Table 4.

Results based on 10,000 simulated data sets for estimation and testing of log OR β for a continuous exposure and q for effect modification by a dichotomous stratum-specific factor using a design with 1:1 matching and N=960 strata(pairs). The log OR for the main effect of the effect modifier, γ, was 0.00 for these simulations.

		Pool sizea
Parameters		1	2	4	6
β = −0.2	Mean of β̂	−0.201	−0.202	−0.204	−0.207
	Empirical standard errorb of β̂	0.040	0.043	0.046	0.049
	Model-based standard errorc of β̂	0.040	0.041	0.044	0.048
	Powerd	1.000	1.000	1.000	1.000
	Coverage of nominal 95% C.I.e	0.948	0.949	0.951	0.958
θ = −0.3	Mean of θ̂	−0.312	−0.324	−0.346	−0.398
	Empirical standard error of θ̂	0.109	0.129	0.185	0.343
	Model-based standard error of θ̂	0.112	0.131	0.180	0.305
	Power	0.885	0.840	0.737	0.607
	Coverage of nominal 95% C.I.	0.963	0.958	0.960	0.956
β = 0.2	Mean of β̂	0.202	0.203	0.206	0.209
	Empirical standard error of β̂	0.025	0.028	0.034	0.042
	Model-based standard error of β̂	0.025	0.028	0.034	0.043
	Power	1.000	1.000	1.000	1.000
	Coverage of nominal 95% C.I.	0.951	0.951	0.959	0.964
θ = −0.3	Mean of θ̂	−0.311	−0.313	−0.320	−0.327
	Empirical standard error of θ̂	0.059	0.062	0.071	0.082
	Model-based standard error of θ̂	0.061	0.064	0.071	0.080
	Power	1.000	1.000	1.000	1.000
	Coverage of nominal 95% C.I.	0.963	0.960	0.962	0.968

^apool size = 1 means standard analysis based on unpooled or individual exposure measurements.

^bsquare root of the empirical variance based 10,000 estimates; divide by 100 to get the standard error of the mean β̂.

^csquare root of the average model-based variance. For sufficiently large N, this value is proportional to the expected length of the Wald confidence interval.

^dPower based on likelihood ratio tests.

^enominal 95% confidence intervals were calculated using model-based standard error (Wald intervals)