How Estimating Nuisance Parameters Often Reduces the Variance (With Variance Correction)

• Activity Number: 47 - Causal Inference in the Presence of Nuisance Parameters: Latest Developments
• Type: Invited
• Date/Time: Sunday, August 7, 2022 : 4:00 PM to 5:50 PM
• Sponsor: IMS
• Author(s): Judith Jacqueline Lok*
• Companies: Boston University
• Keywords: nuisance parameters; causal inference; ubiased estimating equations; variance estimation; HIV; doubly robust

Abstract

We often estimate a parameter of interest when the identifying conditions involve a nuisance parameter. Examples are Inverse Probability Weighting, Marginal Structural Models and Structural Nested Models, which are all based on unbiased estimating equations. I present 4 results for estimators psi-hat based on unbiased estimating equations including a nuisance parameter theta. 1. I show that counter-intuitively, the limiting variance of psi-hat is typically smaller when theta is estimated by solving (partial) score equations, compared to if a known theta were plugged in. 2. I show that if estimating theta using (partial) score equations is ignored, the resulting sandwich estimator for the variance of psi-hat is conservative. 3. I provide a consistent estimator of the variance which provides results fast: no bootstrap. 4. I show that if psi-hat with the true theta plugged in is efficient, the limiting variance of psi-hat does not depend on whether theta is estimated, and the sandwich estimator for the variance ignoring estimation of theta is consistent. To illustrate I estimate how the effect of 1 year of ART depends on its initiation time in HIV-infected patients. arxiv:2109.02690.