Bias in regression coefficient estimates when assumptions for handling missing data are violated: a simulation study


  • Sander MJ van Kuijk Maastricht University
  • Wolfgang Viechtbauer Maastricht University
  • Louis L Peeters Maastricht University Medical Centre
  • Luc Smits Maastricht University




The purpose of this simulation study is to assess the performance of multiple imputation compared to complete case analysis when assumptions of missing data mechanisms are violated.


The authors performed a stochastic simulation study to assess the performance of Complete Case (CC) analysis and Multiple Imputation (MI) with different missing data mechanisms (missing completely at random (MCAR), at random (MAR), and not at random (MNAR)). The study focused on the point estimation of regression coefficients and standard errors.


When data were MAR conditional on Y, CC analysis resulted in biased regression coefficients; they were all underestimated in our scenarios. In these scenarios, analysis after MI gave correct estimates. Yet, in case of MNAR MI yielded biased regression coefficients, while CC analysis performed well.

The authors demonstrated that MI was only superior to CC analysis in case of MCAR or MAR. In some scenarios CC may be superior over MI. Often it is not feasible to identify the reason why data in a given dataset are missing. Therefore, emphasis should be put on reporting the extent of missing values, the method used to address them, and the assumptions that were made about the mechanism that caused missing data.






Statistical Methods