publication . Preprint . 2020

A hybrid landmark Aalen-Johansen estimator for transition probabilities in partially non-Markov multi-state models

Maltzahn, N.; Hoff, R.; Aalen, O. O.; Mehlum, I. S.; Putter, H.; Gran, J. M.;
Open Access English
  • Published: 02 Jul 2020
Abstract
Multi-state models are increasingly being used to model complex epidemiological and clinical outcomes over time. It is common to assume that the models are Markov, but the assumption can often be unrealistic. The Markov assumption is seldomly checked and violations can lead to biased estimation for many parameters of interest. As argued by Datta and Satten (2001), the Aalen-Johansen estimator of occupation probabilities is consistent also in the non-Markov case. Putter and Spitoni (2018) exploit this fact to construct a consistent estimator of state transition probabilities, the landmark Aalen-Johansen estimator, which does not rely on the Markov assumption. A d...
Subjects
free text keywords: Statistics - Methodology
Related Organizations
Download from
21 references, page 1 of 2

Odd O Aalen and Søren Johansen. An empirical transition matrix for non-homogeneous Markov chains based on censored observations. Scandinavian Journal of Statistics, 5(3):141-150, 1978.

Odd O Aalen, Ørnulf Borgan, and Harald Fekjaer. Covariate adjustment of event histories estimated from Markov chains: the additive approach. Biometrics, 57(4):993-1001, 2001. [OpenAIRE]

Odd O Aalen, Ørnulf Borgan, and Hakon Gjessing. Survival and Event History Analysis: A Process Point of View. Springer, New York, NY, 2008.

Alan Agresti and Brent A. Coull. Approximate is better than “exact” for interval estimation of binomial proportions. The American Statistician, 52:119-126, 1998. [OpenAIRE]

Arthur Allignol, Jan Beyersmann, Thomas Gerds, and Aurélien Latouche. A competing risks approach for nonparametric estimation of transition probabilities in a non-Markov illness-death model. Lifetime Data Analysis, 20(4):495-513, 2014.

Per K Andersen and Niels Keiding. Multi-state models for event history analysis. Statistical Methods in Medical Research, 11(2):91-115, 2002.

Per K Andersen, Ørnulf Borgan, Richard D. Gill, and Niels Keiding. Statistical Models Based on Counting Processes. Springer, New York, NY, 1993.

Somnath Datta and Glen A Satten. Validity of the Aalen-Johansen estimators of stage occupation probabilities and Nelson-Aalen estimators of integrated transition hazards for non-Markov models. Statistics & Probability Letters, 55(4):403-411, 2001. [OpenAIRE]

Somnath Datta and Glen A Satten. Estimation of integrated transition hazards and stage occupation probabilities for non-Markov systems under dependent censoring. Biometrics, 58(4):792-802, 2002. [OpenAIRE]

Jacobo de Uña-Álvarez and Luís Meira-Machado. Nonparametric estimation of transition probabilities in the nonMarkov illness-death model: A comparative study. Biometrics, 71(2):364-375, 2015.

Liesbeth C. de Wreede, Marta Fiocco, and Hein Putter. mstate: An R package for the analysis of competing risks and multi-state models. Journal of Statistical Software, 38(7):1-30, 2011.

Richard D Gill and Soren Johansen. A survey of product-integration with a view toward application in survival analysis. The Annals of Statistics, 18(4):1501-1555, 1990.

David V Glidden. Robust inference for event probabilities with non-Markov event data. Biometrics, 58(2):361-368, 2002.

Nina Gunnes, Ørnulf Borgan, and Odd O Aalen. Estimating stage occupation probabilities in non-Markov models. Lifetime Data Analysis, 13(2):211-240, 2007. [OpenAIRE]

Rune Hoff, Hein Putter, Ingrid Sivesind Mehlum, and Jon Michael Gran. Landmark estimation of transition probabilities in non-Markov multi-state models with covariates. Lifetime Data Analysis, 25(4):660-680, 2019.

