title: Comparison of imputation methods for handling missing covariate data when fitting a Cox proportional hazards model: a resampling study.
abstract: BACKGROUND
  The appropriate handling of missing covariate data in prognostic modelling studies is yet to be conclusively determined. A resampling study was performed to investigate the effects of different missing data methods on the performance of a prognostic model.
  
  
  METHODS
  Observed data for 1000 cases were sampled with replacement from a large complete dataset of 7507 patients to obtain 500 replications. Five levels of missingness (ranging from 5% to 75%) were imposed on three covariates using a missing at random (MAR) mechanism. Five missing data methods were applied; a) complete case analysis (CC) b) single imputation using regression switching with predictive mean matching (SI), c) multiple imputation using regression switching imputation, d) multiple imputation using regression switching with predictive mean matching (MICE-PMM) and e) multiple imputation using flexible additive imputation models. A Cox proportional hazards model was fitted to each dataset and estimates for the regression coefficients and model performance measures obtained.
  
  
  RESULTS
  CC produced biased regression coefficient estimates and inflated standard errors (SEs) with 25% or more missingness. The underestimated SE after SI resulted in poor coverage with 25% or more missingness. Of the MI approaches investigated, MI using MICE-PMM produced the least biased estimates and better model performance measures. However, this MI approach still produced biased regression coefficient estimates with 75% missingness.
  
  
  CONCLUSIONS
  Very few differences were seen between the results from all missing data approaches with 5% missingness. However, performing MI using MICE-PMM may be the preferred missing data approach for handling between 10% and 50% MAR missingness.
authors.affiliation: Centre for Statistics in Medicine, University of Oxford, Oxford, UK. andrea.marshall@warwick.ac.uk
authors.forename: Andrea
authors.initials: A
authors.lastname: Marshall
authors.forename: Douglas G
authors.initials: DG
authors.lastname: Altman
authors.forename: Roger L
authors.initials: RL
authors.lastname: Holder
mesh_terms: D000368:Aged; D015179:Colorectal Neoplasms; D003627:Data Interpretation, Statistical; D005260:Female; D006801:Humans; D008297:Male; D008875:Middle Aged; D015999:Multivariate Analysis; D016016:Proportional Hazards Models; D012494:Sampling Studies