Maximization of the marginal likelihood of grouped survival data

Debajyoti Sinha; Martin A. Tanner; W. J. Hall

doi:10.1093/biomet/81.1.53

Maximization of the marginal likelihood of grouped survival data

Debajyoti Sinha^*, Martin A. Tanner, W. J. Hall

^*Corresponding author for this work

Statistics and Data Science

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

SUMMARY: Grouped failure time data occur in studies where subjects are monitored periodically to determine whether failure has occurred in the intervening interval. Here the model under consideration is Cox's (1972, 1975) proportional hazards model, but the commonly used method of partial likelihood needs modification with grouped data due to a potentially large number of ties. This paper demonstrates how the Monte Carlo em algorithm (Wei & Tanner, 1990) can be used on grouped data to find the maximum likelihood estimate from the marginal likelihood based on the incomplete ranks of the event times. The methodology is exemplified with a data set with precise failure times after artificially introducing grouping.

Original language	English (US)
Pages (from-to)	53-60
Number of pages	8
Journal	Biometrika
Volume	81
Issue number	1
DOIs	https://doi.org/10.1093/biomet/81.1.53
State	Published - Mar 1994

Funding

This work was facilitated by the National Institute of Health and the National Science Foundation. We thank David Oakes, Dianne Finkelstein and Mitchel Gail for valuable advice and criticism.

Keywords

Data augmentation
Importance sampling
Monte Carlo em
Partial likelihood
Peto's real probability
Proportional hazards

ASJC Scopus subject areas

Statistics and Probability
General Mathematics
Agricultural and Biological Sciences (miscellaneous)
General Agricultural and Biological Sciences
Statistics, Probability and Uncertainty
Applied Mathematics

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10.1093/biomet/81.1.53

Cite this

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title = "Maximization of the marginal likelihood of grouped survival data",

abstract = "SUMMARY: Grouped failure time data occur in studies where subjects are monitored periodically to determine whether failure has occurred in the intervening interval. Here the model under consideration is Cox's (1972, 1975) proportional hazards model, but the commonly used method of partial likelihood needs modification with grouped data due to a potentially large number of ties. This paper demonstrates how the Monte Carlo em algorithm (Wei & Tanner, 1990) can be used on grouped data to find the maximum likelihood estimate from the marginal likelihood based on the incomplete ranks of the event times. The methodology is exemplified with a data set with precise failure times after artificially introducing grouping.",

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author = "Debajyoti Sinha and Tanner, {Martin A.} and Hall, {W. J.}",

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AU - Sinha, Debajyoti

AU - Tanner, Martin A.

AU - Hall, W. J.

N1 - Funding Information: This work was facilitated by the National Institute of Health and the National Science Foundation. We thank David Oakes, Dianne Finkelstein and Mitchel Gail for valuable advice and criticism.

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N2 - SUMMARY: Grouped failure time data occur in studies where subjects are monitored periodically to determine whether failure has occurred in the intervening interval. Here the model under consideration is Cox's (1972, 1975) proportional hazards model, but the commonly used method of partial likelihood needs modification with grouped data due to a potentially large number of ties. This paper demonstrates how the Monte Carlo em algorithm (Wei & Tanner, 1990) can be used on grouped data to find the maximum likelihood estimate from the marginal likelihood based on the incomplete ranks of the event times. The methodology is exemplified with a data set with precise failure times after artificially introducing grouping.

AB - SUMMARY: Grouped failure time data occur in studies where subjects are monitored periodically to determine whether failure has occurred in the intervening interval. Here the model under consideration is Cox's (1972, 1975) proportional hazards model, but the commonly used method of partial likelihood needs modification with grouped data due to a potentially large number of ties. This paper demonstrates how the Monte Carlo em algorithm (Wei & Tanner, 1990) can be used on grouped data to find the maximum likelihood estimate from the marginal likelihood based on the incomplete ranks of the event times. The methodology is exemplified with a data set with precise failure times after artificially introducing grouping.

KW - Data augmentation

KW - Importance sampling

KW - Monte Carlo em

KW - Partial likelihood

KW - Peto's real probability

KW - Proportional hazards

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Maximization of the marginal likelihood of grouped survival data

Abstract

Funding

Keywords

ASJC Scopus subject areas

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