  Machine learning is increasingly being used to generate prediction models for
use in a number of real-world settings, from credit risk assessment to clinical
decision support. Recent discussions have highlighted potential problems in the
updating of a predictive score for a binary outcome when an existing predictive
score forms part of the standard workflow, driving interventions. In this
setting, the existing score induces an additional causative pathway which leads
to miscalibration when the original score is replaced. We propose a general
causal framework to describe and address this problem, and demonstrate an
equivalent formulation as a partially observed Markov decision process. We use
this model to demonstrate the impact of such `naive updating' when performed
repeatedly. Namely, we show that successive predictive scores may converge to a
point where they predict their own effect, or may eventually tend toward a
stable oscillation between two values, and we argue that neither outcome is
desirable. Furthermore, we demonstrate that even if model-fitting procedures
improve, actual performance may worsen. We complement these findings with a
discussion of several potential routes to overcome these issues.
