Analysis of multiple informant/ multiple source data in Stata

1
Analysis of multiple informant/multiple source
data in Stata

• Nicholas J. Horton
• Department of Mathematics
• Smith College, Northampton MA
• Garrett M. Fitzmaurice
• Harvard University
• nhorton at email.smith.edu
• http//www.biostat.harvard.edu/multinform

2
Acknowledgements

• Joint research project with Nan Laird and
  colleagues, Harvard School of Public Health
• Jane Murphy and the Stirling County Study for use
  of their example dataset (see Horton et al AJE,
  2001 for more details)
• Supported by NIH grant RO1-MH54693

3
Outline

• Motivation for multiple source data
• Examples of multiple sources/informants
• Models for correlated multiple source data
• Accounting for complex survey design
• Accounting for incomplete/missing data
• Example (Stirling County Study)
• Conclusions

4
Why multiple source data?

• to provide better measures of some underlying
  construct that is difficult to measure or likely
  to be missing
• also known as multiple informant reports, proxy
  reports, co-informants, etc.
• discordance is expected, otherwise there is no
  need to collect multiple reports
• Statistical framework developed in (Horton and
  Fitzmaurice SIM tutorial, 2004)

5
Definition of multiple source data

• data obtained from multiple informants or raters
  (e.g., self-reports, family members, health care
  providers, teachers)
• or via different/parallel instruments or methods
  (e.g., symptom rating scales, standardized
  diagnostic interviews, or clinical diagnoses)
• None of the reports is a gold standard
• We consider multiple source data that are
  commensurate (multiple measures of the same
  underlying variable on a similar scale)

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Examples of multiple source data

• child psychopathology (ask parents, teachers and
  children about underlying psychological state)
• service utilization studies (collect information
  from subjects and databases)
• medical comorbidity (query providers and charts
  to assess medical problems)

7
Examples of multiple source data (cont.)

• adherence studies (collect self-report of
  adherence, electronic pill caps MEMS plus
  pharmacy records)
• nutritional epidemiology (utilize multiple
  dietary instruments such as food frequency
  questionnaires, 24-hour recalls, food diaries)

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Incomplete/missing reports

• Multiple source reports are commonly incomplete
  since, by definition, they are collected from
  sources other than the primary subject of the
  study
• This missingness may be by design or happenstance
  (or both!)

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Example missing source reports

• Consider service utilization studies that collect
  information from subjects and databases
• Subjects may be lost to follow-up (or only
  contacted periodically)
• Databases may be incomplete (lack of consent,
  lack of appropriate coverage)

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Analytic approach

• Multiple sources can provide information on
  outcomes or predictors (risk factors)
• Multiple source outcome what is the prevalence
  of child psychopathology? (measured using
  parallel parent and teacher reports)
• Fitzmaurice et al (AJE, 1995), Horton et al
  (HSOR, 2002), Horton and Fitzmaurice (SIM
  tutorial, 2004)

11
Analytic approach (cont.)

• Multiple source predictor what are the odds of
  developing depression in adulthood, conditional
  on parallel reports of anxiety (collected from a
  child and a parent)?
• Examples Horton et al (AJE, 2001), Lash et al
  (AJE, 2003), Liddicoat et al (JGIM, 2004), Horton
  and Fitzmaurice (SIM tutorial, 2004)
• We will focus on an example using multiple source
  predictors

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Notation

• Let Y denote a univariate outcome for a given
  subject
• Let denote the lth multiple source
  predictor
• Let Z denote a vector of other covariates for the
  subject
• To simplify exposition, we consider two sources
  with dichotomous reports (L2)

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Questions to consider

• Are the sources reporting on the same underlying
  construct (are they commensurate or
  interchangeable?)
• Is it possible to combine the reports in some
  fashion?
• How to handle missing reports?

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Analytic approaches

• Reviewed in Horton, Laird and Zahner (IJMPR,
  1999)
• Use only one source
• Fit separate models

15
Analytic approaches (cont.)

• Combine (pool) the reports in some fashion
• Include both reports in the model

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Analytic approaches (cont.)

