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Low attendance levels in medical appointments have been associated with poor health outcomes and efficiency problems for service providers. To address this problem, healthcare managers could aim at improving attendance levels or minimizing the operational impact of no-shows by adapting resource allocation policies. However, given the uncertainty of patient behaviour, generating relevant information regarding no-show probabilities could support the decision-making process for both approaches. In this context many researchers have used multiple regression models to identify patient and appointment characteristics than can be used as good predictors for no-show probabilities. This work develops a Decision Support System (DSS) to support the implementation of strategies to encourage attendance, for a preventive care program targeted at underserved communities in Bogotá, Colombia. Our contribution to literature is threefold. Firstly, we assess the effectiveness of different machine learning approaches to improve the accuracy of regression models. In particular, Random Forest and Neural Networks are used to model the problem accounting for non-linearity and variable interactions. Secondly, we propose a novel use of Layer-wise Relevance Propagation in order to improve the explainability of neural network predictions and obtain insights from the modelling step. Thirdly, we identify variables explaining no-show probabilities in a developing context and study its policy implications and potential for improving healthcare access. In addition to quantifying relationships reported in previous studies, we find that income and neighbourhood crime statistics affect no-show probabilities. Our results will support patient prioritization in a pilot behavioural intervention and will inform appointment planning decisions.