Parallel-Process Discrete-Time Survival Modeling via Latent Transition Analysis

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Parallel-Process Discrete-Time Survival Modeling
via Latent Transition Analysis

• Patrick S. Malone
• University of South Carolina
• Katherine E. Masyn
• University of California at Davis
• Dorian A. Lamis Thomas F. Northrup
• University of South Carolina
• 2008 International Meeting of the
• Psychometric Society, Durham, NH, USA

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Acknowledgments

• Center for Child and Family Policy
• Ken Dodge, Director
• Ann B. Brewster, Research Scientist
• Duke/NIDA Transdisciplinary Prevention Research
  Center
• Susan G. Alexander, Director
• National Institute on Drug Abuse P20 DA017589-02
• Prevention Science and Methodology Group
• C. Hendricks Brown, PI
• National Institute on Mental Health and NIDA R01
  MH40859

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Acknowledgments

• Sample data drawn from the study entitled,
• Fast Track/ Multi-Site Prevention of
  Adolescent Problem Behaviors, Conduct Problems
  Prevention Research Group
• Supported by the following grants
• National Institute of Mental Health (NIMH) Grants
  R18 MH48043,
• R18 MH50951, RH18 MH50952, and R18 MH50953
• The Center for Substance Abuse Prevention and the
  National Institute on Drug Abuse also have
  provided support through a memorandum of
  agreement with the NIMH
• Department of Education Grant S184U30002 and NIMH
  Grants K05MH00797 and K05MH01027 also supported
  the study.

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Objectives

• To outline a model for Discrete-Time Survival
  Analysis using Latent Transition Analysis
• To extend that model to parallel DTS processes
• To show a worked example from field data
• To describe simulation research on a
  parallel-process model

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Discrete-Time Survival Analysis

• Time-to-Event Model
• Fewer occasions of measurement than events
• Appropriate for the first occurrence of an event
• Onset of Problem Behavior
• High School Dropout
• Divorce
• Death

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DTSA via Latent Transition Analysis
Time 0
Time 1
Time 2
Time 3
Post-event
Post-event
Event
Pre-event
Event
Event
Pre-event
Pre-event
Pre-event
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Parallel-Process DTSA

• Two time-to-event processes
• Measured concurrently
• Event hazard probability of Process A dependent
  on past event status of Process B, and vice-versa
• Not a competing-risks model both events can
  occur

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Parallel-Process Model
Time 0
Time 1
Time 2
Time 3
Post-event
Post-event
Event
A
Pre-event
Event
Event
Pre-event
Pre-event
Pre-event
Post-event
Post-event
Event
B
Pre-event
Event
Event
Pre-event
Pre-event
Pre-event
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Parallel-Process Model

• Process A
• Logit(hTA) ß0T ß1 IBT-1 ß2 Z
• Process B
• Logit(hT B) ß3T ß4 IAT-1 ß5 Z
• Notes
• Time-invariant Lag-1 Model
• Proportional Hazard Odds

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Example Dataset

• Data derive from Fast Track, a comprehensive,
  multi-site investigation of the development and
  prevention of conduct problems (CPPRG, 1992
  Lochman CPPRG, 1995).

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Sample

• 446 youth in control condition of Fast Track
• Identified as high risk on basis of upper-decile
  behavior problems in kindergarten classes (3
  kindergarten cohorts)
• 48 African American
• 34 female

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Outcome Measures School Dropout

• Collected annually (Spring) from school records
  of last known school
• Detailed reasons for missing data
• Either dropped out or ran away coded as
  dropout
• Other codes (e.g., could not locate record)
  coded as missing
• Detailed data available only for grade 8ff
  (cohort 3), grade 9ff (cohort 2), grade 10ff (all
  cohorts)
• Remainder missing by design

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Outcome MeasuresIllicit Substance Use

• Collected annually (Summer) from child
  self-report
• Any reported use of marijuana, cocaine,
  non-prescribed medications, or other drugs
  (other than alcohol and
  tobacco)
• Detailed data available for grade 4ff (all
  cohorts)

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Covariates

• Ethnicity (African American vs. other)
• Sex
• SES (Hollingshead)
• Site (four sites)
• Cohort
• Absenteeism (grade 3)
• Grades (grade 3)

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Outcome Descriptives
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Results

• Estimated in Mplus v5.1 (Muthén Muthén)
• First dropout is significantly predicted by
  prior-year drug use
• logistic b 1.09, SE 0.46, z 2.37
• hOR (95 CI) 2.96 (1.21, 7.26)
• First illegal drug use may be negatively
  predicted by prior-year high school dropout, but
  very large confidence interval
• logistic b -2.32, SE 1.23, z 1.89
• hOR (95 CI) 0.10 (0.01, 1.09)

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Findings

• The parallel-process survival model is a valuable
  extension to work with time-to-event models.
• Neither survival process is prioritized in the
  methodology thus, able to tease apart
  directionality (effectively a cross-lagged panel
  survival analysis).
• This model is also extensible to mediating and
  moderating processes e.g., drug use may mediate
  link between parental monitoring and dropout, or
  parental monitoring may weaken the link between
  illegal drug use and high school dropout.

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Simulation Study 1

• Logit(h TA) ß0 ß1 IBT-1 ß2 Z
• Logit(h TB) ß3 ß4 IAT-1 ß5 Z
• Vary ß0, ß1, ß3, ß4, N
• ß2 ß5 0
• Large sample size needed

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Simulation Study 2

• Logit(h TA) ß0 ß1 IBT-1 ß2 Z ß6 X
• Logit(h TB) ß3 ß4 IAT-1 ß5 Z ß7 X
• Examine distribution of products
• ß6 ß4
• ß7 ß1

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Limitations and Implications

• Difficult to implement long time-spans
• Work with software authors to reduce computing
  limitations
• Distribution of product of effects plausibly
  guessed, but not known
• Simulation work to explore properties of model
• Simulation work to establish applicability of
  asymmetric empirical confidence interval for
  indirect effects

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For further information

• Patrick S. Malone
• malone.ps_at_gmail.com