We consider the task of automatically annotating free texts describing clinical trials with concepts from a controlled, structured medical vocabulary. Specifically, we aim to build a model to infer distinct sets of (ontological) concepts describing complementary clinically salient aspects of the underlying trials: the populations enrolled, the interventions administered and the outcomes measured, i.e., the PICO elements. This important practical problem poses a few key challenges. One issue is that the output space is vast, because the vocabulary comprises many unique concepts. Compounding this problem, annotated data in this domain is expensive to collect and hence sparse. Furthermore, the outputs (sets of concepts for each PICO element) are correlated: specific populations (e.g., diabetics) will render certain intervention concepts likely (insulin therapy) while effectively precluding others (radiation therapy). Such correlations should be exploited. We propose a novel neural model that addresses these challenges. We introduce a Candidate-Selector architecture in which the model considers setes of candidate concepts for PICO elements, and assesses their plausibility conditioned on the input text to be annotated. This relies on a 'candidate set' generator, which may be learned or relies on heuristics. A conditional discriminative neural model then jointly selects candidate concepts, given the input text. We compare the predictive performance of our approach to strong baselines, and show that it outperforms them. Finally, we perform a qualitative evaluation of the generated annotations by asking domain experts to assess their quality.