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Presmoothing the transition probabilities in the illness-death model

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  • Amorim, Ana Paula
  • de Uña-Álvarez, Jacobo
  • Meira-Machado, Luís

Abstract

One major goal in clinical applications of multi-state models is the estimation of transition probabilities. In a recent paper, Meira-Machado et al. (2006) introduce a substitute for the Aalen-Johansen estimator in the case of a non-Markov illness-death model. The idea behind their estimator is to weight the data by the Kaplan-Meier weights pertaining to the distribution of the total survival time of the process. In this paper we propose a modification of Meira-Machado et al. (2006) estimator based on presmoothing. Consistency is established. We investigate the finite sample performance of the new estimator through simulations. Data from a study on colon cancer are used for illustration purposes.

Suggested Citation

  • Amorim, Ana Paula & de Uña-Álvarez, Jacobo & Meira-Machado, Luís, 2011. "Presmoothing the transition probabilities in the illness-death model," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 797-806, July.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:7:p:797-806
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    References listed on IDEAS

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    1. Stute, W., 1993. "Consistent Estimation Under Random Censorship When Covariables Are Present," Journal of Multivariate Analysis, Elsevier, vol. 45(1), pages 89-103, April.
    2. Ming Yuan, 2005. "Semiparametric censorship model with covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(2), pages 489-514, December.
    3. de Uña-Álvarez, Jacobo & Meira-Machado, Luis F., 2008. "A simple estimator of the bivariate distribution function for censored gap times," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2440-2445, October.
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    1. Luís Meira-Machado & Jacobo Uña-Álvarez & Somnath Datta, 2015. "Nonparametric estimation of conditional transition probabilities in a non-Markov illness-death model," Computational Statistics, Springer, vol. 30(2), pages 377-397, June.
    2. Jacobo de Uña-Álvarez & Luís Meira-Machado, 2015. "Nonparametric estimation of transition probabilities in the non-Markov illness-death model: A comparative study," Biometrics, The International Biometric Society, vol. 71(2), pages 364-375, June.
    3. Rotolo, Federico & Legrand, Catherine & Van Keilegom, Ingrid, 2011. "Simulation of clustered multi-state survival data based on a copula model," LIDAM Discussion Papers ISBA 2011040, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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