Archive for the ‘cheminformatics’ Category
I came across a recent paper from the Tropsha group that discusses the issue of modelability – that is, can a dataset (represented as a set of computed descriptors and an experimental endpoint) be reliably modeled. Obviously the definition of reliable is key here and the authors focus on a cross-validated classification accuracy as the measure of reliability. Furthermore they focus on binary classification. This leads to a simple definition of modelability – for each data point, identify whether it’s nearest neighbor is in the same class as the data point. Then, the ratio of number of observations whose nearest neighbor is in the same activity class to the number observations in that activity class, summed over all classes gives the MODI score. Essentially this is a statement on linear separability within a given representation.
The authors then go show a pretty good correlation between the MODI scores over a number of datasets and their classification accuracy. But this leads to the question – if one has a dataset and associated modeling tools, why compute the MODI? The authors state
we suggest that MODI is a simple characteristic that can be easily computed for any dataset at the onset of any QSAR investigation
I’m not being rigorous here, but I suspect for smaller datasets the time requirements for MODI calculations is pretty similar to building the models themselves and for very large datasets MODI calculations may take longer (due to the requirement of a distance matrix calculation – though this could be alleviated using ANN or LSH). In other words – just build the model!
Another issue is the relation between MODI and SVM classification accuracy. The key feature of SVMs is that they apply the kernel trick to transform the input dataset into a higher dimensional space that (hopefully) allows for better separability. As a result MODI calculated on the input dataset should not necessarily be related to the transformed dataset that is actually operated on by the SVM. In other words a dataset with poor MODI could be well modeled by an SVM using an appropriate kernel.
The paper, by definition, doesn’t say anything about what model would be best for a given dataset. Furthermore, it’s important to realize that every dataset can be perfectly predicted using a sufficiently complex model. This is also known as an overfit model. The MODI approach to modelability avoids this by considering a cross-validated accuracy measure.
One application of MODI that does come to mind is for feature selection - identify a descriptor subset that leads to a predictive model. This is justified by the observed correlation between the MODI scores and the observed classification rates and would avoid having to test feature subsets with the modeling algorithm itself. An alternative application (as pointed out by the authors) is to identify subsets of the data that exhibit a good MODI score, thus leading to a local QSAR model.
More generally, it would be interesting to extend the concept to regression models. Intuitively, a dataset that is continuous in a given representation should have a better modelability than one that is discontinuous. This is exactly the scenario that can be captured using the activity landscape approach. Sometime back I looked at characterizing the roughness of an activity landscape using SALI and applied it to the feature selection problem – being able to correlate such a measure to predictive accuracy of models built on those datasets could allow one to address modelability (and more specifically, what level of continuity should a landscape present to be modelable) in general.
Version 3.5.2 of the fingerprint package has been pushed to CRAN. This update includes a contribution from Abhik Seal that significantly speeds up similarity matrix calculations using the Tanimoto metric.
His patch led to a 10-fold improvement in running time. However his code involved the use of nested for loops in R. This is a well known bottleneck and most idiomatic R code replaces for loops with a member of the sapply/lapply/tapply family. In this case however, it was easier to write a small piece of C code to perform the loops, resulting in a 4- to 6-fold improvement over Abhiks observed running times (see figure summarizing Tanimoto similarity matrix calculation for 1024 bit fingerprints, with 256 bits randomly selected to be 1). As always, the latest code is available on Github.
I’ve pushed updates to the rcdklibs and rcdk packages that support cheminformatics in R using the CDK. The new versions employ the latest CDK master, which as Egon pointed out has significantly fewer bugs, and thanks to Jon, improved performance. New additions to the package include support for the LINGO and Signature fingerprinters (you’ll need the latest version of fingerprint).
I’ve just updated the fingerprint package to v3.5.0 (should show up on CRAN shortly, or else you can get it directly from my Github repository). The main update in this version is better support for feature,count type fingerprints. An example would be ECFP or signature fingerprints. In these types of fingerprints, the output is usually a set of (integer or long) hash values or else structural fragments along with their count of occurrences.
The updated package now provides an S4 class to represent features and their counts. An example of this class is
f1 <- new("feature",
The package provides getters and setters for these objects, allow you to get or set the feature and the count.
> feature(f1) <- 'ABCD'
> count(f1) <- 12
Using this class, feature,count fingerprints are now represented as objects of class featvec. For these fingerprints, instead of bits, one obtains a list of feature objects. For fingerprints read from files that provide the hashed version of the underlying structure (or neighborhood etc), the numeric hashes are read in as features, with a default count of 1. The distance method has also been updated to evaluate similarities for feature,count fingerprints, though currently it does not use the count in the similarity calculation.
As an example, consider a set of ECFP’s available from here
> fps <- fp.read('http://pastebin.com/raw.php?i=gHjTQNKP', lf=ecfp.lf, binary=FALSE)
name = mol01
source = ecfp.lf
features = 17:1 0:1 16:1 3:1 1:1 1747237384:1 1499521844:1 -1539132615:1 1294255210:1 332760439:1 -1549163031:1 1035613116:1 1618154665:1 590925877:1 1872154524:1 -1143715940:1 203677720:1 -1272768868:1 136120670:1 136597326:1 -1460348762:1 -1262922302:1 -1201618245:1 -402549409:1 -1270820019:1 929601590:1 -1597477966:1 -1274743746:1 -1155471474:1 1258428229:1 -1838187238:1 -798628285:1 -1773728142:1 -773983804:1 -453677277:1 1674451008:1 65948508:1 991735244:1 -1412946825:1 846704869:1 -2103621484:1 -886204842:1 1725648567:1 -353343892:1 -585443181:1 -533273616:1 2031084733:1 -801248129:1 1752802620:1 -976015189:1 -992213424:1 2109043264:1 -790336137:1 630139722:1 -505031736:1 -1427697183:1 -2090462286:1 -1724769936:1
> distance(fps[], fps[])
> distance(fps[], fps[])
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.