A%20new%20architecture%20for%20handling%20multiply%20imputed%20data%20in%20Stata

1
A new architecture for handling multiply imputed
data in Stata

• JC Galati1, JB Carlin1,2, P Royston3
• 1Murdoch Childrens Research Institute (MCRI),
  Melbourne
• 2The University of Melbourne
• 3MRC Clinical Trials Unit, London

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Missing data

• Why do we need additional tools for analysing
  datasets with missing values?
• Traditional methods work with complete datasets
• Statistical packages discard incomplete
  observations when analysing an incomplete dataset
• i.e. a complete-case analysis is performed
• This can lead to loss of power, and possibly to
  biased estimates, depending on why the data went
  missing

3
Multiple imputation (MI)

• Introduced by Donald Rubin (1987 book, Wiley)
• Based on Bayesian principles
• Both the data-generating mechanism and the
  missingness mechanism are modelled
• Fairly broad assumptions about data-generating
  model
• Fairly restrictive assumptions about missingness
  mechanism
• Modelling assumptions apply at the imputation
  level
• Statistical modelling is general (once data is
  imputed)
• Post estimation some more work needs to be
  done
• Diagnostics theory and practice not yet worked
  out
• Model-building in its infancy work has started

4
MI data analysis

• Start with a dataset with some values missing
• Missing values are imputed multiple times
• Using a Bayesianly proper imputation method
• This creates m sets of completed data
• Each completed dataset is analysed separately
• Standard complete-data estimation methods are
  used
• E.g. linear regression, logistic regression

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Inference (estimation) using MI

• Coefficient estimates and variances (SEs) from
  complete-data analyses are combined using Rubins
  Rules
• Parameter estimates
• Average of the complete-data parameter estimates
• Variance is the sum of two components
• Within-imputation variance (average of the
  complete-data variances)
• Between-imputation variance (determined from
  complete-data parameter estimates)
• Point estimators divided by SE have approximate t
  distributions
• Estimate d.f. and use t-multipliers to get
  confidence intervals

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Background (MI in Stata)

• What is available in Stata currently?
• MI Tools, Carlin et. al. Stata J. 2003
• Imputed datasets stored in separate dta files
• myfile1.dta, ... , myfilem.dta
• Estimation
• mifit with
• regress, logit, probit, clogit, glm,
• logistic, poisson, svyreg, svylogit,
• svyprobit, svypoisson, xtgee, xtreg
• Post estimation
• milincom, mitestparm
• Data manipulation
• miset, miappend, mimerge, mido, misave

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Background (MI in Stata)

• Main drawbacks of MI Tools
• Loose association between original and imputed
  data
• Loose association between individual imputed
  datasets
• Limit to range of estimation commands supported
  (13)
• Choice of coding of some aspects resulted in slow
  execution time in some cases
• No capacity to perform imputation

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Background (MI in Stata)

• What is available in Stata currently? (cont.)
• ice, micombine, Royston Stata J. 2004/05
• ice stores imputed datasets in a single dta file
• uses impid and obsid vars
• Estimation
• micombine with
• clogit, cnreg, glm, logistic, logit,
• poisson, probit, qreg, regress, rreg,
• xtgee, streg, stcox, ologit, oprobit, mlogit
• Post estimation
• results returned in e(b) , e(V) etc.
• onus on user to know when post-estimation command
  applied directly to combined estimates is valid

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Background (MI in Stata)

• ice, micombine, Royston Stata J. 2004/05 (cont.)
• Data manipulation
• left to user, but stacked format facilitates
  simple transformation of variables etc.
• mijoin, misplit (for conversion between formats)
• Main drawbacks
• Limit to range of estimation commands supported
  (16)
• Manipulation that changes number of observations
  in each dataset not easily supported (eg.
  reshape)
• Not clear when/if post-estimation is valid

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mim A new architecture

• Main aims
• To unify two sets of tools into a single
  architecture
• To combine functionality of both sets of tools
• To simplify the command syntax
• To extend the range of estimation commands
  supported
• Better post-estimation facilities
• testparm, lincom, predict
• Make it harder to do crazy things
• Add other post-estimation commands later

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mim A new architecture

• Scope
• Creation of imputations is NOT included
• But easy for users to put imputed datasets into
  mim format
• Architecture covers analysis and manipulation of
  existing imputed datasets
• Designed to handle
• Estimation
• Data manipulation (reshape, append merge)
• Post-estimation (lincom, testparm predict)
• Replay (management of estimation results)
• Utility functions

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mim A new architecture

• Storage of imputed datasets
• Based on Roystons stacked format
• Fixed names for impid and obsid vars
• _mj (impid) and _mi (obsid)
• no need for
• dataset characteristics to record the names
• additional command options to specify the names
• dedicated set command to manage the
  characteristics
• stacking requires only generate, append and
  replace
• Original data stored in the stack
• _mj 0

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mim A new architecture

• Storage of datasets illustration
• _mj _mi y x
• ----------------------------------
• 0 1 1.1 105
• 0 2 9.2 106
• 0 3 1.1 .
• 0 4 2.3 .
• 0 5 7.5 108
• 0 6 7.9 .
• 1 1 1.1 105
• 1 2 9.2 106
• 1 3 1.1 109.796
• 1 4 2.3 110.456
• 1 5 7.5 108
• 1 6 7.9 102.243
• 2 1 1.1 105
• 2 2 9.2 106
• 2 3 1.1 107.952

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mim A new architecture

• Command structure
• A single command prefix called mim
• mim processes the multiply-imputed dataset
  currently in memory
• Typical syntax
• . mim command
• E.g.
• . use myImputedData, clear
• . mim regress y x1 x2 x3
• . mim predict yhat
• . mim lincom x1x2x3, or

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mim A new architecture

• Commands (cont.)
• General syntax
• Default behaviour of mim may be modified through
  mim options
• mim , mim_options command
• mim_options depend on whether one wishes to do
• estimation
• data manipulation
• post-estimation
• replay

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Using mim

• Estimation
• mim recognises 28 estimation commands
• regress mean proportion ratio logistic
• logit ologit mlogit probit oprobit poisson
• glm binreg blogit clogit cnreg mvreg rreg
• qreg iqreg sqreg bsqreg stcox streg
• xtgee xtreg xtlogit xtmixed
• and 11 svy commands
• svyregress svymean ... svypoisson
• Plus, in principle any Stata estimation command
  may be used
• mim, category(fit) estimation_command

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Using mim

• Data manipulation
• Stacked format allows simple manipulation using
  existing stata commands
• . generate, replace, label etc.
• . by _mj tabulate ...
• mim recognises 3 data manipulation commands
• . mim reshape cmdline
• . mim append using another mim dataset
• . mim, sort(varlist) merge using ...
• In principle, any Stata data manipulation command
  may be used with mim
• mim, category(manip) sort(varlist) manip_command

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Using mim

• mim recognises some post-estimation commands
• . mim lincom cmdline
• . mim testparm cmdline
• . mim predict xbvar , eq(name)
• . mim predict sevar, stdp eq(name)
• Replay combined estimates
• . mim
• Replay individual estimates (th imputed
  dataset)
• . mim, j()

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Using mim

• Interactive example in Stata

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Final comments

• Difficulties faced
• Simplicity of programming versus ease of use and
  flexibility
• Inconsistencies between commands resulted in more
  tailoring than wed hoped
• Progress
• Coding of version 1 complete
• Current version is 1.0.3
• Help file written
• Has been in beta-testing for several months
• Submitted for publication in Stata Journal