–.18%	−.40–1.6%
Log-linear model^b	SENS	0–4.3%	0–7.0%
	SPEC	−.20–1.3%	0–3.7%
Beta-binomial model^c	SENS	−.13–0%	.17–4.3%
	SPEC	−.07–.05%	.14–3.8%

NOTE: The range is over a range of sensitivities and specificities between .65 and .95. The range in relative bias is for P_d = .20, J = 5, and for 50% completely random verification (r = .5).

Bahadur model with two-way correlations of .20 and all correlations of order 3 and higher equal to 0.

Log-linear model with log P(Y_i|d_i) = β_{d_i} + .5I + Δ, where I is an indicator that is equal to 1 if at least three or more of the Y_ij's are equal to 1 and where Δ is a normalizing constant so that P(Y_i|d_i) sum to 1 over all possible Y_i. The parameters β_{d_i} were chosen to correspond to the different values of sensitivity and specificity.

P(Y_i|d_i) followed beta-binomial distributions with β = .4 (for both d_i = 0 or 1) and α varied corresponding to the desired sensitivity or specificity.