  Supervised learning models, also known as quantitative structure-activity
regression (QSAR) models, are increasingly used in assisting the process of
preclinical, small molecule drug discovery. The models are trained on data
consisting of a finite dimensional representation of molecular structures and
their corresponding target specific activities. These models can then be used
to predict the activity of previously unmeasured novel compounds. In this work
we address two problems related to this approach. The first is to estimate the
extent to which the quality of the model predictions degrades for compounds
very different from the compounds in the training data. The second is to adjust
for the screening dependent selection bias inherent in many training data sets.
In the most extreme cases, only compounds which pass an activity-dependent
screening are reported. By using a semi-supervised learning framework, we show
that it is possible to make predictions which take into account the similarity
of the testing compounds to those in the training data and adjust for the
reporting selection bias. We illustrate this approach using publicly available
structure-activity data on a large set of compounds reported by GlaxoSmithKline
(the Tres Cantos AntiMalarial Set) to inhibit in vitro P. falciparum growth.
