This paper studies a decision theoretic method for timing medical exam
inations. The specific model is motivated by screening asymptomatic in
dividuals for hidden disease or risk-increasing conditions. Ideas and
strategies may be applied more broadly to problems in which a stochast
ic process is monitored over time with a costly and possibly faulty da
ta collection procedure. The decision space is modelled as a space of
functions, termed screening intensity functions. Results include expli
cit rules for deciding whether or not an individual of given age and r
isk factors should be screened for a disease, and for deciding when an
individual examined today should be examined again. Breast cancer scr
eening is used as an illustration.