Causal analysis of continuous treatments with soft constraints
N. T. Longford
Abstract
Approaches based on balancing weights are firmly established
in causal analysis of binary treatments in observational studies.
Their extension to treatments defined on ordinal scales,
which arise in dose- and exposure-response studies,
remains a methodological challenge.
We develop a method of balancing that naturally extends
from binary treatment to a continuum of treatment doses.
The solution, the estimated average dose-response function
in a given sample or population, depends on a set of tuning parameters
that quantify the relative priorities of balancing the background variables.
The closed form of this function facilitates
a detailed analysis of its finite-sample properties,
including a sensitivity analysis for hidden bias.
All the constraints considered in other approaches are converted
in this method to penalties, and so are satisfied only approximately
but according to the priorities specified by the analyst.
The method is applied to a study of the effect of campaign advertising
on donations in the 2008 U.S. presidential elections.
Submitted.
August 2025.