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The underlying statistical model is specified via a mixture factorization of the joint distribution of the event type and the time to the event. The time to event distributions conditional on the event type are modeled using smooth semi\u2010nonparametric densities. One strength of this approach is that it can handle arbitrary censoring and truncation while relying on mild parametric assumptions. A stepwise forward algorithm for model estimation and adaptive selection of smooth semi\u2010nonparametric polynomial degrees is presented, implemented in the statistical software R, evaluated in a sequence of simulation studies, and applied to data from a clinical trial in cryptococcal meningitis. The simulations demonstrate that the proposed method frequently outperforms both parametric and nonparametric alternatives. They also support the use of \u2018ad hoc\u2019 asymptotic inference to derive confidence intervals. 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