3.4.7. DELTA Models™
There are many reasons a global model may not perform as well as desired on a particular data set. Assay conditions may differ somewhat from the experiments that the global model was trained on, for example, or the compounds of interest may contain unusual substructures absent or underrepresented in the global training pool. Alternatively, you may want to focus the model on a particular part of the descriptor space. One option in such circumstances is to create a purely local model in ADMET Modeler and deploy it within ADMET Predictor.
Such a local model will probably lack the scope of the diverse and carefully curated data sets that ADMET Predictor models are typically built on, however, and therefore is not likely to extrapolate as well. Moreover, it may suffer from implicit limits on its applicability domain because compounds in the local data set only exhibit limited variability in an attribute that is relevant to the endpoint of interest when examined over a broader range.
Another option is to use the difference between the values predicted by a primary, reference model and the experimental values observed for a secondary data set (e.g., one based on data from an in-house assay) to construct a perturbation model. The sum of the reference and perturbation predictions defines the DELTA Model™. The descriptor sets for the original global and perturbation models may overlap but will typically be different, because the latter is trying to account for things that the former does not. In the DELTA Model, the reference model accounts for generic effects, leaving the perturbation model free to focus on effects specific to the local training set.
Let E denote experimental observations and R predictions by the reference model. The perturbation model P is trained against the set of differences:
{Ei - Ri; i=1,…,N}
where N is the size of the training set. The resulting Pi values are used by ADMET Predictor to compute the DELTA model predictions, D:
{Di = Ri + Pi; i=1,…,N}
In Model Editor the reference model to a given DELTA Model is listed in the Auxiliary factor column. If the modeling is performed in transformed space, e.g., in decimal log space, then perturbations are trained on the differences of transformed variables. e.g.
logPi : {logEi - logRi; i=1,…,N}
{logDi = logRi + logPi; i=1,…,N}
In this case caution is advised if the reference model is already registered with ADMET Predictor. In that case the program calculates the back-transformed Ri values and logRi are not available. This is why the transformed reference model (e.g., “+Log(R)”) is set as Auxiliary factor in Model Editor.
The reference variable is typically the output from a global model, but it can also be a suitably scaled measurement from some surrogate endpoint, e.g., results from an in vitro assay. In this case the model transform function is unknown and is assumed to be the same as the one employed for the perturbation model.
We used the DELTA Model methodology to perform a simple form of transfer learning. We originally developed it for microsomal clearance assay data lacking control incubations without NADPH. Using CYP_HLM_CLint as the reference variable produced a model that accounted for microsomal esterase activities. The technique also shows promise for using aquatic toxicity data collected for Daphnia to augment models for minnow toxicity. In ADMET Predictor 14, we use DELTA Models to transfer knowledge between species. For example, fumic_rat (fraction unbound to rat microsomes) uses the human analog, fumic_hum, as its reference.
Though we have only explored the technique's use with ANNE models in any depth, the implementation in ADMET Modeler supports SVM, KPLS and MLR applications as well. It does not support classification models at this time.
A tutorial has been provided to illustrate the workflow for ANNE regression.