Archive for the ‘cheminformatics’ Category
So, how do I enjoy my first day of furlough? Go out for a nice ride. And then read up on some statistics. More specifically, I was browsing the The R Book and came across survival models. Such models are used to characterize time to events, where an event could be death of a patient or failure of a part and so on. In these types of models the dependent variable is the number of time units that pass till the event in question occurs. Usually the goal is to model the time to death (or failure) as a function of some properties of the individuals.
It occurred to me that molecules in a drug development pipeline also face a metaphorical life and death. More specifically, a drug development pipeline consists of a series of assays – primary, primary confirmation, secondary (orthogonal), ADME panel, animal model and so on. Each assay can be thought of as representing a time point in the screening campaign at which a compound could be discarded (“death”) or selected (“survived”) for further screening. While there are obvious reasons for why some compounds get selected from an assay and others do not (beyond just showing activity), it would be useful if we could quantify how molecular properties affect the number and types of compounds making it to the end of the screening campaign. Do certain scaffolds have a higher propensity of “surviving” till the in vivo assay? How does molecular weight, lipophilicity etc. affect a compounds “survival”? One could go up one level of abstraction and do a meta-analysis of screening campaigns where related assays would be grouped (so assays of type X all represent time point Y), allowing us to ask whether specific assays can be more or less indicative of a compounds survival in a campaign. Survival models allow us to address these questions.
How can we translate the screening pipeline to the domain of survival analysis? Since each assay represents a time point, we can assign a “survival time” to each compound equal to the number of assays it is tested in. Having defined the Y-variable, we must then select the independent variables. Feature selection is a never-ending topic so there’s lots of room to play. It is clear however, that descriptors derived from the assays (say ADMET related descriptors) will not be truly independent if those assays are part of the sequence.
Having defined the X and Y variables, how do we go about modeling this type of data? First, we must decide what type of survivorship curve characterizes our data. Such a curve characterizes the proportion of individuals alive at a certain time point. There are three types of survivorship curves: I, II and III corresponding to scenarios where individuals have a higher risk of death at later times, a constant risk of death and individuals have a higher risk of death at earlier times, respectively.
For the case of the a screening campaign, a Type III survivorship curve seems most appropriate. There are other details, but in general, they follow from the type of survivorship curve selected for modeling. I will note that the hazard function is an important choice to be made when using parametric models. There a variety of functions to choose from, but either require that you know the error distribution or else are willing to use trial and error. The alternative is to use a non-parametric approach. The most common approach for this class of models is the Cox proportional hazards model. I won’t go into the details of either approach, save to note that using a Cox model does not allow us to make predictions beyond the last time point whereas a parametric model would. For the case at hand, we are not really concerned with going beyond the last timepoint (i.e., the last assay) but are more interested in knowing what factors might affect survival of compounds through the assay sequence. So, a Cox model should be sufficient. The survival package provides the necessary methods in R.
OK – it sounds cute, but has some obvious limitations
- The use of a survival model assumes a linear time line. In many screening campaigns, the individual assays may not follow each other in a linear fashion. So either they must be collapsed into a linear sequence or else some assays should be discarded.
- A number of the steps represent ‘subjective selection’. In other words, each time a subset of molecules are selected, there is a degree of subjectivity involved – maybe certain scaffolds are more tractable for med chem than others or some notion of interesting combined with a hunch that it will work out. Essentially chemists will employ heuristics to guide the selection process – and these heuristics may not be fully quantifiable. Thus the choice of independent variables may not capture the nuances of these heuristics. But one could argue that it is possible the model captures the underlying heuristics via proxy variables (i.e., the descriptors) and that examination of those variables might provide some insight into the heuristics being employed.
- Data size will be an issue. As noted, this type of scenario requires the use of a Type III survivorship curve (i.e., most death occurs at earlier times and the death rate decreases with increasing time). However, decrease in death rate is extremely steep – out of 400,000 compounds screened in a primary assay, maybe 2000 will be cherry picked for confirmation and about 50 molecules may be tested in secondary, orthogonal assays. If we go out further to ADMET and in vivo assays, we may have fewer than 10 compounds to work with. At this stage I don’t know what effect such a steeply decreasing survivorship curve would have on the model.
