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Causal weighted quantile treatment effects (WQTE) are a useful compliment tostandard causal contrasts that focus on the mean when interest lies at thetails of the counterfactual distribution. To-date, however, methods forestimation and inference regarding causal WQTEs have assumed complete data onall relevant factors. Missing or incomplete data, however, is a widespreadchallenge in practical settings, particularly when the data are not collectedfor research purposes such as electronic health records and disease registries.Furthermore, in such settings may be particularly susceptible to the outcomedata being missing-not-at-random (MNAR). In this paper, we consider the use ofdouble-sampling, through which the otherwise missing data is ascertained on asub-sample of study units, as a strategy to mitigate bias due to MNAR data inthe estimation of causal WQTEs. With the additional data in-hand, we presentidentifying conditions that do not require assumptions regarding missingness inthe original data. We then propose a novel inverse-probability weightedestimator and derive its' asymptotic properties, both pointwise at specificquantiles and uniform across a range of quantiles in (0,1), when the propensityscore and double-sampling probabilities are estimated. For practical inference,we develop a bootstrap method that can be used for both pointwise and uniforminference. A simulation study is conducted to examine the finite sampleperformance of the proposed estimators.

Estimating weighted quantile treatment effects with missing outcome data by double sampling