title: Combining estimates of interest in prognostic modelling studies after multiple imputation: current practice and guidelines.
abstract: BACKGROUND
  Multiple imputation (MI) provides an effective approach to handle missing covariate data within prognostic modelling studies, as it can properly account for the missing data uncertainty. The multiply imputed datasets are each analysed using standard prognostic modelling techniques to obtain the estimates of interest. The estimates from each imputed dataset are then combined into one overall estimate and variance, incorporating both the within and between imputation variability. Rubin's rules for combining these multiply imputed estimates are based on asymptotic theory. The resulting combined estimates may be more accurate if the posterior distribution of the population parameter of interest is better approximated by the normal distribution. However, the normality assumption may not be appropriate for all the parameters of interest when analysing prognostic modelling studies, such as predicted survival probabilities and model performance measures.
  
  
  METHODS
  Guidelines for combining the estimates of interest when analysing prognostic modelling studies are provided. A literature review is performed to identify current practice for combining such estimates in prognostic modelling studies.
  
  
  RESULTS
  Methods for combining all reported estimates after MI were not well reported in the current literature. Rubin's rules without applying any transformations were the standard approach used, when any method was stated.
  
  
  CONCLUSIONS
  The proposed simple guidelines for combining estimates after MI may lead to a wider and more appropriate use of MI in future prognostic modelling studies.
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
authors.forename: Patrick
authors.initials: P
authors.lastname: Royston
mesh_terms: D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans; D016014:Linear Models; D015233:Models, Statistical; D015999:Multivariate Analysis; D011379:Prognosis; D016032:Randomized Controlled Trials as Topic; D013269:Stochastic Processes