17.5 How it’s used with regressions

• estimate one regression of the outcome on the time period before the event
• estimate outcome on the time period after the event
• check difference
• doesn’t have to be linear

\[ Outcome = \beta_0 + \beta_1 t + \beta_2 After + \beta_3 t \times After + \epsilon \]

• more precise estimate of time trend than going day by day
• but limited by shape
• but need to be careful about significance testing (autocorrelation)
• use HAC standard errors

17.5.1 Example: Improved ambulance care

• heart attack performance \((AMI) \sim Week - 27\)

\[ AMI = \beta_0 + \beta_1 (Week - 27) + \beta_2 After + \beta_3 (Week-27) \times After + \epsilon \]