Generalizing a causal effect: sensitivity analysis and missing covariates

by   Bénédicte Colnet, et al.

While a randomized controlled trial (RCT) readily measures the average treatment effect (ATE), this measure may need to be shifted to generalize to a different population. Standard estimators of the target population treatment effect are based on the distributional shift in covariates, using inverse propensity sampling weighting (IPSW) or modeling response with the g-formula. However, these need covariates that are available both in the RCT and in an observational sample, which often qualifies very few of them. Here we analyze how the classic estimators behave when covariates are missing in at least one of the two datasets - RCT or observational. In line with general identifiability conditions, these estimators are consistent when including only treatment effect modifiers that are shifted in the target population. We compute the expected bias induced by a missing covariate, assuming Gaussian covariates and a linear model for the conditional ATE function. This enables sensitivity analysis for each missing covariate pattern. In addition, this method is particularly useful as it gives the sign of the expected bias. We also show that there is no gain imputing a partially-unobserved covariate. Finally we study the replacement of a missing covariate by a proxy, and the impact of imputation. We illustrate all these results on simulations, as well as semi-synthetic benchmarks using data from the Tennessee Student/Teacher Achievement Ratio (STAR), and with a real-world example from the critical care medical domain.


page 1

page 2

page 3

page 4


Entropy Balancing for Generalizing Causal Estimation with Summary-level Information

In this paper, we focus on estimating the average treatment effect (ATE)...

Reweighting the RCT for generalization: finite sample analysis and variable selection

The limited scope of Randomized Controlled Trials (RCT) is increasingly ...

Covariate Selection for Generalizing Experimental Results

Scientists are interested in generalizing causal effects estimated in an...

Estimating Conditional Average Treatment Effects with Missing Treatment Information

Estimating conditional average treatment effects (CATE) is challenging, ...

Transporting treatment effects with incomplete attributes

The simultaneous availability of experimental and observational data to ...

Multistage Estimators for Missing Covariates and Incomplete Outcomes

We study problems with multiple missing covariates and partially observe...

Systematically Missing Data in Causally Interpretable Meta-Analysis

Causally interpretable meta-analysis combines information from a collect...