Table 1. Simulation results for the mean ratio (exposed vs unexposed), using the APV and the derived mean estimation from a latent (conventional) log-logit model, and the direct mean estimation from a marginal log-logit working model, with data generated from ZINB models.

		Latent log-logit working model									Marginal log-logit working model
		APV estimation				Derived marginal mean estimation					Direct marginal mean estimation
True MR	n∓	EMR	RB(%)	MSE	CP(%)	EMR	RB(%)	MSE	CP(%)	AIC	EMR	RB(%)	MSE	CP(%)	AIC
Data generated from a ZINB model with a latent mean
0.543	100	0.547	0.743	0.017	92.7	0.545	0.314	0.019	99.8	434.14	0.548	0.915	0.018	92.6	434.17
	200	0.547	0.740	0.008	94.8	0.546	0.452	0.008	98.6	863.40	0.547	0.675	0.008	95.1	863.44
	400	0.546	0.546	0.005	92.1	0.545	0.281	0.005	99.9	1716.61	0.546	0.480	0.005	93.4	1716.68
	1000	0.545	0.301	0.002	94.2	0.543	0.024	0.002	>99.9	4285.21	0.544	0.224	0.002	95.3	4285.30
Data generated from a ZINB model with a marginal mean
0.607	100	0.625	3.086	0.021	94.7	0.625	3.071	0.045	96.7	475.74	0.626	3.281	0.021	94.7	475.72
	200	0.614	1.288	0.011	93.1	0.613	1.003	0.011	99.9	945.35	0.614	1.192	0.011	93.3	945.35
	400	0.609	0.435	0.005	94.7	0.608	0.254	0.005	>99.9	1883.04	0.608	0.395	0.005	94.5	1883.00
	1000	0.608	0.228	0.002	95.6	0.607	0.055	0.002	>99.9	4704.47	0.607	0.146	0.002	95.6	4704.40

^∓n/2 is sample size per group