BMC Medical Research Methodology

Table 1 Results of both MLE and Firth’s Penalized Likelihood Estimation for both β_b and β_c under Weibull Distribution. Each cell represents mean and standard deviation of estimates over number of valid cases (removing the simulations that were failed to achieve convergence) 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	Estimate	SE	Sim.SE	Width	Estimates	SE	Sim.SE	Width
						(95% CI)				(95% CI)
30	20	β_c=1.2	1.198	0.155	0.171	0.606	1.190	0.142	0.170	0.557
	40		1.344	0.193	0.219	0.758	1.185	0.174	0.216	0.681
	60		1.528	0.266	0.334	1.04	1.174	0.225	0.325	0.880
	20	β_b=0.7	0.689	0.272	0.307	1.067	0.681	0.245	0.304	0.960
	40		0.686	0.321	0.362	1.259	0.663	0.279	0.350	1.095
	60		0.948	56.262	1.203	220.325	0.639	0.340	0.461	1.332
50	20	β_c=1.2	1.210	0.120	0.121	0.469	1.205	0.114	0.120	0.446
	50		1.222	0.170	0.180	0.665	1.202	0.157	0.176	0.616
	80		1.781	0.311	7.080	1.218	1.190	0.268	0.640	1.049
	20	β_b=0.7	0.695	0.212	0.224	0.832	0.690	0.199	0.223	0.780
	50		0.704	0.276	0.291	1.082	0.684	0.250	0.284	0.979
	80		3.026	124.560	26.619	486.810	0.983	0.378	8.814	1.482
100	20	β_c=1.2	1.200	0.083	0.083	0.325	1.197	0.081	0.082	0.317
	50		1.209	0.117	0.120	0.458	1.199	0.112	0.119	0.440
	80		4.807	0.210	48.926	0.824	1.175	0.193	0.217	0.756
	20	β_b=0.7	0.703	0.150	0.150	0.587	0.701	0.145	0.150	0.568
	50		0.708	0.193	0.197	0.758	0.698	0.184	0.194	0.720
	80		3.855	0.327	65.946	1.274	0.668	0.290	0.305	1.137

β_c= Coefficient of continuous covariate and β_b= Coefficient of binary covariate

Back to article page

ISSN: 1471-2288

Contact us

General enquiries: journalsubmissions@springernature.com