doi:10.1016/j.csda.2004.06.013
Copyright © 2004 Elsevier B.V. All rights reserved.
Multiple imputation of missing values in a cancer mortality analysis with estimated exposure dose
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Nicola Sartoria, 
, 
, Alberto Salvanb and Karl Thomasethc
aDipartimento di Statistica, Università “Ca' Foscari” di Venezia, Campiello Sant'Agostin, San Polo 2347, 30125 Venezia, Italy
bIstituto di Analisi dei Sistemi ed Informatica “A. Ruberti”, Consiglio Nazionale delle Ricerche, viale Manzoni 30, 00185 Roma, Italy
cIstituto di Ingegneria Biomedica, Consiglio Nazionale delle Ricerche, Corso Stati Uniti 4, 35127 Padova, Italy
Received 3 May 2004;
revised 15 June 2004;
accepted 15 June 2004.
Available online 8 July 2004.
Abstract
Imputation of missing values in a cancer mortality analysis in relation to estimated dose of dioxin for a cohort of chemical workers is considered. In particular, some subjects of the cohort have the body mass index (BMI) missing. This quantity is an essential ingredient for a toxicokinetic model that gives the estimated absorbed dose, which is then used for risk estimation in a proportional hazards model. Imputation of BMI allows to recover information and to use the entire cohort for risk estimation. Both conditional mean imputation and multiple imputation are used. The latter is a simulation-based approach to the analysis of missing data which takes into account the uncertainty of the imputation process using several imputations for each missing value. In the present context, the two imputation methods gave similar results, both correcting for bias (although with some questions) and leading to increased efficiency with respect to the complete-case analysis that simply discards the partially unobserved individuals.
Keywords: Dioxin; Markov Chain Monte Carlo; Missing value; Multiple imputation; Proportional hazards model; Toxicokinetic model
Fig. 2. NIOSH subcohort: comparison between completely observed (R=1) and partially observed (R=0) individuals: (a) t0 (Age at first employment); (b) t1 (Age at time of second measurement of TCDD); (c) BMI(t1).
Fig. 3. NIOSH cohort: comparison between completely observed (R=1) and partially observed (R=0) individuals: (a) t0 (Age at first employment); (b) Duration of employment.
Fig. 4. Distribution of BMI(t0) for: the 4049 observed units (left), the 886 CI imputed values (center) and one set of 886 MI imputed values (right).
Table 1.
Model for BMI(t): Parameter estimates and standard errors with complete-case (CC), conditional mean with linear model (CML), conditional mean with mixed model (CMM), and multiple imputation (MI) methods, with several values of m
For multiple imputation, the degrees of freedom (d.f.), the relative increase in variance due to nonresponse (r), and the estimate of the fraction of missing information (
) are also reported.
Table 2.
Proportional hazards model for the All Cancer outcome: Parameter estimates and standard errors for log-dose. Model with exposure lag of 10 years and additional covariates (see text): complete-case (CC), conditional mean (CM) and multiple imputation (MI) methods
We used two imputation models: (I) Age at first employment, (II) Age at first employment and additional variables. For multiple imputation, the degrees of freedom (d.f.), the relative increase in variance due to nonresponse (r), and the estimate of the fraction of missing information (
) are also reported.
Corresponding author. Tel.: +39-0412347432; fax: +39-041710355.
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