BMC Medical Research Methodology

Table 3 Simulation results: estimations of bias and mean squared error for the Weibull model

From: Estimating time-to-onset of adverse drug reactions from spontaneous reporting databases

						Naive estimator		TBE
					$\hat{λ}$		$\hat{β}$		$\hat{λ}$		$\hat{β}$
λ	β	p	n	BIAS	MSE	BIAS	MSE	BIAS	MSE	BIAS	MSE	NPM
0.05	0.5	0.25	100	4.04	16.7	0.200	0.044	0.465	0.51	0.046	0.007	312
			500	3.95	15.6	0.195	0.039	0.106	0.04	0.013	0.001	201
0.05	0.5	0.50	100	0.762	0.60	0.167	0.031	0.068	0.018	0.024	0.005	172
			500	0.747	0.56	0.164	0.028	0.015	0.003	0.003	0.001	22
0.05	0.5	0.80	100	0.160	0.027	0.119	0.017	0.008	0.002	0.009	0.004	9
			500	0.156	0.025	0.113	0.013	0.001	<0.001	0.001	<0.001	0
1	0.5	0.25	100	80.4	6612	0.201	0.044	8.68	183	0.046	0.007	300
			500	78.9	6249	0.194	0.038	2.07	17	0.012	0.001	186
1	0.5	0.50	100	15.0	233	0.174	0.034	1.53	7.99	0.031	0.006	163
			500	15.0	225	0.164	0.028	0.32	1.17	0.003	0.001	24
1	0.5	0.80	100	3.20	10.8	0.117	0.017	0.16	0.67	0.007	0.004	13
			500	3.15	10.0	0.112	0.013	0.041	0.15	<0.001	<0.001	0
0.05	2	0.25	100	0.121	0.015	0.354	0.16	<0.001	0.002	0.097	0.075	8
			500	0.120	0.014	0.333	0.12	-0.004	0.001	0.020	0.016	2
0.05	2	0.50	100	0.065	0.004	0.278	0.11	-0.004	<0.001	0.047	0.074	6
			500	0.064	0.004	0.264	0.08	-0.002	<0.001	0.004	0.016	0
0.05	2	0.80	100	0.032	0.001	0.182	0.063	<0.001	<0.001	0.046	0.063	1
			500	0.032	0.001	0.157	0.031	<0.001	<0.001	0.008	0.014	0
1	2	0.25	100	2.41	5.84	0.364	0.17	0.090	0.79	0.10	0.075	1
			500	2.41	5.79	0.336	0.12	-0.082	0.38	0.02	0.015	0
1	2	0.50	100	1.29	1.68	0.283	0.12	-0.073	0.33	0.052	0.069	3
			500	1.29	1.65	0.261	0.07	-0.065	0.12	-0.002	0.017	0
1	2	0.80	100	0.638	0.41	0.186	0.065	-0.024	0.086	0.045	0.064	0
			500	0.636	0.40	0.154	0.030	-0.007	0.014	0.004	0.013	0

The mean squared error formula is $MSE (\hat{λ}) = Var (\hat{λ}) + {(BIAS (\hat{λ}))}^{2}$ . Calculations were made on the replications where there was no problem of maximization. In the last column appear the number of problems of maximization for the truncation-based approach. There was no problem of maximization for the naive approach. Abbreviations : TBE truncation-based estimator, MSE mean squared error, NPM number of maximization problems.

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