Causal inference for multiple treatments via sufficiency and ratios of generalized propensity scores
Date Issued
2012
Author(s)
Abstract
The coarsest balancing score for multiple treatments T is the minimal
sufficient statistic s for the covariates' distributions, DT ; of
populations {Pt; t ∈ T } receiving each treatment t ∈ T : A unit in
Pr with covariates x is a good match with respect to T for a unit
in Pt with covariates y; when x and y provide similar information
for DT ; i.e. when s(x) ≈ s(y): For finite, countably finite and often
continuous treatments, s(x) is shown to be equivalent to ~e; a vector
of propensities' ratios. The units in {Pt; t ∈ T } can be divided into
subpopulations where causal comparisons are simultaneously valid.
Satisfactory s-matchings are obtained for simulated covariates in R3:
The use of ~e's estimate rather than s's estimate allows to avoid the
x-curse of dimensionality, but the available data's size in each case
is critical for the final choice.
sufficient statistic s for the covariates' distributions, DT ; of
populations {Pt; t ∈ T } receiving each treatment t ∈ T : A unit in
Pr with covariates x is a good match with respect to T for a unit
in Pt with covariates y; when x and y provide similar information
for DT ; i.e. when s(x) ≈ s(y): For finite, countably finite and often
continuous treatments, s(x) is shown to be equivalent to ~e; a vector
of propensities' ratios. The units in {Pt; t ∈ T } can be divided into
subpopulations where causal comparisons are simultaneously valid.
Satisfactory s-matchings are obtained for simulated covariates in R3:
The use of ~e's estimate rather than s's estimate allows to avoid the
x-curse of dimensionality, but the available data's size in each case
is critical for the final choice.
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