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

Table 5 Weibull Parameter estimates and estimated mean survival times, patients with metastatic colorectal cancer, Norway 1991-2005

Period	Estimation	$\hat{log (λ)}$ (s.e.)	$\hat{γ}$ (s.e.)	Mean	s.e.	Median	5%	95%
1991-1996	MI	0.2662 (0.0669)	0.4945 (0.0287)	1.196	0.086	1.194	1.057	1.340
	MC	0.2662 (0.0669)	0.4944 (0.0287)	1.196	0.086	1.194	1.057	1.340
	MA	0.1982 (0.0799)	0.3741 (0.0256)	1.203	0.086	1.201	1.064	1.346
	NT	-0.6520 (0.0358)	0.9200 (0.0185)	2.116	0.065	2.115	2.011	2.223
1997-2001	MI	-0.0700 (0.0679)	0.5962 (0.0334)	1.709	0.095	1.706	1.556	1.867
	MC	-0.0700 (0.0679)	0.5962 (0.0334)	1.709	0.095	1.706	1.556	1.867
	MA	-0.1752 (0.0685)	0.5801 (0.0319)	1.713	0.094	1.710	1.561	1.871
	NT	-0.8462 (0.0399)	1.0051 (0.0230)	2.317	0.071	2.314	2.204	2.435
2002-2005	MI	-0.5902 (0.0664)	0.9425 (0.0516)	1.926	0.074	1.925	1.806	2.051
	MC	-0.5904 (0.0664)	0.9428 (0.0516)	1.925	0.074	1.925	1.806	2.050
	MA	-0.6118 (0.0659)	0.9506 (0.0509)	1.926	0.074	1.925	1.807	2.050
	NT	-1.0586 (0.0467)	1.3282 (0.0386)	2.043	0.057	2.042	1.952	2.138
All	MI	-0.0650 (0.0385)	0.6099 (0.0197)	1.641	0.052	1.641	1.555	1.728
	MC	-0.0650 (0.0385)	0.6099 (0.0197)	1.641	0.052	1.641	1.555	1.728
	MA	-0.0722 (0.0424)	0.5048 (0.0178)	1.645	0.052	1.645	1.559	1.731
	NT	-0.8148 (0.0229)	1.0132 (0.0133)	2.224	0.040	2.223	2.159	2.291

Weibull parameter estimates for the three observation periods for survival after colon-rectal cancer based on data from the Cancer Registry of Norway. Estimated mean survival time for each of the three periods. Mean, s.e., median, 5%, and 95% percentiles all refer to the distribution of computed means obtained when sampling from the distribution of estimates. All subjects with event times smaller than three months are excluded by design. MI is multiple imputation (Equation 4), MC means replacing censored observations with the midpoint of their interval (Equation 5), MA means replacing all events and censored observations with the midpoint of their interval (Equation 6), NT means multiple imputation, but ignoring the truncation (Equation 4 with the term S_Y (M)^-1 omitted).

ISSN: 1756-0500