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Convolutional neural networks have enabled significant improvements in medical image-based diagnosis. It is, however, increasingly clear that these models are susceptible to performance degradation when facing spurious correlations and dataset shift, leading, e.g., to underperformance on underrepresented patient groups. In this paper, we compare two classification schemes on the ADNI MRI dataset: a simple logistic regression model using manually selected volumetric features, and a convolutional neural network trained on 3D MRI data. We assess the robustness of the trained models in the face of varying dataset splits, training set sex composition, and stage of disease. In contrast to earlier work in other imaging modalities, we do not observe a clear pattern of improved model performance for the majority group in the training dataset. Instead, while logistic regression is fully robust to dataset composition, we find that CNN performance is generally improved for both male and female subjects when including more female subjects in the training dataset. We hypothesize that this might be due to inherent differences in the pathology of the two sexes. Moreover, in our analysis, the logistic regression model outperforms the 3D CNN, emphasizing the utility of manual feature specification based on prior knowledge, and the need for more robust automatic feature selection.