18.10 Final thoughts

“In our experience with real and artificial data…, the practical conclusion appears to be that multiple imputation, when carefully done, can be safely used with real problems even when the ultimate user may be applying models or analyses not contemplated by the imputer.” - Little & Rubin (Book, p. 218)

  • Don’t ignore missing data.
  • Impute sensibly and multiple times.
  • It’s typically desirable to include many predictors in an imputation model, both to
    • improve precision of imputed values
    • make MAR assumption more plausible
  • But the number of covariance parameters goes up as the square of the number of variables in the model,
    • implying practical limits on the number of variables for which parameters can be estimated well
  • MI applies to subjects who have a general missingness pattern, i.e., they have measurements on some variables, but not on others.
  • But, subjects can be lost to follow up due to death or other reasons (i.e., attrition).
  • Here we have only baseline data, but not the outcome or other follow up data.
  • If attrition subjects are eliminated from the sample, they can produce non-response or attrition bias.
  • Use attrition weights.
    • Given a baseline profile, predict the probability that subject will stay and use the inverse probability as weight.
    • e.g., if for a given profile all subjects stay, then the predicted probability is 1 and the attrition weight is 1. Such a subject “counts once”.
    • For another profile, the probability may be 0.5, attrition weight is 1/.5 = 2 and that person “counts twice”.
  • For differential drop-out, or self-selected treatment, you can consider using Propensity Scores.