{smcl}
{* 7sep2007}{* Ian White}
{hline}
{cmd:help metamiss}
{hline}
{title:Meta-analysis with missing data}
{title:Description}
{pstd}
{cmd:metamiss} performs a meta-analysis of studies comparing a binary outcome between two groups (such as in a randomised controlled trial) where the outcome may be missing. Three methods are available:
{pstd}
(i) imputation methods as described in Higgins et al. Missing values
may be imputed as failures, successes, same as control group, same as
experimental group, same as own group, or using IMORs (see below). When reasons for
missingness are known, a mixture of the methods may be used.
{pstd}or
{pstd}
(ii) methods allowing for uncertainty about how informative the missing data are, as in White et al based on Forster and Smith (1998).
These use the following model for outcome Y, missingness M and group X:
{p_end}
M|X=i ~ Bernoulli(alpha_i)
Y|M=0,X=i ~ Bernoulli(pi_i)
OR(Y,M|X=i) = IMOR_i (informative missingness odds ratio)
{pstd}
The values of logIMOR_i in the two groups can be specified exactly or through a Normal prior distribution.
{pstd}or
{pstd}(iii) the "uncertainty method" of Gamble and Hollis (2005).
{pstd}
{cmd:metamiss} only prepares the data for each study: it then calls {help metan} to
perform the meta-analysis.
A note "(Calling metan ...)" is printed at this point
to help the user identify the source of any error messages.
We have tried to make {cmd:metamiss} compatible with all versions of {cmd:metan}.
{title:Data}
{pstd}
{cmd:metamiss} requires 6 variables specifying the numbers of successes,
failures and missing values in each group. The first group is considered to be the experimental group and the second group the control group, although applications outside randomised controlled trials are also possible.
{title:Syntax}
Simple imputation:
{phang}
{cmd:metamiss} {it:rE fE mE rC fC mC}, {it:imputation_type} {cmd:w1|w2|w3|w4}
[{it:meta_options} {it:imor_spec}]
{phang}
where {it:imputation_type} is {cmd:aca|ica0|ica1|icapc|icape|icap|icab|icaw|icaimor}
Imputation using reasons:
{phang}
{cmd:metamiss} {it:rE fE mE rC fC mC}, {it:imputation_type_1}{cmd:(#|var [#|var])}
[{it:imputation_type_2}{cmd:(#|var [#|var])} [...]]
{cmd:w1|w2|w3|w4} [{it:meta_options} {it:imor_spec}]
{phang}
where {it:imputation_type_1}, {it:imputation_type_2} etc. are {cmd:ica0|ica1|icapc|icape|icap|icaimor}.
Bayesian analysis using priors:
{phang}
{cmd:metamiss} {it:rE fE mE rC fC mC}, {cmdab:sd:logimor(#|var [#|var])}
[{it:meta_options} {it:imor_spec} {cmdab:corr:logimor(#|var)}
{cmd:method(GH|Taylor|MC)} {cmd:reps(#)} {cmd:nip(#)} {cmdab:miss:prior(# # [# #])}
{cmdab:resp:prior(# # [# #])} {cmd:details} {cmd:nodots}]
Gamble-Hollis analysis:
{phang}
{cmd:metamiss} {it:rE fE mE rC fC mC}, {cmdab:gamble:hollis} [{it:meta_options}]
{phang}
{it:meta_options} are meta-analysis options including {cmd:or rr rd log id(varname)}
and any valid option for {help metan} including {cmd:random, by(), xlab()}.
{phang}
{it:imor_spec} is {cmd:imor(#|var [#|var])} or {cmd:logimor(#|var [#|var])}.
{title:Meta-analysis options}
{phang}
{cmd:rr, or, rd} specify the measures to be analysed.
Usually, only one measure may be specified; the default is {cmd:rr}.
The exception is using {cmd:method(mc)}, when all 3 measures may be obtained for no extra effort,
so any combination is allowed, and the default is all 3. However, the formal meta-analysis
is not performed if more than 1 measure is specified.
{phang}
{cmd:log} has the results reported on the log RR or log OR scale.
{phang}
{cmd:id(var)} specifies a trial identifier for the forest plot.
{phang}
All other options allowed with {help metan} are allowed: for example, {cmd:by()}, {cmd:random}.
{title:Imputation options}
{phang}{cmd:aca} performs an available cases analysis.
{phang}{cmd:ica0} imputes missing values as zeroes.
