Estimating Balancing Weights for Continuous Treatments Using Constrained Optimization

In the absence of randomization, common causes of a treatment and an outcome create an association between them that does not correspond to the causal effect of the treatment. When a sufficient set of these confounding variables have been measured, statistical methods such as regression and propensity score weighting can be used to adjust for the common causes and arrive at an unbiased estimate of the causal effect. For continuous treatments, current weighting methods suffer from imprecision, bias, and reliance on correct model specification. Here, I derived the bias of the unadjusted estimate of a linear average dose-response function and developed optweights, a convex optimization-based weight estimation method that targets each component of the bias with constraints. In two simulation studies, I evaluated the performance of optweights, comparing it to regression and other weighting methods. In a common data setting, with many more units than covariates, optweights performed better than the other weighting methods in most scenarios and performed comparably to regression. In scenarios where the number of covariates approached the number of units, optweights could outperform regression in terms of mean squared error when relaxing its constraints to manage the bias-variance tradeoff. The results indicate that optweights should be considered a strong alternative to regression and other weighting methods for estimating the effects of continuous treatments, though further research is required on how to optimize its performance.Doctor of Philosoph