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A significant level of stigma and inequality exists in mental healthcare, especially in under-served populations. Inequalities are reflected in the data collected for scientific purposes. When not properly accounted for, machine learning (ML) models leart from data can reinforce these structural inequalities or biases. Here, we present a systematic study of bias in ML models designed to predict depression in four different case studies covering different countries and populations. We find that standard ML approaches show regularly biased behaviors. We also show that mitigation techniques, both standard and our own post-hoc method, can be effective in reducing the level of unfair bias. No single best ML model for depression prediction provides equality of outcomes. This emphasizes the importance of analyzing fairness during model selection and transparent reporting about the impact of debiasing interventions. Finally, we provide practical recommendations to develop bias-aware ML models for depression risk prediction., Comment: 11 pages, 2 figures