Discussion of Survival Models and Health Sequences Setup: Subjects - - PDF document

Discussion of “Survival Models and Health Sequences” Setup:

• Subjects indexed by i
• Standard independence assumption relaxed

to exchangeable.

• Exchangeable within covariate pattern, if

applicable.

• Status variables Yi(t)
• t represents time
• Y ∈ ℜK ∪ {♭}, where ♭ represents an ab-

sorbing state, generally representing death.

• Yi(t) includes time-dependent covariates.
• Survival time Ti = supT≥0{Yi(t) = ♭}.
• Let Zi(s) = Yi(Ti − s)
• Runs time backwards from time of death
• Called revival process.

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Objective Model Zi(s)

• Look for pattern in E [Zi(s)] predicting death
• Model Zi(s) as a Gaussian process

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Key Observation Zi(s) should be independent of Ti

• Assumption is called revival assumption.
• Heuristically, time reversal captures all depen-

dence of Y on T

• Survival processes are aligned at failure time,

rather than at randomization

• Avoids extra variability induced by hetero-

geneity in disease stage at enrollment.

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Place of common survival analysis concepts in revival framework

• Treatment: modeled as time-dependent
• In this framework the only change is at ran-

domization.

• Assume value of Z depends on treatment
• nly through current treatment arm
• Censoring: Stratify based on whether censor-

ing has occurred.

• Pattern of interest should be apparent in

the uncensored individuals

• Pattern should be attenuated in censored

individuals

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Open Questions

• Can we use the information in censored ob-

servations more intensively?

• If one reverses at censoring times, the expec-

tation of covariates should be a mixture of the expectations for observations near fail- ure, and less extreme observations.

• Can we model this?

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