title: Diagnosing problems with imputation models using the Kolmogorov-Smirnov test: a simulation study.
abstract: BACKGROUND
  Multiple imputation (MI) is becoming increasingly popular as a strategy for handling missing data, but there is a scarcity of tools for checking the adequacy of imputation models. The Kolmogorov-Smirnov (KS) test has been identified as a potential diagnostic method for assessing whether the distribution of imputed data deviates substantially from that of the observed data. The aim of this study was to evaluate the performance of the KS test as an imputation diagnostic.
  
  
  METHODS
  Using simulation, we examined whether the KS test could reliably identify departures from assumptions made in the imputation model. To do this we examined how the p-values from the KS test behaved when skewed and heavy-tailed data were imputed using a normal imputation model. We varied the amount of missing data, the missing data models and the amount of skewness, and evaluated the performance of KS test in diagnosing issues with the imputation models under these different scenarios.
  
  
  RESULTS
  The KS test was able to flag differences between the observations and imputed values; however, these differences did not always correspond to problems with MI inference for the regression parameter of interest. When there was a strong missing at random dependency, the KS p-values were very small, regardless of whether or not the MI estimates were biased; so that the KS test was not able to discriminate between imputed variables that required further investigation, and those that did not. The p-values were also sensitive to sample size and the proportion of missing data, adding to the challenge of interpreting the results from the KS test.
  
  
  CONCLUSIONS
  Given our study results, it is difficult to establish guidelines or recommendations for using the KS test as a diagnostic tool for MI. The investigation of other imputation diagnostics and their incorporation into statistical software are important areas for future research.
authors.affiliation: Clinical Epidemiology & Biostatistics Unit, Murdoch Childrens Research Institute, The Royal Children's Hospital, Flemington Road Parkville, Melbourne, Victoria 3052, Australia. cattram.nguyen@mcri.edu.au.
authors.forename: Cattram D
authors.initials: CD
authors.lastname: Nguyen
authors.forename: John B
authors.initials: JB
authors.lastname: Carlin
authors.forename: Katherine J
authors.initials: KJ
authors.lastname: Lee
mesh_terms: D001315:Australia; D002675:Child, Preschool; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans; D016014:Linear Models; D008137:Longitudinal Studies; D015999:Multivariate Analysis; D017063:Outcome Assessment, Health Care; D016487:Parenting; D012959:Socioeconomic Factors; D018709:Statistics, Nonparametric