• We considered simultaneous estimation of the
  marginal models
• Non-standard application of GEE
• Method independently suggested by Pepe et al
  (SIM, 1999)

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Advantages of new approach

• can be used to test for source differences in
  association with the outcome
• can test if the effects of other risk factors on
  the outcome differ by source

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Advantages of new approach

• different source effects where necessary
• a pooled model can be fit if no significant
  source effects (potentially more efficient)
• can be fit using general purpose statistical
  software (Stata and others)

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Accounting for survey design

• Many health services or epidemiologic studies
  arise from complex survey samples
• Need to address stratification, multi-stage
  clustering and unequal sampling weights
• Failing to properly account for survey design may
  lead to bias and incorrect estimation of
  variability

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Accounting for survey design (cont.)

• Estimation proceeds using the approximate (quasi)
  log-likelihood (weighted version of the usual
  score equations for a GLM, accounting for the
  multi-stage clustering, including multiple source
  reports)
• Can be fit using general purpose statistical
  software (elegant and powerful implementation in
  Stata)

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Accounting for incomplete source reports

• Missing source reports are missing predictors
• Use weighted estimating equation methodology of
  Robins et al (JASA, 1994) and Xie and Paik
  (Biometrics, 1997), applied by Horton et al,
  (AJE, 2001)
• Adds an additional missingness weight
• Complications to variance estimation

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Example Stirling County Study

• Outcome time to event (death) over 16 year
  follow-up period (1952-1968) (n1079)
• multiple source predictors partially observed
  dichotomous physician report or self report of
  psychiatric disorder (dpax)
• other predictors age (3 categories), gender
• statistical model piecewise exponential survival
  with 4 intervals each of 4 years duration
  (subjects contribute time at risk in each
  interval)

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Stirling County survey design
Strata 1
Stratum 1
Stratum k
Stratum K
PSU 1
PSU J
PSU j
self- report
phys.- report
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Implementation in Stata

• Specify probability sampling unit (subject),
  probability sampling weights (weight) and
  stratification variable (district)
• svyset id pweightweight, strata(district)
• Describe the sampling design
• svydes

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• Survey Describing stage 1 sampling units
• pweight weight
• VCE linearized
• Strata 1 district
• SU 1 id
• FPC 1 ltzerogt
• 
  Obs per Unit
• --------------------
  --------
• Stratum Units Obs min mean
  max
• -------- -------- -------- -------- --------
  --------
• 1 93 654 2 7.0
  8
• 2 37 284 4 7.7
  8
• 3 51 346 2 6.8
  8
• 4 202 1488 2 7.4
  8
• 5 291 2104 2 7.2
  8
• 6 128 946 2 7.4
  8
• 7 50 374 4 7.5
  8

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Implementation in Stata (cont.)

• xi svy poisson event dpax int1 int2 int3 female
  ageind1 ageind2 diag i.diagageind1
  i.diagageind2
  i.dpaxfemale i.dpaxageind1
  i.dpaxageind2 i.dpaxdiag, exposure(atrisk)

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Implementation in Stata (cont.)

• Can then test for significant informant effects
  (any term with dpax self-report in the model)

test dpax0 test _IdpaXfemal_1, accumulate test
_IdpaXagein_1, accumulate test _IdpaXageina1,
accumulate test _IdpaXdiag_1, accumulate
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Results (separate parameters)

• Initially fit model with separate parameters
• No evidence for source interactions
• Implies that the association between risk factors
  and mortality did not differ by source
• Dropped these terms from the model, yielding
  parsimonious shared parameter model with smaller
  standard errors

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Implementation (shared parameter)

• xi svy poisson event int1 int2 int3 female
  ageind1 ageind2 diag i.diagageind1
  i.diagageind2, exposure(atrisk)

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Results (shared parameter)

