Bounding average treatment effects with misclassification error: a linear programming approach

• This paper discusses identification of average treatment effect (ATF) in presence of misclassification error;

• The bounds for ATE are found using linear programming approach where misclassification information is incorporated into false positive and false negative probabilities;

• Aside from general case, several misclassification patterns were considered:

  • Partial misclassification;
  • Asymmetric misclassification;
  • Mixed misclassification.

• Special cases of the response function are considered, including Monotone Treatment Response (MTR), Mean Monotone Treatment Response (MMTR), Monotone Instrumental Variable (MIV).

• Consistency of FP/FN to misclassification pattern are derived and shown to be automatically satisfied for optimization problem;

• In case of partial misclassification, ATE optimization problem gives sharp bounds iff sum over partial FP match sum of partial FN;

• Similar results is found for asymmetric classification;

• Results 2 and 3 are combined in a single proposition;

• Would be wonderful to see the model that can incorporate non-binary response;

• How wide is the bounds of the general case compared to the special case?

• Graphical representation will be extremely useful in understanding the underlying theory;

Minor:

• Finiteness of discrete data;

• Sensitivity and specificity;

• ATE in case of multiple treatments.