Joint modelling of competing risks in antiepileptic drug trials

1
Joint modelling of competing risks in
anti-epileptic drug trials

• Ruwanthi Kolamunnage-Dona, Paula Williamson,
  Carrol Gamble
• Centre for Medical Statistics and Health
  Evaluation
• University of Liverpool
• Pete Philipson
• School of Mathematic and Statistics
• University of Newcastle

MRC Grant G0400615
2
Outline

• Background of joint modelling
• Extension to competing risks
• Anti-epileptic drug (AED) trials
• Further work

3
Longitudinal data

• Repeated observations made on individuals over
  time.
• Linear model

4
Survival (event time) data

• Collection of times on individuals when an event
  of interest (eg. a failure) is observed.
• Observe failure time s together with failure
  indicator
• Cox proportional hazards model

5
Joint modelling

• Combine longitudinal and survival elements in
  larger meta-model (Y, S, ?, X, ?)
• Association is via the respective latent processes

6
Competing risks of failure

• Important to consider why failures occur
  competing risks
• Let causes of failure.
• Observe failure time s min(T1, , TK) together
  with failure indicator

7
Joint modellingExtension to competing risks

• Standard methods for joint modelling
• Have only one failure type and an assumption of
  non-informative censoring
• Extension
• Fit cause-specific hazards sub-models to allow
  for competing risks, with a separate latent
  association between longitudinal measurements and
  each cause of failure

8
Competing risks joint model

• Longitudinal data
• A Gaussian linear model
• Competing risks survival data
• Cause-specific hazards sub-model for ? l

9
Competing risks joint model

• Assume
• where (U0 ,U1) are zero-mean bivariate Gaussian
  random effects.
• Assume proportional association between
  longitudinal measurements and competing risks
  through parameter gamma,
• Assume competing risks are conditionally
  independent given W1

10
Estimation

• Factorise the likelihood for observed data
• marginal distribution of Y
• conditional distributions of competing events ?
  given the
• observed values of Y
• Likelihood function
• where

• EM estimation algorithm (Wulfsohn Tsiatis,
  1997)

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Anti-epileptic drug trials

• Epilepsy is characterised by seizures.
• Newly diagnosed usually prescribed single
  anti-epileptic drug (AED) treatment
• AED considered successful if the person taking it
  becomes seizure free with little in the way of
  side effects

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Competing risks of AED treatment failure

• Reasons for drug withdrawal
• Unacceptable adverse effects (UAE)
• Inadequate seizure control (ISC)
• Overall treatment failure analysis may miss
• differential effects of AED.
• Carbamazepine (CBZ) versus Lamotrigine (LTG)

13
Dependence between UAE and ISC

• Association between event types through
  time-varying measures

14
Quality of life (QoL) in Epilepsy

• Increasingly recognised as an important outcome
  in epilepsy
• Adverse event scale (problems in past 4 weeks)
• A measure representing emotional, social and
  physical effects of AEDs and epilepsy.
• e.g. tiredness, memory problems, disturbed
  sleep, hair loss, weight gain, rash
• Higher score poor QoL
• Postal assessments sent out at
• baseline, 3 months, 1 year, 2 years

15

QoL score
Longitudinal data Infrequent, variable response
times
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Questions of interest

• Dose a poor QoL lead to treatment failure?
• differential drug effect?
• change in QoL over time?

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Mean profiles CBZ and LTG
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Mean profilesReason for drug withdrawal
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Competing risks joint model longitudinal
component
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Competing risks joint model Survival component
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Further work

• Joint model fit how well is the correlation
  structure in the data captured?
• Residual analysis e.g. Dobson and Henderson 2003
• Consider different models for
• Other covariates e.g. age, number of seizures
• How to deal with informative observation in QoL
  do patients decide when to return questionnaires
  based on current condition?

22
References

• Dobson A. and Henderson R. (2003) Diagnostics for
  joint longitudinal and dropout timing modeling.
  Biostatistics, 59,741-751.
• Henderson R., Diggle P. and Dobson A. (2000).
  Joint modelling of longitudinal measurements and
  event time data. Biostatistics, 1, 4, 465-480.
• Williamson P. R., Kolamnunnage-Dona R. and Tudur
  Smith C. (2007). The influence of competing
  risks setting on the choice of hypothesis test
  for treatment effect. Biostatistics. doi
  10.1093/biostatistics/kxl040
• Williamson P. R., Tudur Smith C, Josemir W. S.
  and Marson A. G. (2007). Importance of competing
  risks in the analysis of anti-epileptic drug
  failure. Trials 812 doi 10.1186/1745-6215-8-12
• Wulfsohn M. S. and Tsiatis A. A. (1997). A joint
  model for survival and longitudinal data measured
  with error. Biomertics 53, 330-339.