Sensitivity analysis for not-at-random missing data in ... · Leurent B, et al. Missing data in...
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Sensitivity analysis for not-at-random missingdata in trial-based cost-effectiveness analysis
using multiple imputation
Baptiste Leurent, Manuel Gomes, Rita Faria,Steve Morris, Richard Grieve, James Carpenter
ISPOR EuropeNovember 2018
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Introduction
Missing data are common in RCTs→ Loss of power→ Risk of bias
Particularly important in CEAComplex dataLong term follow-up
Typically assume data are "missing at random"But risk of being missing could depend on the data valueitself→ MNAR
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Missing Not At Random
MAR: Missingness only depends of observed variablesCan get valid inference using the observed data
MNAR: missingness depends of outcome value itselfE.g. less likely to complete a health questionnaire when ill
! Cannot judge from the data! Need additional assumptions to conduct the analysis
But often plausible
Guidelines→ Should assess whether results robust toMNAR assumptionsClear gap between recommendations and practice
(NRC 2010)
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Pattern-mixture models
Pattern-mixture models (PMM) are one possibleapproach for MNAR analysisDistribution = mixture of observed and missing distributionsFor example: assuming missing and observed data havesame distribution, but with mean shifted by δ
Ymiss = Yobs + δ
δ = average difference between missing and observedvalues (conditionally on observed data )Can also use a multiplicative factor c:
Ymiss = Yobs × c
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Pattern-mixture models
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Implementation of PMM with ultiple Imputation
Multiple Imputation (MI) commonly used in trial-based CEATypically under MAR, but can accommodate MNARIdea is simple:
1 Conduct usual MIUnder MAR
2 Modify imputed data to reflect MNAR assumptione.g. reduce imputed data by 10%
3 Analyse as usual MI datasetUsing Rubin’s rules
Sensitivity analysis can be conducted over a range ofplausible values for δ, to see how affect conclusions
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Example: the 10 Top Tips trial
RCT, evaluating a brief intervention for weightloss, in UK general practicesPrimary outcome: weight loss at 3 monthsFollow-up: 2 years (3, 6, 12, 18, 24 months)CEA:
Costs: NHS resource use over 2 yearsEffectiveness: EQ-5D at each visit→ QALYsover 2 years
N=537 patientsBut only 60% at 24M, and 30%complete cost-effectiveness dataMore likely to drop out if lesssuccessful→ MNAR
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MNAR sensitivity analysis of 10TT
Applying PMM approach to 10TT:Let’s denote c = MNAR multiplicative parameter for theQoL scorese.g. c = 0.9: the missing QoL are assumed 10% lower thanunder MARWhat values for c?
c = {1,0.95,0.90} (= drop out probably worst off,somewhere between MAR, and 10% worst)c could differ between arms, but more likely to be close toeach other→ 7 scenarios considered
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10TT sensitivity analysis - Results
→ Under MAR, 48% probability 10TT cost-effective→ But results sensitive to departure from MAR
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Discussion
Easy to implementResults can be sensitive (not always the case!)Challenges:
Choosing sensitivity parametersExpert opinionTipping-point
ReportingClarity is essential
Alternative: reference-basedimputation
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Conclusion
Can never recover missing information⇒ avoiding missingdata best solution
Missing data→ make assumptions→ what if do not hold?
Multiple imputation offers a convenient way to conductthese sensitivity analyses
Some challenges: elicitation, reporting, etc.⇒ But not excuses not to conduct them
Likely will evolve over time, as become more routinelyconducted
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Acknowledgements
James Carpenter1, Manuel Gomes2, Rita Faria3, SteveMorris2, and Richard Grieve1
1 London School of Hygiene and Tropical Medicine2 University College London3 University of York
The 10TT investigators
Funded by the National Institute for Health Research
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References
Leurent B, et al. Sensitivity Analysis for Not-at-Random Missing Data in Trial-BasedCost-Effectiveness Analysis: A Tutorial. PharmacoEconomics 2018
Faria R, et al. A Guide to Handling Missing Data in Cost-Effectiveness AnalysisConducted Within Randomised Controlled Trials. PharmacoEconomics 2014Leurent B, et al. Missing data in trial-based cost-effectiveness analysis: an incompletejourney. Health Econ 2018Mason AJ, et al. Development of a practical approach to expert elicitation forrandomised controlled trials with missing health outcomes: Application to theIMPROVE trial. Clin. Trials. 2017Beeken RJ, et al. A brief intervention for weight control based on habit-formation theorydelivered through primary care: results from a randomised controlled trial. Int. J. Obes.2017
National Research Council, 2010. The Prevention and Treatment of Missing Data inClinical Trials, National Academies PressLittle, R. & Rubin, D., 2014. Statistical analysis with missing data, John Wiley & Sons.Carpenter, J. & Kenward, M., 2012. Multiple imputation and its application, John Wiley& Sons.
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