Watchfully waiting: medical intervention as an optimal investment decision

Watchfully waiting involves monitoring a patient's health state over time and deciding whether to undertake a medical intervention, or to postpone it and continue observing the patient. In this paper, we consider the timing of medical intervention as an optimal stopping problem. The development of the patient's health state in the absence of intervention follows a stochastic process (geometric Brownian motion). Spontaneous recovery occurs in case the absorbing state of "good health" is reached. We determine optimal threshold values for initiating the intervention, and derive comparative statics results with respect to the model parameters. In particular, an increase in the degree of uncertainty over the patient's development in most cases makes waiting more attractive. However, this may not hold if the patient's health state has a tendency to improve. The model can be extended to allow for risk aversion and for sudden, Poisson-type shocks to the patient's health state.