In this paper, we consider estimation of the effect of a randomized treatment on time to disease progression and death, possibly adjusting for high-dimensional baseline prognostic factors. We assume that patients may or may not have a specific type of disease progression prior to death and those who have this endpoint are followed for their survival information. Progression and survival may also be censored due to loss to follow-up or study termination. We posit a semi-parametric bivariate quantile-quantile regression failure time model and show how to construct estimators of the regression parameters. The causal interpretation of the parameters depends on non-identifiable assumptions. We discuss two assumptions: the first applies to situations where it is reasonable to view disease progression as well defined after death and the second applies to situations where such a view is unreasonable. We conduct a simulation study and analyze data from a randomized trial for the treatment of brain cancer.
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