Small-area estimation - a confusion of paradigms.
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.
In our method all the constraints considered in alternative approaches
are converted to penalties, and so are satisfied only
approximately but according to the specified priorities.
June 2025