Transcript Keith Abrams

Modelling Partially & Completely Missing
Preference-Based Outcome Measures
(PBOMs)
Keith Abrams
Department of Health Sciences,
University of Leicester, UK
John Brazier, Tony O’Hagan, Samer Kharroubi
Centre for Bayesian Statistics in Health Economics (CHEBS),
University of Sheffield, UK
Aki Tsuchiya
Sheffield Health Economics Group (SHEG),
University of Sheffield, UK
Outline
• Missing PBOM Data
• Modelling Missing PBOM Data
• Example - IBS Study
• Other Scenarios & Links with Other Work
Why is data missing?
• Partially Missing
– Missing PBOM on some individuals
– Missing dimensions of PBOM
• Completely Missing Data
– Only collected on a sub-sample
– Not collected at all
Why is missing data important?
• Efficiency
• Precision
• Missing at Random (MAR) conditional
on covariates & other outcomes, e.g.
random sub-sample
• Informative missing data, e.g. death,
produce biased results
Solutions to missing data?
• Collect PBOMs in RCTs evaluating healthcare interventions
• Minimise missing data
• Complete case analysis – problem if
substantial ‘missing data’
• Model missing data
– Mean value imputation – limited applicability
– Multiple Imputation – accounts for uncertainty
– Regression imputation – uses relationship between covariates &
PBOMs
– Bayesian approach …
Multivariate Model - 1
2
 P NP 

 y Pi 
  P   P


 ~ N 
, 
     
2 
y 

 P 
 NPi 
 NP   P NP
 P ~ [,],  NP ~ [,]
1
Σ ~Wishart(R ,k )
Missing data are treated as parameters &
imputed/predicted using the posterior predictive
distribution
Multivariate Model - 2
• Product Normal Formulation:
y Pi ~ N [  P ,  ]
2
P
y NPi ~ N [ i , ]
2
 i   0  1 y Pi  
 P ~ [,],  ~ [, ]
 ~ [,],  ~ [,]
2
P
2
Example – IBS Study
• N=161 patients with Irritable Bowel Syndrome
(IBS)
• PBOMs: SF-6D & EQ-5D
• NPBOMs: IBS-QoL [34 items] (Overall & 8
sub-scales)
• Demographic data: age & sex
• Assessed at Baseline & 3 months follow-up
• Missing Data
–
–
–
–
Age & Sex complete
IBS n=13
EQ-5D n=4
IBS & EQ-5D n=1
Example – IBS Study
Using Multivariate Model for EQ-5D & IBS
(+ age & sex) implemented in WinBUGS using
‘vague’ priors
• Overall (n=161)
– EQ-5D: 64.21 (2.039) & 95% CrI: 60.15 to 68.18
• Assume 81 patients do not have EQ-5D
• Complete Case Analysis (n=80)
– EQ-5D: 60.44 (3.117) & 95% CrI: 54.11 to 66.38
• Predictive Analysis (n=80+81)
– EQ-5D: 60.58 (2.789) & 95% CrI: 54.93 to 65.88
IBS Study – Extension &
Further Work 1
• Distributional assumptions (both model &
prior distributions), e.g. IBS study EQ-5D: -7.7
to +100
• Sensitivity to prior distributions, especially on
variance parameters
• Use of other studies which may have
considered both EQ-5D & IBS-QoL – prior
distributions, possibly down weighted
according to patient population considered
• Modelling of 8 sub-scales of IBS-QoL &
relationship with EQ-5D
IBS Study – Extension &
Further Work 2
• Additional baseline demographics, e.g.
employment
• Consideration of whether certain individuals
(defined by demographics & IBS-QoL scores)
are ‘poorly’ predicted – Conditional Predictive
Ordinates (CPOs)
• Assessment of predictive performance –
cross-validation
Applications to Other Scenarios
• Studies which have not used a PBOM at all
• BUT where there are other studies which
have, i.e. ‘Borrowing Strength’
• Assumptions – Exchangeable, i.e. the
relationship between PBOM & NPBOM is the
same across studies
• ‘Bank of Reference Studies’ for common
conditions/diseases, BUT …
– Should not be seen as a replacement for well
designed studies which use PBOMs
– Limited use when there is a treatment-baseline
interaction, which might be different for PBOMs &
NPBOMs
Links with Other Work
• Regression-based approaches (‘mapping’)
(Tsuchiya et al, 2003)
• Cross-Calibration (Parmigiani et al, 2003) –
categorical data
• Modelling missing cost data (Lambert et al,
2003)
• Missing data due to death (informative
missing data)
– `Quality Adjusted Survival’ techniques (including
multi-state modelling)
– Joint modelling of both PBOM/NPBOMs &
Missing/Death Process (Billingham, 2002)
References
Akehurst RL et al. Health-Related Quality of Life and Cost Impact of
Irritable Bowel Syndrome in a UK Primary Care Setting.
Pharmacoeconomics 2002;20(7):455-462.
Billingham LJ, Abrams KR. A Bayesian method for synthesizing
evidence. The Confidence Profile Method. SMMR 1990;6(1):31-55.
Lambert PC et al. Glasziou P & Irwig L. An evidence-based approach to
individualising treatment. BMJ 1995;311:1356-1359.
Prevost TC et al. Hierarchical models in generalised synthesis of
evidence: an example based on studies of breast cancer. Stat Med
2000;19:3359-76.
Sutton AJ & Abrams KR. Bayesian methods in meta-analysis and
evidence synthesis. SMMR 2001;10(4):277-303.
Spiegelhalter DJ, Abrams KR, Myles JP. Bayesian Approaches to
Clinical Trials & Health-care Evaluation. London: Wiley, 2003.