Average dose-response functions are widely used to summarize causal effects of continuous treatments, but most existing methods assume that the observed sample represents the target population. We study a covariate-shift setting in which covariates, treatment, and outcome are observed in a labelled source sample, while only covariates are observed in the target sample. We develop a two-sample local polynomial regression framework based on pseudo-outcomes that use source outcomes to address confounding and target covariates to define the population of interest. We further propose a source-to-target extension of distance covariance optimal weighting (DCOW), designed to remove treatment-covariate dependence in the source sample while aligning the weighted source covariate distribution with the target population. A central theoretical contribution is a weight-level analysis of this optimization-based procedure: we show that the population criterion identifies the oracle source-to-target weights and that approximate empirical minimizers, including exact minimizers as a special case, converge uniformly to these weights under regularity conditions. We also establish consistency and asymptotic normality of the resulting estimator. Simulations show that the proposed method improves target dose-response estimation relative to DCOW, generalized-propensity-score weighting, entropy balancing, and unweighted alternatives. We illustrate the method in a county-level analysis of PM2.5 exposure and subsequent heart-disease mortality using a source-target validation design.
We study causal effect estimation with compositional treatments, where the exposure lies on a simplex and the estimand is defined over compositions rather than scalar or binary values. By considering a projection of the average potential outcome onto the treatment space, a kernel-based covariate functional balancing approach is adopted for weight construction. The weights are obtained by directly minimizing a worst-case balancing error over a reproducing kernel Hilbert space (RKHS) defined on the joint space of treatments and covariates, instead of being estimated under a treatment assignment model. Building on these weights, an augmented weighted estimator (AWE) is proposed, where the outcome function is estimated via kernel ridge regression and combined with a marginal augmentation over the covariate distribution. Despite the complex structure of the resulting objective, a finite-dimensional convex optimization problem is formulated via a representer theorem and a low-rank approximation. The proposed estimator achieves $\sqrt{n}$-consistency without requiring consistent estimation or smoothness of the weights. An asymptotic normality result is established around a sample-specific target. Empirical performance is demonstrated through simulation studies and a real data application.