The next step is to put together a dataset to see what we can pull out of a survival analysis of a screening campaign.
Deep learning has been getting some press in the last few months, especially with the Google paper on recognizing cats (amongst other things) from Youtube videos. The concepts underlying this machine learning approach have been around for many years, though recent work by Hinton and others have led to fast implementations of the algorithms as well as better theoretical understanding.
It took me a while to realize that deep learning is really about learning an optimal, abstract representation in an unsupervised fashion (in the general case), given a set of input features. The learned representation can be then used as input to any classifier. A key aspect to such learned representations is that they are, in general, agnostic with respect to the final task for which they are trained. In the Google “cat” project this meant that the final representation developed the concept of cats as well as faces. As pointed out by a colleague, Bengio et al have published an extensive and excellent review of this topic and Baldi also has a nice review on deep learning.
In any case, it didn’t take too long for this technique to be applied to chemical data. The recent Merck-Kaggle challenge was won by a group using deep learning, but neither their code nor approach was publicly described. A more useful discussion of deep learning in cheminformatics was recently published by Lusci et al where they develop a DAG representation of structures that is then fed to a recursive neural network (RNN). They then use the resultant representation and network model to predict aqueous solubility.
A key motivation for the new graph representation and deep learning approach was the observation
one cannot be certain that the current molecular descriptors capture all the relevant properties required for solubility prediction
A related motivation was that they desired to apply deep learning methods directly to the molecular graph, which in general, is of variable size compared to fixed length representations (fingerprints or descriptor sets). It’s an interesting approach and you can read the paper for more details, but a few things caught my eye:
- The motivation for the DAG based structure description didn’t seem very robust. Shouldn’t a learned representation be discoverable from a set of real-valued molecular descriptors (or even fingerprints)? While it is possible that all the physical aspects of aquous solubility may not be captured in the current repetoire of molecular descriptors, I’d think that most aspects are. Certainly some characterizations may be too time consuming (QM descriptors) for a cheminformatics setting.
- The results are not impressive, compared to pre-existing model for the datasets they used. This is all the more surprising given that the method is actually an ensemble of RNN’s. For example, in Table 2 the best RNN model has an R2 of 0.92 versus 0.91 for the pre-existing model (a 2D kernel). But R2 is usually a good metric for non-linear regression. But even the RMSE is only 0.03 units better than the pre-existing model.However, it is certainly true that the unsupervised nature of the representation learning step is quite attractive – this is evident in the case of the intrinsic solubility dataset, where they achieve similar results to the prior model. But the prior model employed a manually selected set of topological descriptors.
- It would’ve been very interesting to look at the transferabilty of the learned representation by using it to predict another physical property unrelated (at least directly) to solubility.
One characteristic of deep learning methods is that they work better when provided a lot of training data. With the exception of the Huuskonen dataset (4000 molecules), none of the datasets used were very large. If training set size is really an issue, the Burnham solubility dataset with 57K observations would have been a good benchmark.
Overall, I don’t think the actual predictions are too impressive using this approach. But the more important aspect of the paper is the ability to learn an internal representation in an unsupervised manner and the promise of transferability of such a representation. In a way, it’d be interesting to see what an abstract representation of a molecule could be like, analogous to what a deep network thinks a cat looks like.
Benjamin Good recently asked about the existence of public repositories of predictive molecular signatures. From his description, he’s looking for platforms that are capable of deploying predictive models. The need for something like this is certainly not restricted to genomics – the QSAR field has been in need for this for many years. A few years back I described a system to deploy R models and more recently the OCHEM platform attempts to address this. Pipelining tools usually have a web deployment mode that also supports this idea. One problem faced by such platforms in the cheminformatics area is that the deployed model must include the means to evaluate the input features (a.k.a., descriptors). Depending on the licenses associated with descriptor software such a bundle may not be easily deployed. A gene-based predictor obviously doesn’t suffer from this problem, so it should be easier to implement. Benjamin points out the Synapse platform which looks quite nice, but only supports R models (not necessarily a bad thing!). A very recent candidate for generic predictive model (amongst other things) deployment is via plugins for the BARD platform.
