  The effects of continuous treatments are often characterized through the
average dose response function, which is challenging to estimate from
observational data due to confounding and positivity violations. Modified
treatment policies (MTPs) are an alternative approach that aim to assess the
effect of a modification to observed treatment values and work under relaxed
assumptions. Estimators for MTPs generally focus on estimating the conditional
density of treatment given covariates and using it to construct weights.
However, weighting using conditional density models has well-documented
challenges. Further, MTPs with larger treatment modifications have stronger
confounding and no tools exist to help choose an appropriate modification
magnitude. This paper investigates the role of weights for MTPs showing that to
control confounding, weights should balance the weighted data to an unobserved
hypothetical target population, that can be characterized with observed data.
Leveraging this insight, we present a versatile set of tools to enhance
estimation for MTPs. We introduce a distance that measures imbalance of
covariate distributions under the MTP and use it to develop new weighting
methods and tools to aid in the estimation of MTPs. We illustrate our methods
through an example studying the effect of mechanical power of ventilation on
in-hospital mortality.
