Table 1:

Simulation summary statistics for marginal single failure hazard ratio parameters β₁₀ and β₀₁ and for double failure hazard ratio parameter β₁₁, and for related estimators from sandwich-form variance estimators, under the Clayton–Oakes model (9) with β₁₀ = β₀₁ = $\gamma$ and a binary covariate z. This model implies marginal hazard ratio (for z = 1 versus z = 0) of $e^{\gamma }$ for both T₁ and T₂, and double failure hazard ratio of $e^{\gamma }(e^{\gamma }+\theta )/(1+\theta ).$

		$(\theta =2,\gamma =0)$
Sample size (n)		250				500				100
T1 and T2 failing %		16.7				16.7				100
Double failure %		5.3				5.3				100
	True	Samplea	Sampleb	Sandwichb	95% CIb	Sample	Sample	Sandwich	95% CI	Sample	Sample	Sandwich	95% CI
		Mean	SD	SD	Coverage	Mean	SD	SD	Coverage	Meana	SD	SD	Coverage
β 10	0	0.003	0.315	0.316	0.953	0.006	0.227	0.222	0.951	−0.001	0.213	0.203	0.933
β 01	0	0.007	0.327	0.317	0.948	−0.008	0.224	0.221	0.952	−0.005	0.216	0.203	0.943
β 11	0	−0.001	1.222	0.606	0.961	−0.007	0.440	0.420	0.949	−0.003	0.282	0.263	0.928
		$(\theta =2,\gamma =\text{log}2)$
Sample size (n)		250				500				100
T1 and T2 failing %		22.6				22.6				100
Double failure %		8.2				8.2				100
β 10	0.693	0.706	0.281	0.281	0.966	0.705	0.203	0.198	0.941	0.696	0.222	0.212	0.942
β 01	0.693	0.707	0.287	0.282	0.959	0.697	0.199	0.197	0.955	0.696	0.223	0.212	0.937
β 11	0.981	1.056	0.798	0.525	0.956	1.004	0.381	0.364	0.951	0.986	0.315	0.288	0.929

^aBased on 1000 simulations at each sampling configuration.

^bAbbreviations: Sample SD is sample standard deviation of the regression parameter estimates; Sandwich SD is the corresponding average of standard deviation estimates derived from the sandwich form estimator of variance for $\widehat{\beta },$ and 95% CI coverage is the fraction of simulated samples from which the approximate 95% confidence interval, formed from $\widehat{\beta }$ and its sandwich-form variance estimator, includes the true β.