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Meta-analysis with missing data: metamiss

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Missing outcome data compromise trials. So they also compromise meta-analyses. We may want to ... meta-analysis of clinical trials. Clinical Trials, submitted. ... – PowerPoint PPT presentation

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Title: Meta-analysis with missing data: metamiss


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
  Haloperidol Haloperidol Haloperidol Haloperidol Placebo Placebo Placebo Placebo missing 
  r1 f1 m1 n1 r2 f2 m2 n2 missing 
Arvanitis 25 25 2 52 18 33 0 51 2
Beasley 29 18 22 69 20 14 34 68 41
Bechelli 12 17 1 30 2 28 1 31 3
Borison 3 9 0 12 0 12 0 12 0
Chouinard 10 11 0 21 3 19 0 22 0
Durost 11 8 0 19 1 14 0 15 0
Garry 7 18 1 26 4 21 1 26 4
Howard 8 9 0 17 3 10 0 13 0
Marder 19 45 2 66 14 50 2 66 3
Nishikawa 82 1 9 0 10 0 10 0 10 0
Nishikawa 84 11 23 3 37 0 13 0 13 6
Reschke 20 9 0 29 2 9 0 11 0
Selman 17 1 11 29 7 4 18 29 50
Serafetinides 4 10 0 14 0 13 1 14 4
Simpson 2 14 0 16 0 7 1 8 4
Spencer 11 1 0 12 1 11 0 12 0
Vichaiya 9 20 1 30 0 29 1 30 3
rsuccesses ffailures mmissing ntotal
5
Standard approaches to missing data
  • Available cases (complete cases) ignore the
    missing data
  • assumes MAR missingness is independent of
    outcome given arm
  • Assume missingfailure
  • 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
    missingfailure and available cases
  • but these could agree by chance
  • Explore best / worst cases
  • Use reasons for missingness
  • Explicit assumptions about informative
    missingness (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 (missingsuccess 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
  • Cant 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)

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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

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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

24
Bayesian approach allowing for uncertain IMORs
(Rubin, 1977)
25
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)

26
Understanding priors for log IMOR implied prior
for P(success missing) when P(success
observed) 1/2
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Proposal 4 sensitivity analyses
IMORs Options (e.g.) Sensitive to Works via
fixed equal imor(2 2) Imbalance in missingness Point estimates
fixed opposite imor(2 1/2) Amount of missing data Point estimates
random equal sdlogimor(2) corr(1) Imbalance in missingness Weightings
random uncorrelated sdlogimor(2) corr(0) Amount of missing data Weightings
31
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

32
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.ca
    m.ac.uk/BSUsite/Software/Stata.shtml

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Extra slides
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