{phang}{cmd:ica1} imputes missing values as ones.
{phang}{cmd:icab} performs best-case analysis, which imputes missing values as ones
in the experimental group and zeroes in the control group.
Note that if {it:rE} and {it:rC} count adverse events,
not beneficial events, then {cmd:icab} will yield a worst-case analysis.
{phang}{cmd:icaw} performs worst-case analysis, which imputes missing values as
zeroes in the experimental group and ones in the control group.
Note that if {it:rE} and {it:rC} count adverse events,
not beneficial events, then {cmd:icaw} will yield a best-case analysis.
{phang}{cmd:icape} imputes missing values using the observed probability in the experimental group.
{phang}
{cmd:icapc} imputes missing values using the observed probability in the control group.
{phang}
{cmd:icap} imputes missing values using the observed probability within groups.
{phang}
{cmd:icaimor} imputes missing values using the IMORs specified by {cmd:imor()} or {cmd:logimor()} within groups.
{phang}
The default is {cmd:icaimor} if {cmd:imor()} or {cmd:logimor()} is specified, and otherwise {cmd:aca}.
{title:Imputation using reasons}
{pstd}
Alternatively, different subgroups of missing values may be assigned using
different reasons. Thus for example ica0(mfE mfC) icap(mpE mpC) indicates
that mfE individuals in group E and mfC individuals in group C are imputed using
ICA0, while mpE individuals in group E and mpC individuals in group C are imputed
using ICAp. If, for some group, the total over all reasons does not equal the number of missing observations (e.g. if mfE+mpE does not equal mE), then
the missing observations are shared between imputation types in the given ratio.
If the total is zero for some group then the missing observations are shared
between imputation types in the ratio formed by summing over all studies.
If the total is zero for all groups then an error is returned.
Numerical values may also be given: e.g. ica0(50 50) icap(50 50) indicates that 50%
missing values in each group are imputed using ICA0 and the rest are imputed
using ICAp.
{title:Imputation weight options}
{phang}
{cmd:w1} specifies that standard errors be computed treating the imputed
values as if they were observed. This is included for didactic purposes
and should not be used in real analyses.
{phang}
{cmd:w2} specifies that standard errors from the available cases analysis should be used.
{phang}
{cmd:w3} specifies that standard errors be computed by scaling the imputed data down to the number
of available cases in each group, and treating these data as if they were observed.
{phang}
{cmd:w4} specifies that standard errors be computed algebraically, conditional
on the IMORs. Note that conditioning on the IMORs is not strictly correct for
schemes including ICA-pE or ICA-pC, but the conditional standard errors appear
to be more realistic than the unconditional standard errors in this setting.
{title:Imputation debugging options}
{phang}
{cmd:listnum} lists the reason counts for each study implied by the {cmd:ica0} etc. options.
{phang}
{cmd:listall} lists the reason counts for each study after scaling to match the number
of missing values and imputing missing for studies with no reasons.
{phang}
{cmd:listp} lists the imputed probabilities for each study.
{title:Bayes options}
{phang}
{cmd:logimor()} sets the prior means for the experimental and control groups.
Both values default to 0.
{phang}
{cmd:sdlogimor()} sets the prior standard deviation for the experimental and
control groups. Both values default to 0.
{phang}
{cmd:corrlogimor()} sets the prior correlation between logIMOR's in the 2 groups. Default is 0.
{phang}
{cmd:method(MC|Taylor|GH)}. {cmd: method(GH)} uses 2-dimensional Gauss-Hermite quadrature to integrate over the distribution of the IMORs and is the recommended
method (and the default). {cmd: method(MC)} performs a full Bayesian analysis by sampling
directly from the posterior. This is time-consuming, so dots display progress, and you can request
more than one of the measures RR, OR, RD. {cmd: method(Taylor)} uses a Taylor series approximation
as in section 4 of Forster and Smith (1998) and is faster than the default but inaccurate
for wide log IMOR distributions.
{phang}
{cmd:nip(#)} specifies the number of integration points under {cmd:method(gh)}. Default is 10.
{phang}
{cmd:reps(#)} specifies the number of MC draws under {cmd:method(mc)}. Default is 100.
{phang}
{cmd:missprior(# # [# #])} and {cmd:respprior(# # [# #])} specify beta(#,#) priors for alpha and pi under {cmd:method(mc)}.
The 3rd and 4th arguments, if present, apply to the control group; otherwise the 1st and 2nd arguments are applied to both groups. Defaults are beta(1,1).
