  In 1951 Robbins and Monro published the seminal article on stochastic
approximation and made a specific reference to its application to the
"estimation of a quantal using response, nonresponse data." Since the 1990s,
statistical methodology for dose-finding studies has grown into an active area
of research. The dose-finding problem is at its core a percentile estimation
problem and is in line with what the Robbins--Monro method sets out to solve.
In this light, it is quite surprising that the dose-finding literature has
developed rather independently of the older stochastic approximation
literature. The fact that stochastic approximation has seldom been used in
actual clinical studies stands in stark contrast with its constant application
in engineering and finance. In this article, I explore similarities and
differences between the dose-finding and the stochastic approximation
literatures. This review also sheds light on the present and future relevance
of stochastic approximation to dose-finding clinical trials. Such connections
will in turn steer dose-finding methodology on a rigorous course and extend its
ability to handle increasingly complex clinical situations.
