. Author manuscript; available in PMC: 2019 Dec 19.

Published in final edited form as: Biom J. 2019 Mar 25;61(4):1020–1032. doi: 10.1002/bimj.201800275

TABLE 3.

Imputation of two censored covariates based on Cox proportional hazards model

		X₁					X₂
Size	Method	Bias^*	SE	ESE	MSE	CP	Bias^*	SE	ESE	MSE	CP
250		(1a) Light censoring (25% censoring)
	Full	0.808	0.254	0.254	0.065	0.963	0.004	0.129	0.129	0.017	0.963
	CC	0.014	0.477	0.504	0.228	0.957	0.004	0.412	0.450	0.170	0.949
	CI	0.009	0.301	0.502	0.091	0.950	0.004	0.174	0.220	0.030	0.960
	CI-B	0.009	0.2911	0.311	0.085	0.960	0.004	0.178	0.191	0.032	0.949
		(1b) Heavy censoring (50% censoring)
	Full	0.008	0.254	0.254	0.065	0.963	0.004	0.129	0.129	0.017	0.963
	CC	0.039	1.070	1.205	1.146	0.925	0.094	1.103	1.224	1.225	0.921
	CI	0.010	0.380	0.432	0.145	0.950	0.007	0.271	0.413	0.073	0.960
	CI-B	0.010	0.399	0.415	0.159	0.957	0.007	0.271	0.300	0.073	0.949
500		(2a) Light censoring (25% censoring)
	Full	0.004	0.179	0.182	0.032	0.964	0.003	0.091	0.092	0.008	0.968
	CC	0.013	0.330	0.336	0.109	0.964	0.004	0.268	0.261	0.072	0.967
	CI	0.004	0.200	0.353	0.040	0.954	0.003	0.116	0.171	0.013	0.967
	CI-B	0.004	0.216	0.222	0.047	0.964	0.003	0.137	0.142	0.019	0.950
		(2b) Heavy censoring (50% censoring)
	Full	0.004	0.179	0.182	0.032	0.964	0.003	0.091	0.092	0.008	0.968
	CC	0.028	0.722	0.755	0.522	0.944	0.009	0.706	0.749	0.499	0.954
	CI	0.006	0.256	0.306	0.066	0.950	0.005	0.168	0.288	0.028	0.964
	CI-B	0.006	0.268	0.295	0.072	0.951	0.005	0.191	0.222	0.037	0.950
750		(3a) Light censoring (25% censoring)
	Full	0.004	0.144	0.149	0.021	0.965	0.002	0.072	0.071	0.005	0.968
	CC	0.013	0.268	0.285	0.072	0.964	0.003	0.216	0.224	0.047	0.967
	CI	0.004	0.160	0.183	0.026	0.960	0.003	0.092	0.209	0.008	0.955
	CI-B	0.004	0.168	0.183	0.028	0.964	0.003	0.094	0.121	0.008	0.955
		(3b) Heavy censoring (50% censoring)
	Full	0.004	0.144	0.149	0.021	0.965	0.002	0.072	0.071	0.005	0.968
	CC	0.009	0.580	0.590	0.336	0.960	0.007	0.551	0.594	0.304	0.954
	CI	0.005	0.204	0.245	0.042	0.960	0.007	0.130	0.244	0.017	0.964
	CI-B	0.005	0.210	0.230	0.044	0.957	0.007	0.143	0.175	0.020	0.951

Note. Full = full data; CC = complete-case; CI = conditional imputation; CI-B = CI with bootstrap; SE = (model-based) standard error; ESE = empirical standard error; CP = estimated coverage probability of 95% confidence intervals.

* $Relative bias % = (\frac{\hat{β} - β}{β}) \times 100 %$ .