• Survey Poisson regression
• Number of strata 9
  Number of obs 7420
• Number of PSUs 1079
  Population size 64723.522
• 
  Design df 1070
• 
  F( 9, 1062) 21.94
• 
  Prob gt F 0.0000
• --------------------------------------------------
  ----------------------------
• Linearized
• event Coef. Std. Err. t
  Pgtt 95 Conf. Interval
• -------------------------------------------------
  ----------------------------
• int1 -.9594993 .2058191 -4.66
  0.000 -1.363354 -.5556444
• int2 -.5680445 .1936756 -2.93
  0.003 -.9480716 -.1880174
• int3 -.360743 .2002561 -1.80
  0.072 -.7536821 .0321962
• female -.1298938 .1493215 -0.87
  0.385 -.42289 .1631024
• ageind1 2.484883 .2820244 8.81
  0.000 1.931499 3.038266
• ageind2 3.530875 .2894511 12.20
  0.000 2.962919 4.098831
• diag 1.62166 .3256041 4.98
  0.000 .982765 2.260555

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Results (shared parameters)
Parameter (log MRR) Estimate (SE)
female -0.13 (0.15)
mid-age 2.48 (0.28)
older-age 3.53 (0.33)
diagnosis 1.62 (0.33)
diagnosismid-age -1.35 (0.38)
diagnosisolder-age -1.31 (0.46)
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Interpretation of results (annual mortality rate)
Age lt 50 Age gt 70
Diagnosis0 0.001 0.056
Diagnosis1 0.007 0.093
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Results (2 df test of interaction of age and
diagnosis)

• . test _IdiaXagein_10
• Adjusted Wald test
• ( 1) event_IdiaXagein_1 0
• F( 1, 1070) 12.65
• Prob gt F 0.0004
• . test _IdiaXageina1, accumulate
• Adjusted Wald test
• ( 1) event_IdiaXagein_1 0
• ( 2) event_IdiaXageina1 0
• F( 2, 1069) 6.67
• Prob gt F 0.0013

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Results (calculation of MRR and 95 CI)

• . lincom diag, eform
• ( 1) eventdiag
• --------------------------------------------------
  ----------------
• event exp(b) Std.Err. t Pgtt 95
  Conf. Interval
• -------------------------------------------------
  ----------------
• (1) 5.0615 1.6480 4.98 0.000
  2.6718 9.5884
• --------------------------------------------------
  ----------------
• . lincom diag _IdiaXagein_1, eform
• ( 1) eventdiag event_IdiaXagein_1 0
• --------------------------------------------------
  ----------------
• event exp(b) Std.Err. t Pgtt 95
  Conf. Interval
• -------------------------------------------------
  ----------------
• (1) 1.3102 .25297 1.40 0.162
  .89703 1.9137
• --------------------------------------------------
  ----------------

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Conclusions

• new methods of analysis of multiple source data
  are available
• can be implemented using existing software
• methods allow the assessment of the relative
  association of each source
• each source yielded similar conclusions
  association between psychiatric disorder and
  mortality is stronger for younger subjects
• unified model has less variability, pools
  information after testing for systematic
  differences

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Conclusions (cont.)

• methods account for complex survey designs
• methods incorporate partially observed subjects
  to contribute, under MAR (Little and Rubin book)
  assumptions
• multiple source reports arise in many settings
  (not just for children anymore!)

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Future work

• Maximum-likelihood estimation instead of GEE
  approach
• May yield efficiency gains
• Particularly useful for missing reports
• Non-commensurate reports
• Different scales
• Different underlying constructs
• Consider latent variable models (e.g. work of
  Normand and colleagues)
• See also gllamm and forthcoming Stata book by
  Rabe-Hesketh and Skrondal)

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Analysis of multiple informant/multiple source
data in Stata

• Nicholas Horton
• Department of Mathematics
• Smith College, Northampton MA
• nhorton at email.smith.edu
• http//www.biostat.harvard.edu/multinform