Table 2.

Survival timesfor groups 1 and 2 simulated from gamma(5, 2) and gamma(1.5, 4) distributions, respectively. For group 1, left and right truncation times correctly assumed to come from a gamma(3,1) and gamma(5, 2) distribution, respectively, resulting in 54% of the observations truncated. For group 2, left and right truncation times correctly assumed to come from a gamma(1.5, 3) and gamma(12.5, 1) distribution, respectively, resulting in 53% of the observations truncated. The sample sizes are 50 and 30 for groups 1 and 2, respectively. For t = 3, 6, 9,12, we compute the bias, standard deviation (SD), and estimated standard error ($\widehat{SE}$) of Δ₁₂ = ${\widehat{S}}_1$(t) − ${\widehat{S}}_2$(t), which is the difference in survival probabilities between group 1 and group 2 at time t. The true differences between the survival probabilities at time t = 3, 6, 9, 12 are 0.30, 0.42, 0.32, 0.17, respectively.

	SPMLE			NPMLE			eCDF
t	bias(${\widehat{\Delta }}_{12}$)	SD(${\widehat{\Delta }}_{12}$)	$\widehat{\mathrm{SE}}({\widehat{\Delta }}_{12})$	bias(${\widehat{\Delta }}_{12}$)	SD(${\widehat{\Delta }}_{12}$)	$\widehat{\mathrm{SE}}({\widehat{\Delta }}_{12})$	bias(${\widehat{\Delta }}_{12}$)	SD(${\widehat{\Delta }}_{12}$)	$\widehat{\mathrm{SE}}({\widehat{\Delta }}_{12})$
3	−0.01	0.14	0.14	0.01	0.15	0.13	−0.16	0.07	0.04
6	−0.01	0.13	0.13	0.00	0.13	0.13	−0.20	0.11	0.10
9	−0.01	0.15	0.14	0.00	0.15	0.14	−0.21	0.10	0.09
12	0.00	0.16	0.15	0.00	0.17	0.13	−0.14	0.06	0.05