BMC Medical Research Methodology

Table 2 Results of both β₀ and b from Maximum Likelihood Estimation and Firth’s Penalized Likelihood Estimation under Weibull Distribution. Each cell represents mean and standard deviation of estimates from valid cases out of 1000 simulations. The maximum number of convergence failure for MLE is 60 when sample sizze is 50 and censoring rate 80%

From: On estimation for accelerated failure time models with small or rare event survival data

			MLE			Firth
Sample Size (n)	Cens.%	True Coefficients	Estimates	SE	Sim.SE	Estimates	SE	Sim.SE
30	20	β₀=3	2.989	0.187	0.213	2.989	0.129	0.212
	40		3.452	0.216	0.246	2.984	0.144	0.242
	60		3.726	0.292	0.354	2.976	0.176	0.333
	20	b=0.67	0.618	0.100	0.107	0.616	0.096	0.107
	40		0.607	0.113	0.123	0.603	0.108	0.122
	60		0.597	0.136	0.159	0.585	0.123	0.153
50	20	β₀=3	2.987	0.146	0.154	2.988	0.104	0.153
	50		2.987	0.189	0.197	2.983	0.127	0.194
	80		5.893	6.859	22.755	3.649	0.207	11.591
	20	b=0.67	0.642	0.079	0.083	0.641	0.077	0.083
	50		0.635	0.097	0.103	0.631	0.093	0.102
	80		0.598	0.146	0.177	0.584	0.169	0.348
100	20	β₀=3	2.988	0.104	0.107	2.989	0.075	0.107
	50		2.988	0.134	0.139	2.986	0.092	0.137
	80		21.583	0.276	385.896	3.512	0.152	12.415
	20	b=0.67	0.654	0.057	0.058	0.653	0.055	0.058
	50		0.649	0.070	0.072	0.647	0.067	0.071
	80		0.633	0.106	0.122	0.626	0.115	0.112

β₀= Intercept and b= Scale parameter of the location-scale distribution

Back to article page

ISSN: 1471-2288

Contact us

General enquiries: journalsubmissions@springernature.com