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A notoriously difficult problem in traffic safety is the verification of the so-called safety-in-numbers (SiN) effect. This term refers to the observation that the individual risk R for a road user is inversely related to the absolute number X of road users of the corresponding type and suggests that a larger number of such road users is the reason for an increase of their individual safety. We propose a model to identify the causal relation between the correlated phenomena. It includes temporal information to verify which of the correlated phenomena precedes the other. We employ the model for an analysis of bicycle volumes and crashes between bicycles and motorized vehicles in Berlin, where different temporal and spatial aggregation levels are considered. Interestingly, we find a slight indication for a SiN effect on an annual scale while more fine-grained temporal resolutions rather indicate the opposite effect of increasing risks due to higher volumes. [ABSTRACT FROM AUTHOR]