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Multiple imputations and the missing censoring indicator model

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  • Subramanian, Sundarraman

Abstract

Semiparametric random censorship (SRC) models (Dikta, 1998) provide an attractive framework for estimating survival functions when censoring indicators are fully or partially available. When there are missing censoring indicators (MCIs), the SRC approach employs a model-based estimate of the conditional expectation of the censoring indicator given the observed time, where the model parameters are estimated using only the complete cases. The multiple imputations approach, on the other hand, utilizes this model-based estimate to impute the missing censoring indicators and form several completed data sets. The Kaplan-Meier and SRC estimators based on the several completed data sets are averaged to arrive at the multiple imputations Kaplan-Meier (MIKM) and the multiple imputations SRC (MISRC) estimators. While the MIKM estimator is asymptotically as efficient as or less efficient than the standard SRC-based estimator that involves no imputations, here we investigate the performance of the MISRC estimator and prove that it attains the benchmark variance set by the SRC-based estimator. We also present numerical results comparing the performances of the estimators under several misspecified models for the above mentioned conditional expectation.

Suggested Citation

  • Subramanian, Sundarraman, 2011. "Multiple imputations and the missing censoring indicator model," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 105-117, January.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:1:p:105-117
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    References listed on IDEAS

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    1. Srivastava, Muni S. & Dolatabadi, Mohammad, 2009. "Multiple imputation and other resampling schemes for imputing missing observations," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 1919-1937, October.
    2. Kaifeng Lu & Anastasios A. Tsiatis, 2001. "Multiple Imputation Methods for Estimating Regression Coefficients in the Competing Risks Model with Missing Cause of Failure," Biometrics, The International Biometric Society, vol. 57(4), pages 1191-1197, December.
    3. Anastasios A. Tsiatis, 2002. "Multiple imputation methods for testing treatment differences in survival distributions with missing cause of failure," Biometrika, Biometrika Trust, vol. 89(1), pages 238-244, March.
    4. Subramanian, Sundarraman & Bean, Derek, 2008. "The missing censoring indicator model and the smoothed bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 471-476, December.
    5. Dikta, Gerhard & Kvesic, Marsel & Schmidt, Christian, 2006. "Bootstrap Approximations in Model Checks for Binary Data," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 521-530, June.
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    1. Dikta, Gerhard, 2014. "Asymptotically efficient estimation under semi-parametric random censorship models," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 10-24.
    2. Dikta, Gerhard & Reißel, Martin & Harlaß, Carsten, 2016. "Semi-parametric survival function estimators deduced from an identifying Volterra type integral equation," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 273-284.

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