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Meta-analysis with missing data: metamiss

Meta-analysis with missing data: metamiss. Ian White and Julian Higgins MRC Biostatistics Unit, Cambridge, UK Stata users’ group, London 10 September 2007. Motivation. Missing outcome data compromise trials So they also compromise meta-analyses We may want to

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Meta-analysis with missing data: metamiss

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  1. Meta-analysis with missing data: metamiss Ian White and Julian HigginsMRC Biostatistics Unit, Cambridge, UK Stata users’ group, London 10 September 2007

  2. Motivation • Missing outcome data compromise trials • So they also compromise meta-analyses • We may want to • correct for bias due to missing data • down-weight trials with more missing data • NB missing data within trials, not missing trials

  3. Plan Meta-analysis of binary data • Haloperidol example • Standard approaches to missing data • Imputation methods • IMORs • Methods that allow for uncertainty • Demonstration

  4. Haloperidol meta-analysis r=successes f=failures m=missing n=total

  5. Standard approaches to missing data • Available cases (complete cases): ignore the missing data • assumes MAR: missingness is independent of outcome given arm • Assume missing=failure • implausible, but not too bad for health-related behaviours • Neither assumption is likely to be correct

  6. Other ideas • Sensitivity analyses, e.g. do both missing=failure and available cases • but these could agree by chance • Explore best / worst cases • Use reasons for missingness • Explicit assumptions about informativemissingness (IM) • IM: missingness is dependent on outcome

  7. metamiss.ado • Processes data on successes, failures and missing by arm & feeds results to metan • Available cases analysis (ACA) • Imputed case analyses (ICA): • impute as failure: ICA-0 • impute as success: ICA-1 • best-case: ICA-b (missing=success in E, failure in C) • worst-case: ICA-w • impute with same probability as in control arm: ICA-pC • impute with same probability as in experimental arm: ICA-pE • impute with same probability as in own arm: ICA-p (agrees with ACA) • impute using IMORs: ICA-IMOR (see next slide)

  8. More general imputation: IMORs • Measure Informative Missingness using the Informative Missing Odds Ratio (IMOR): • Odds ratio between outcome and missingness • Can’t estimate IMOR from the data, but given any value of IMOR, we can analyse the data • Generalises other ideas: e.g. • ICA-0 uses IMORs 0, 0 • ICA-1 uses IMORs ,  • ICA-b uses IMORs , 0 • ICA-p uses IMORs 1, 1 • ICA-pC uses IMORs OR, 1 where OR is odds ratio between arm and outcome in available cases

  9. Getting standard errors (weighting) right • Weight 1: treat imputed data as real • Weight 2: use standard errors from ACA • Weight 3: scale imputed data to same sample size as available cases • Weight 4: algebraic standard errors • same as weight 1 for ICA-0, ICA-1, ICA-b, ICA-w • same as weight 2 for ICA-p • uses Taylor expansion for ICA-IMOR • for ICA-pC & ICA-pE, we condition on the IMOR (I can explain…)

  10. Allowing for reasons (ICA-R) • Specify number of missing individuals in each arm to be imputed by each scheme ICA-0, ICA-1, ICA-pC, ICA-pE, ICA-p, ICA-IMOR. • Can take these data from a different outcome: metamiss scales to #missing • If missing in a particular study, metamiss imputes using combined studies

  11. Allowing for uncertainty • So far we have pretended we really know the IMORs • This is never really correct • Now we allow them to be unknown but from a user-specified distribution

  12. Bayesian approach allowing for uncertain IMORs (Rubin, 1977)

  13. Bayesian analysis • Elicit prior for dE, dC or use N(0,12) or N(0,22) • Get posterior distribution by integrating over the 2-dimensional distribution of dE, dC. • metamiss does this fast & accurately by: • Standard normal approximation to posterior given dE, dC • Integrate using Gauss-Hermite quadrature. • Alternatives: • Taylor expansion (inaccurate for large SD of log IMOR) • Full Bayesian Monte Carlo (slow, little gain in accuracy)

  14. Understanding priors for log IMOR: implied prior for P(success | missing) when P(success | observed) = 1/2

  15. Proposal: 4 sensitivity analyses

  16. Summary • Tool for sensitivity analysis • Requires thought about plausible missing data mechanisms • Would be nice to overlay sensitivity analysis with ACA • Further work includes combining uncertainty with reasons • I also have a program mvmeta for multivariate meta-analysis

  17. References • 1st part: Higgins JPT, White IR, Wood A. Imputation methods for missing outcome data in meta-analysis of clinical trials. Clinical Trials, submitted. • 2nd part: White IR, Higgins JPT, Wood AM. Allowing for uncertainty due to missing data in meta-analysis. 1. Two-stage methods. Statistics in Medicine, in press. • Related: White IR, Welton NJ, Wood AM, Ades AE, Higgins JPT. Allowing for uncertainty due to missing data in meta-analysis. 2. Hierarchical models. Statistics in Medicine, in press. • metamiss.ado available from http://www.mrc-bsu.cam.ac.uk/BSUsite/Software/Stata.shtml

  18. Extra slides

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