  An adaptive design adjusts dynamically as information is accrued and a
consequence of applying an adaptive design is the potential for inducing
small-sample bias in estimates. In psychometrics and psychophysics, a common
class of studies investigate a subject's ability to perform a task as a
function of the stimulus intensity, meaning the amount or clarity of the
information supplied for the task. The relationship between the performance and
intensity is represented by a psychometric function. Such experiments routinely
apply adaptive designs, which use both previous intensities and performance to
assign stimulus intensities, the strategy being to sample intensities where the
information about the psychometric function is maximised. Similar schemes are
often applied in drug trials to assign doses dynamically using doses and
responses from earlier observations. The present paper investigates the
influence of adaptation on statistical inference about the psychometric
function focusing on estimation, considering both parametric and non-parametric
estimation under both fixed and adaptive designs in schemes encompassing within
subject independence as well as dependence through random effects. We study the
scenarios analytically, focussing on a latent class model to derive results
under random effects, and numerically through a simulation study. We show that
while the asymptotic properties of estimators are preserved under adaptation,
the adaptive nature of the design introduces small-sample bias, in particular
in the slope parameter of the psychometric function. We argue that this poses a
dilemma for a study applying an adaptive design in the form of a trade-off
between more efficient sampling and the need to increase the number of samples
to ameliorate small-sample bias.
