title: A method for imputing missing data in longitudinal studies.
abstract: OBJECTIVE
  In a cohort in which racial data are unknown for some persons, race-specific persons and person-years are imputed using a model-based iterative allocation algorithm (IAA).
  
  
  METHODS
  An EM algorithm-based approach to address misclassification in a censored data regression setting can be adapted to estimate the probability that a person of unknown race is white. The corresponding race-specific person-years are obtained as a by-product of the estimation procedure. Variance estimates are computed using the bootstrap. The proposed approach is compared with the proportional allocation method (PAM).
  
  
  RESULTS
  In an occupational cohort where racial data were missing for 41% of the workers, the age-time-race-specific person-years were estimated within a relative variation of approximately 20%, using the IAA. The deaths were less reliably estimated. The standardized mortality ratios (SMRs) for all-cause mortality estimated using the IAA and the PAM were more similar for the non-white workers than for a smaller subgroup of white workers.
  
  
  CONCLUSIONS
  The IAA provides a method to reliably estimate race-specific person-year denominators in cohort studies with missing racial data. This method is applicable to other incompletely observed non-time-dependent categorical covariates. Internal cohort rates or SMRs can be computed and modeled, with bootstrap confidence intervals that account for the uncertainty in the determination of race.
authors.affiliation: Department of Biostatistics, Graduate School of Public Health, University of Pittsburgh, Pittsburgh, PA 15261, USA. ayouk@pitt.edu
authors.forename: Ada O
authors.initials: AO
authors.lastname: Youk
authors.forename: Roslyn A
authors.initials: RA
authors.lastname: Stone
authors.forename: Gary M
authors.initials: GM
authors.lastname: Marsh
mesh_terms: D000293:Adolescent; D000328:Adult; D000368:Aged; D000465:Algorithms; D000704:Analysis of Variance; D001699:Biometry / Q000379:methods*; D002423:Cause of Death; D002648:Child; D003627:Data Interpretation, Statistical; D006801:Humans; D016013:Likelihood Functions; D008137:Longitudinal Studies; D008297:Male; D008875:Middle Aged; D015233:Models, Statistical; D009784:Occupational Diseases / Q000208:ethnology* / Q000401:mortality*; D010414:Pennsylvania / Q000453:epidemiology; D016016:Proportional Hazards Models; D012044:Regression Analysis; D012984:Software; D013783:Textile Industry; D013997:Time Factors; D044465:White People / Q000145:classification / Q000706:statistics & numerical data*; D000078329:Workforce