Title: Joint modelling of competing risks in antiepileptic drug trials
1Joint 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
2Outline
- Background of joint modelling
- Extension to competing risks
- Anti-epileptic drug (AED) trials
- Further work
3Longitudinal data
- Repeated observations made on individuals over
time. - Linear model
4Survival (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
5Joint modelling
- Combine longitudinal and survival elements in
larger meta-model (Y, S, ?, X, ?) - Association is via the respective latent processes
6Competing 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 -
7Joint 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
8Competing risks joint model
- Longitudinal data
- A Gaussian linear model
- Competing risks survival data
- Cause-specific hazards sub-model for ? l
9Competing 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
10Estimation
- 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)
11Anti-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
12Competing 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)
13Dependence between UAE and ISC
- Association between event types through
time-varying measures -
14Quality 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
15QoL score
Longitudinal data Infrequent, variable response
times
16Questions of interest
- Dose a poor QoL lead to treatment failure?
- differential drug effect?
- change in QoL over time?
17Mean profiles CBZ and LTG
18Mean profilesReason for drug withdrawal
19Competing risks joint model longitudinal
component
20Competing risks joint model Survival component
21Further 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?
22References
- 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.