Latent variable models for time-to-event data

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Latent variable models for time-to-event data

• A joint presentation
• by
• Katherine Masyn Klaus Larsen
• UCLA
• PSMG Meeting, 2/13/2002

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Overview

• 1) Introduction to survival data
• 2) Discrete-time survival mixture
• analysis (Katherine)
• 3) Latent variable models for (continuous)
• time-to-event data (Klaus)
• 4) Extensions

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Time-to-event Data

• A record of when events occur (relative to some
  beginning) for a sample of individuals
• For example, time from sero-conversion to death
  in HIV/AIDS patients, age of first alcohol use in
  school-aged children, time to heroine use
  following completion of methadone treatment

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• Methods for this type of data must consider an
  important feature, known as censoring The event
  is not observed for all subjects
• Methods must also handle covariates that may
  change with time, e.g., CD4 count
• Data Time (interval) of event or censoring,
  indicator for whether or not the event occurred,
  and relevant covariates

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Discrete vs. Continuous Time

• Continuous The exact time of an event
  (or censoring) for each subject is known, e.g.,
  time of death
• Discrete The time of an event (or censoring)
  for each subject is only recorded for an interval
  of time, e.g., grade of school drop out

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Discrete-Time Survival Mixture Analysis (DTSMA)

• Katherine Masyn, UCLA
• Based on the work of
• Muthén and Masyn (2001) and Masyn (2002)
• Research supported under grants from NIAAA,
  NIMH, NIDA, and in collaboration with
  Bill Fals-Stewart at the Research Institute
  for Addictions at SUNY-Buffalo

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• Let T be the time interval in which the event
  occurs T 1, 2, 3,...
• S(t), called the survival probability, is defined
  as the probability of surviving beyond time
  interval t, i.e., the probability that the event
  occurs after interval t S(t) P(T gt t)
• h(t), called the hazard probability, is defined
  as the probability of the event occurring in the
  time interval t, provided it has not occurred
  prior to t h(t) P(T t T ? t)

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Hazard Probability Plot
Survival Probability Plot
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DTSMA with Covariates
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Recidivism Intervention
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GGMM DTSMA
UM1
UM2
UM3
UMJ
. . .
C
z
i
s
Y1
Y2
Y3
YM
. . .
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Aggression and School Removal
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Drinking and Work Absence