  Many scientific questions require estimating the effects of continuous
treatments. Outcome modeling and weighted regression based on the generalized
propensity score are the most commonly used methods to evaluate continuous
effects. However, these techniques may be sensitive to model misspecification,
extreme weights or both. In this paper, we propose Kernel Optimal Orthogonality
Weighting (KOOW), a convex optimization-based method, for estimating the
effects of continuous treatments. KOOW finds weights that minimize the
worst-case penalized functional covariance between the continuous treatment and
the confounders. By minimizing this quantity, KOOW successfully provides
weights that orthogonalize confounders and the continuous treatment, thus
providing optimal covariate balance, while controlling for extreme weights. We
valuate its comparative performance in a simulation study. Using data from the
Women's Health Initiative observational study, we apply KOOW to evaluate the
effect of red meat consumption on blood pressure.