But in my mind, the deeper issue that should be addressed is that of model specification. With a robust specification, evaluation of the model could implemented in arbitrary languages and platforms – essentially decoupling model definition and model implementation. PMML is one approach to predictive model specifications and is quite general (and a good solution for the gene predictor models that Benjamin is interested in). A field-specific example would be QSAR-ML (also see here) for QSAR models. One could then imagine repositories of model specifications, with an ecosystem of tools and services that instantiate models from these specs.
I’ve just pushed a new version of the fingerprint package that contains an update provided by Abhik Seal that significantly speeds up calculation of pairwise similarity matrices when using the Dice similarity method. A ran a simple comparison using different numbers of random fingerprints (1024 bits, with 512 bits set to one, randomly) and measured the time to evaluate the pairwise similarity matrix. As you can see from the figure alongside, the new code is significantly faster (with speed ups of 450x to 500x). The code to generate the timings is below – it probably should wrapped in a loop to multiple times for each set size.
fpls <- lapply(seq(10,300,by=10),
function(x) random.fingerprint(1024, 512)))
times <- sapply(fpls,
function(fpl) system.time(fp.sim.matrix(fpl, method='dice')))
While at the ACS National Meeting in Philadelphia I attended a talk by David Thompson of Boehringer Ingelheim (BI), where he spoke about a recent competition BI sponsored on Kaggle – a web site that hosts data mining competitions. In this instance, BI provided a dataset that contained only object identifiers and about 1700 numerical features and a binary dependent variable. The contest was open to anybody and who ever got the best classification model (as measured by log loss) was selected as the winner. You can read more about the details of the competition and also on Davids’ slides.
But I’m curious about the utility of such a competition. During the competition, all contestents had access to were the numerical features. So the contestants had no idea of the domain from where the data came – placing the onus on pure modeling ability and no need for domain knowledge. But in fact the dataset provided to them, as announced by David at the ACS, was the Hansen AMES mutagenicity dataset characterized using a collection of 2D descriptors (continuous topological descriptors as well as binary fingerprints).
BI included some “default” models and the winning models certainly performed better (10% for the winning model). This is not surprising, as they did not attempt build optimized models. But then we also see that the top 5 models differed only incrementally in their log loss values. Thus any one of the top 3 or 4 models could be regarded as a winner in terms of actual predictions.
What I’d really like to know is how well such an approach leads to better chemistry or biology. First, it’s clear that such an approach leads to the optimization of pure predictive performance and cannot provide insight into why the model makes an active or inactive call. In many scenario’s this is sufficient, but more often than not, domain specific diagnostics are invaluable. Second, how does the relative increase in model performance lead to better decision making? Granted, the crowd-sourced, gamified approach is a nice way to eke out the last bits of predictive performance on a dataset – but does it really matter that one model performs 1% better than the next best model? The fact that the winning model was 10% better than the “default” BI model is not too informative. So a specific qustion I have is, was there a benefit, in terms of model performance, and downstream decision making by asking the crowd for a better model, compared to what BI had developed using (implicit or explicit) chemical knowledge?
My motivation is to try and understand whether the winning model was an incremental improvement or whether it was a significant jump, not just in terms of numerical performance, but in terms of the predicted chemistry/biology. People have been making noises of how data trumps knowledge (or rather hypotheses and models) and I believe that in some cases this can be true. But I also wonder to what extent this holds for chemical data mining.
But it’s equally important to understand what such a model is to be used for. In a virtual screening scenario, one could probably ignore interpretability and go for pure predictive performance. In such cases, for increasingly large libraries, it might make sense for one to have a model that s 1% better than the state of the art. (In fact, there was a very interesting talk by Nigel Duffy of Numerate, where he spoke about a closed form, analytical expression for the hit rate in a virtual screen, which indicates that for improvements in the overall performance of a VS workflow, the best investment is to increase the accuracy of the predictive model. Indeed, his results seem to indicate that even incremental improvements in model accuracy lead to a decent boost to the hit rate).
I want to stress that I’m not claiming that BI (or any other organization involved in this type of activity) has the absolute best models and that nobody can do better. I firmly believe that however good you are at something, there’s likely to be someone better at it (after all, there are 6 billion people in the world). But I’d also like to know how and whether incrementally better models do when put to the test of real, prospective predictions.