Covariate balance is crucial in obtaining unbiased estimates of treatment effects in observational studies. Methods that target covariate balance have been successfully proposed and largely applied to estimate treatment effects on continuous outcomes. However, in many medical and epidemiological applications, the interest lies in estimating treatment effects on time-to-event outcomes. With this type of data, one of the most common estimands of interest is the marginal hazard ratio of the Cox proportional hazards model. In this article, we start by presenting robust orthogonality weights, a set of weights obtained by solving a quadratic constrained optimization problem that maximizes precision while constraining covariate balance defined as the correlation between confounders and treatment. By doing so, robust orthogonality weights optimally deal with both binary and continuous treatments. We then evaluate the performance of the proposed weights in estimating marginal hazard ratios of binary and continuous treatments with time-to-event outcomes in a simulation study. We finally apply robust orthogonality weights in the evaluation of the effect of hormone therapy on time to coronary heart disease and on the effect of red meat consumption on time to colon cancer among 24,069 postmenopausal women enrolled in the Women’s Health Initiative observational study.
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