{phang}
{cmd:nodots} suppresses the dots that are displayed to mark the number of MC draws completed.
{title:Saved variables}
{pstd}
{cmd:metamiss} saves variables in the same way as {help metan}: _ES _selogES etc. _SS,
the sample size, excludes the missing values, but an additional variable _SSmiss
gives the total number of missing values.
{pstd}
When {cmd:method(mc)} is run, the following variables are saved for each {it:measure}:
the ACA estimate ESTRAW_{it:measure}, the ACA variance VARRAW_{it:measure}, the corrected
estimate ESTSTAR_{it:measure}, and the corrected variance VARSTAR_{it:measure}.
{title:Examples}
Data contain variables author r1 f1 m1 r2 f2 m2
Available case analysis (two equivalent commands):
{phang}{cmd:. metan r1 f1 r2 f2, rr fixedi label(namevar=author)}
{phang}{cmd:. metamiss r1 f1 m1 r2 f2 m2, rr id(author) aca}
ICA-0, impute missing as zeroes (two equivalent commands):
{phang}{cmd:. metamiss r1 f1 m1 r2 f2 m2, rr id(author) ica0 w4}
{phang}{cmd:. metamiss r1 f1 m1 r2 f2 m2, rr id(author) ica0(m1 m2) w4}
Impute using reasons for missingness:
{phang}{cmd:. metamiss r1 f1 m1 r2 f2 m2, fixed id(author) ica0(df1 df2) ica1(ds1 ds2) icapc(dc1 dc2) icap(dg1 dg2) w4}
Fixed equal IMORs (two equivalent commands):
{phang}{cmd:. metamiss r1 f1 m1 r2 f2 m2, rr id(author) imor(2) nograph}
{phang}{cmd:. metamiss r1 f1 m1 r2 f2 m2, rr id(author) logimor(log(2)) nograph}
Fixed opposite IMORs:
{phang}{cmd:. metamiss r1 f1 m1 r2 f2 m2, rr id(author) imor(2 1/2) nograph}
Random equal IMORs:
{phang}{cmd:. metamiss r1 f1 m1 r2 f2 m2, rr id(author) logimor(0) sdlogimor(1) corrlogimor(1)}
Random uncorrelated IMORs:
{phang}{cmd:. metamiss r1 f1 m1 r2 f2 m2, rr id(author) logimor(0) sdlogimor(1) corrlogimor(0)}
{p}Possible ways to improve - unlikely to make much difference in practice:
{phang}{cmd:. metamiss r1 f1 m1 r2 f2 m2, rr id(author) logimor(0) sdlogimor(1) corrlogimor(1) method(mc) reps(10000)}
{phang}{cmd:. metamiss r1 f1 m1 r2 f2 m2, rr id(author) logimor(0) sdlogimor(1) corrlogimor(0) method(gh) nip(50)}
{title:Note}
{pstd}Different methods may give slightly different answers due to
different handling of zero cells. For example,
{phang}{cmd:. metamiss r1 f1 m1 r2 f2 m2, ica1 w4}
{pstd}and
{phang}{cmd:. metamiss r1 f1 m1 r2 f2 m2, logimor(99) w4}
{pstd} differ slightly in the haloperidol data: the logimor analysis adds 1/2 to r1, f1, r2 and f2 for 6 studies with r2==0, whereas the ica0 analysis
only does this for 3 studies with r2+m2==0.
{title:Authors}
{pstd}Ian White and Julian Higgins, MRC Biostatistics Unit, Institute of Public Health,
Robinson Way, Cambridge CB2 0SR, UK.
{title:References}
{pstd}Forster JJ, Smith PWF. Model-based inference for categorical survey data
subject to non-ignorable non-response. Journal of the Royal Statistical
Society (B) 1998; 60: 57-70.
{pstd}Gamble C, Hollis S. Uncertainty method improved on best-worst case analysis
in a binary meta-analysis. Journal of Clinical Epidemiology 2005; 58: 579-588.
{pstd}Higgins JPT, White IR, Wood A.
Imputation methods for missing outcome data in meta-analysis of clinical trials.
Clinical Trials 2008; 5: 225-239.
{pstd}White IR, Higgins JPT, Wood AM. Allowing for uncertainty due to missing data
in meta-analysis. 1. Two-stage methods. Statistics in Medicine 2008; 27: 711-727.
{title:See also}
{help metan}