Simple parametric survival analysis with anonymized register data: A cohort study with truncated and interval censored event and censoring times

Støvring, Henrik; Kristiansen, Ivar S

doi:10.1186/1756-0500-4-308

Table 3 Simulation results comparing analyses with multiple imputation or single midpoint imputation in terms of bias, coverage probability and relative efficiency

From: Simple parametric survival analysis with anonymized register data: A cohort study with truncated and interval censored event and censoring times

				1 month			2 months			6 months			12 months
Parameter	Censoring	Estimation	n	RB	Cov	SEIF	RB	Cov	SEIF	RB	Cov	SEIF	RB	Cov	SEIF
log(λ)	3%	MC	500	3.0	95.5	0.8	-3.2	94.9	1.6	7.8	94.9	6.4	17.7	94.7	16.8
			1,000	0.0	94.7	0.8	3.5	94.3	1.7	2.6	95.6	6.4	14.5	94.9	16.7
			10,000	0.4	95.4	0.8	-0.3	94.9	1.7	2.9	95.5	6.4	14.2	91.0	16.8
		MI	500	3.0	95.5	0.8	-3.4	94.9	1.6	5.7	94.9	6.4	11.1	95.0	16.8
			1,000	-0.1	94.8	0.8	3.3	94.3	1.7	1.0	95.4	6.4	8.2	94.8	16.7
			10,000	0.3	95.4	0.8	-0.3	94.9	1.7	1.3	95.6	6.4	8.0	94.0	16.8
	6%	MC	500	2.3	95.7	0.7	0.6	94.7	1.6	9.4	95.4	6.3	29.6	94.0	16.6
			1,000	0.4	94.8	0.7	1.2	95.5	1.6	9.1	95.7	6.3	29.6	94.0	16.7
			10,000	1.1	94.7	0.8	0.7	94.6	1.7	9.0	94.0	6.3	30.7	77.6	16.8
		MI	500	2.2	95.7	0.7	0.4	94.7	1.6	6.9	95.2	6.3	19.7	94.6	16.8
			1,000	0.3	94.7	0.7	1.1	95.5	1.6	7.2	95.7	6.3	21.3	94.6	16.9
			10,000	1.0	94.7	0.8	0.5	94.6	1.7	6.8	95.0	6.4	22.5	85.7	17.0
	9%	MC	500	0.4	95.4	0.8	-0.9	95.3	1.6	11.1	95.4	6.2	49.7	92.8	16.9
			1,000	0.6	95.4	0.7	0.9	95.4	1.5	12.2	95.0	6.2	46.7	91.8	16.8
			10,000	0.7	95.1	0.8	1.5	94.9	1.6	12.2	91.9	6.2	45.7	57.1	16.8
		MI	500	0.3	95.4	0.8	-0.9	95.4	1.6	8.3	95.4	6.3	39.3	93.8	17.2
			1,000	0.6	95.4	0.7	0.5	95.4	1.5	9.5	95.1	6.3	35.9	93.3	17.1
			10,000	0.5	95.1	0.8	1.2	94.8	1.6	9.4	93.4	6.3	34.9	73.7	17.1
γ	3%	MC	500	0.6	95.0	2.0	1.0	94.8	4.1	3.9	94.5	13.5	7.6	94.8	30.2
			1,000	0.8	95.4	2.1	2.1	95.1	4.4	1.6	95.0	13.6	6.9	95.0	30.3
			10,000	-0.2	95.3	2.0	0.5	95.1	4.2	1.6	94.9	13.6	6.0	90.7	30.3
		MI	500	0.4	94.8	2.0	0.9	94.8	4.1	2.0	94.5	13.4	2.6	94.8	29.8
			1,000	0.6	95.4	2.1	2.0	95.0	4.4	-0.0	94.8	13.5	2.1	95.0	29.9
			10,000	-0.4	95.2	2.0	0.4	95.2	4.2	-0.1	95.1	13.4	1.2	94.4	29.8
	6%	MC	500	2.4	95.7	2.0	1.7	94.6	4.1	6.4	94.8	14.1	12.8	94.1	31.6
			1,000	-0.4	95.5	2.0	1.8	95.4	4.4	4.5	94.6	14.1	13.3	93.9	31.8
			10,000	0.1	94.3	2.2	0.7	94.6	4.5	3.7	92.9	14.3	12.8	79.8	31.9
		MI	500	2.2	95.6	2.0	1.5	94.6	4.1	4.1	94.9	14.0	6.8	94.4	31.3
			1,000	-0.6	95.5	1.9	1.7	95.4	4.5	2.6	94.4	14.1	7.3	94.8	31.6
			10,000	-0.0	94.2	2.2	0.6	94.6	4.5	1.8	94.2	14.2	6.8	91.3	31.7
	9%	MC	500	3.9	95.6	2.6	3.0	95.7	4.7	6.1	95.4	15.2	20.3	92.4	33.8
			1,000	1.9	95.5	2.2	1.8	94.4	4.7	7.2	95.4	15.0	21.0	92.3	33.6
			10,000	-0.1	95.5	2.3	1.1	95.0	4.7	5.4	92.4	15.0	20.6	57.1	33.6
		MI	500	3.7	95.6	2.6	2.8	95.7	4.7	3.5	95.6	15.2	12.9	93.5	33.7
			1,000	1.7	95.6	2.2	1.6	94.4	4.7	4.8	95.4	15.0	13.3	94.6	33.5
			10,000	-0.3	95.4	2.3	0.9	95.2	4.7	3.2	94.2	15.0	12.9	80.4	33.5

Simulation results for estimation of log(λ) and γ from datasets with Weibull distributed event times, constant censoring rates, ten years of follow-up, and varying widths of interval censorings. Results for each setting represent analyses of 2,500 generated datasets. Column headers in months indicate width of intervals inducing interval censoring; censoring refers to annual proportion of censoring; Estimation refers to estimation procedure: MC to single imputation of midpoint for censoring events (Equation 5) MI to multiple imputation, (Equation 4). RB is median relative bias in percent, Cov is coverage probability of nominal 95% confidence intervals, while SEIF is percent increase in median standard error relative to analysis with ordinary censoring, but no interval censoring.

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ISSN: 1756-0500

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