Introduction to Missing Data (8/22/2012)

Types of Missing Data

• Missing completely at random (MCAR)
  • Admistrative errors/accidents
• Missing at random (MAR) (“Although missing at random (MAR) is a non-testable assumption, it has been pointed out in the literature that we can get very close to MAR if we include enough variables in the imputation models”)
  • Missingness related to known patient characteristics, time or place (“MAR on \( x \)”), or to the outcome (“MAR on \( y \)”)
• Informative missing (non-ignorable non-response)
  • Missingness related to value of predictor or characteristics not available in the analysis

Prelude to Modeling

• Quantify extent of missing data
• Characterize types of subjects with missing data
• Find sets of variables missing on same subjects

Missing Values for Different Response Variables

• Serial data with subjects dropping out (not covered in this course)
• \( y \)=time to event, follow-up curtailed: covered under survival analysis (White and Royston provide a method for multiply imputing missing covariate values using censored survival time data.)
• Often discard observations with completely missing \( y \) but sometimes wasteful
• Characterize missings in \( y \) before dropping obs.

Problems with simple alternatives to imputation

Deletion of records—

• Badly biases parameter estimates when the probability of a case being incomplete is related to \( y \) and not just \( x \)
• Deletion because of a subset of \( x \) being missing always results in inefficient estimates
• Deletion of records with missing \( y \) can result in biases but is the preferred approach under MCAR (Multiple imputation of \( y \) in that case does not improve the analysis and assumes the imputation model is correct.)

• However von Hippel found advantages to a “use
  all variables to impute all variables then drop observations with
  missing \( y \)” approach

• Only discard obs. when

  • MCAR can be justified
  • Rarely missing predictor of overriding importance that can't be imputed from other data
  • Fraction of obs. with missings small and \( n \) is large

• No advantage of deletion except savings of analyst time

• Making up missing data better than throwing away real data

Adding extra categories of categorical predictors—

• Including missing data but adding a category missing' causes serious biases
• Problem acute when values missing because subject too sick
• Difficult to interpret
• Fails even under MCAR
• May be OK if values are missing" because ofnot applicable", e.g. you have a measure of marital happiness, dichotomized as high or low, but your sample contains some unmarried people. OK to have a 3-category variable with values high, low, and unmarried.

Likewise, serious problems are caused by setting missing continuous
predictors to a constant (e.g., zero) and adding an indicator variable
to try to estimate the effect of missing values.