Adversarial attacks are considered a potentially serious security threat for machine learning systems. Medical image analysis (MedIA) systems have recently been argued to be vulnerable to adversarial attacks due to strong financial incentives and the associated technological infrastructure. In this paper, we study previously unexplored factors affecting adversarial attack vulnerability of deep learning MedIA systems in three medical domains: ophthalmology, radiology, and pathology. We focus on adversarial black-box settings, in which the attacker does not have full access to the target model and usually uses another model, commonly referred to as surrogate model, to craft adversarial examples. We consider this to be the most realistic scenario for MedIA systems. Firstly, we study the effect of weight initialization (ImageNet vs. random) on the transferability of adversarial attacks from the surrogate model to the target model. Secondly, we study the influence of differences in development data between target and surrogate models. We further study the interaction of weight initialization and data differences with differences in model architecture. All experiments were done with a perturbation degree tuned to ensure maximal transferability at minimal visual perceptibility of the attacks. Our experiments show that pre-training may dramatically increase the transferability of adversarial examples, even when the target and surrogate's architectures are different: the larger the performance gain using pre-training, the larger the transferability. Differences in the development data between target and surrogate models considerably decrease the performance of the attack; this decrease is further amplified by difference in the model architecture. We believe these factors should be considered when developing security-critical MedIA systems planned to be deployed in clinical practice.