21 references, page 1 of 2
Abstract
Multi-state models are increasingly being used to model complex epidemiological and clinical outcomes over time. It is common to assume that the models are Markov, but the assumption can often be unrealistic. The Markov assumption is seldomly checked and violations can lead to biased estimation for many parameters of interest. As argued by Datta and Satten (2001), the Aalen-Johansen estimator of occupation probabilities is consistent also in the non-Markov case. Putter and Spitoni (2018) exploit this fact to construct a consistent estimator of state transition probabilities, the landmark Aalen-Johansen estimator, which does not rely on the Markov assumption. A d...
Subjects
free text keywords: Statistics - Methodology
Related Organizations
Download from
21 references, page 1 of 2

Odd O Aalen and Søren Johansen. An empirical transition matrix for non-homogeneous Markov chains based on censored observations. Scandinavian Journal of Statistics, 5(3):141-150, 1978.

Odd O Aalen, Ørnulf Borgan, and Harald Fekjaer. Covariate adjustment of event histories estimated from Markov chains: the additive approach. Biometrics, 57(4):993-1001, 2001. [OpenAIRE]

Odd O Aalen, Ørnulf Borgan, and Hakon Gjessing. Survival and Event History Analysis: A Process Point of View. Springer, New York, NY, 2008.

Alan Agresti and Brent A. Coull. Approximate is better than “exact” for interval estimation of binomial proportions. The American Statistician, 52:119-126, 1998. [OpenAIRE]

Arthur Allignol, Jan Beyersmann, Thomas Gerds, and Aurélien Latouche. A competing risks approach for nonparametric estimation of transition probabilities in a non-Markov illness-death model. Lifetime Data Analysis, 20(4):495-513, 2014.

Per K Andersen and Niels Keiding. Multi-state models for event history analysis. Statistical Methods in Medical Research, 11(2):91-115, 2002.

Per K Andersen, Ørnulf Borgan, Richard D. Gill, and Niels Keiding. Statistical Models Based on Counting Processes. Springer, New York, NY, 1993.

Somnath Datta and Glen A Satten. Validity of the Aalen-Johansen estimators of stage occupation probabilities and Nelson-Aalen estimators of integrated transition hazards for non-Markov models. Statistics & Probability Letters, 55(4):403-411, 2001. [OpenAIRE]

Somnath Datta and Glen A Satten. Estimation of integrated transition hazards and stage occupation probabilities for non-Markov systems under dependent censoring. Biometrics, 58(4):792-802, 2002. [OpenAIRE]

Jacobo de Uña-Álvarez and Luís Meira-Machado. Nonparametric estimation of transition probabilities in the nonMarkov illness-death model: A comparative study. Biometrics, 71(2):364-375, 2015.

Liesbeth C. de Wreede, Marta Fiocco, and Hein Putter. mstate: An R package for the analysis of competing risks and multi-state models. Journal of Statistical Software, 38(7):1-30, 2011.

Richard D Gill and Soren Johansen. A survey of product-integration with a view toward application in survival analysis. The Annals of Statistics, 18(4):1501-1555, 1990.

David V Glidden. Robust inference for event probabilities with non-Markov event data. Biometrics, 58(2):361-368, 2002.

Nina Gunnes, Ørnulf Borgan, and Odd O Aalen. Estimating stage occupation probabilities in non-Markov models. Lifetime Data Analysis, 13(2):211-240, 2007. [OpenAIRE]

Rune Hoff, Hein Putter, Ingrid Sivesind Mehlum, and Jon Michael Gran. Landmark estimation of transition probabilities in non-Markov multi-state models with covariates. Lifetime Data Analysis, 25(4):660-680, 2019.

21 references, page 1 of 2
Powered by OpenAIRE Research Graph
Any information missing or wrong?Report an Issue