Notes from book: What if (Part x)

Instrumental variables

Instrumental variable estimation is one way that does not rely on the assumptions where all variables to adjust for confounding and selection bias to be identified and correctly measured.

flowchart LR
  Z[Z] --> A[A]
  A[A] --> Y{Y}
  U(U) --> A[A]
  U(U) --> Y{Y}

• Z is the random assignment indicator (1 treatment 0 placebo)
• A is the treatment (1 yes 0 no), not all adhere to original assignment
• Y is the outcome
• U is the unmeasured variables that affect both treatment adherence and outcome

Conditions for instrument Z

1. Z is associated with A (treatment)
2. Z does not affect Y through its potential effect on A
3. Z and Y do not share causes

The three conditions are satisfied in a double blind randomized controlled trial as

1. those who are assigned to treatment (Z=1) are more likely to receive treatment (A=1), indicating association
2. expected in double blind design
3. expected by random assignment

There is a fourth condition of heterogeneity / monotonicity.

If an instrument is unmeasured, sometimes a proxy or surrogate instrument associated with the unmeasured instrument \(U_z\) can be used.

In observational studies

In observational studies we do not have the random assignment indicator Z. Some common categories of IV:

• genetic factors
• preference
• access to treatment

Compare with other methods

The conditional exchangeability required by IP weighting, standardization is replaced by other assumptions. The choice of method depends on whether it is easier to identify and measure the confounders, or find an instrument Z and expect monotonicity and heterogeneity.

Violation of assumptions 1-4 may result in large biases; IP weighting and standardization are more robust compared to IV.

When there are time varying treatment, IV is not ideal as it is suited for point intervention.

ivreg package

Check out this post for an example. Only normal errors.