Table 2.

Sample sizes for the optimal and standard log-rank tests for various cure rates in two groups with a nominal type I error of 5% and power of 90%. Here, sample sizes were calculated under the exponential model, with a hazard parameter λ = 1 and a uniform accrual over the interval [0, τ], where τ is determined by the percentage of censoring.

Cure rate (π1, π2)
		(.05, .15)	(.05, .2)	(.1, .2)	(.1, .3)	(.2, .4)	(.3, .5)	(.4, .6)
Test	Cens			Sample size
L	None	598	301	738	217	257	279	281
	10%	766	379	916	263	304	323	321
	20%	1067	513	1218	338	375	388	379
	30%	1566	730	1697	453	481	483	460
	40%	2323	1058	2415	623	632	616	573
	50%	3479	1577	3509	881	860	813	740
LK	None	394	215	554	177	230	261	270
	10%	517	275	698	217	272	303	310
	20%	766	391	964	286	341	367	367
	30%	1233	597	1423	398	445	461	448
	40%	1993	926	2144	569	597	594	562
	50%	3180	1437	3262	831	828	794	729

Censoring time was uniformly distributed over [0, τ], with the value of τ being chosen so that the probability of the failure time being censored for a subject who was not cured was the specified censoring percentage. Abbreviations: Cens: censoring; L: standard log-rank test; L_K: optimal log-rank test.