Many cancer monotherapies demonstrate limited clinical efficacy, making combination therapies a relevant treatment strategy. The extensive number of potential drug combinations and context-specific response profiles complicates the prediction of drug combination responses. Existing computational models are typically trained to predict a single aggregated synergy score, which summarises drug responses across different dosage combinations, such as Bliss or Loewe scores. This oversimplification of the drug-response surface leads to high prediction uncertainty and limited actionability, as these models fail to distinguish between potency and efficacy. We introduce DeepSynBa, an actionable model that predicts the complete dose-response matrix of drug pairs instead of relying on an aggregated synergy score. This is achieved by predicting parameters describing the response surface as an intermediate layer in the model. Evaluated on the NCI-ALMANAC and the O'Neil datasets, DeepSynBa outperforms the state-of-the-art methods in the dose-response matrix prediction task across most evaluation scenarios, including testing on novel drug combinations, cell lines, and drugs, across nine different tissue types. We also show that DeepSynBa yields reliable synergy score predictions. More importantly, DeepSynBa can predict drug combination responses across different dosages for untested combinations. The intermediate dose-response parameter layer enables the separation of efficacy from potency, informing the selection of dosage ranges that optimise efficacy while limiting off-target toxicity in experimental screens. The predictive capability and the downstream actionability make DeepSynBa a powerful tool for advancing drug combination research beyond the limitations of the current approaches. The code and the dataset for DeepSynBa are available at https://github.com/hikuru/DeepSynBa.

MOTIVATION: There exists a range of different quantification frameworks to estimate the synergistic effect of drug combinations. The diversity and disagreement in estimates make it challenging to determine which combinations from a large drug screening should be proceeded with. Furthermore, the lack of accurate uncertainty quantification for those estimates precludes the choice of optimal drug combinations based on the most favourable synergistic effect. RESULTS: In this work, we propose SynBa, a flexible Bayesian approach to estimate the uncertainty of the synergistic efficacy and potency of drug combinations, so that actionable decisions can be derived from the model outputs. The actionability is enabled by incorporating the Hill equation into SynBa, so that the parameters representing the potency and the efficacy can be preserved. Existing knowledge may be conveniently inserted due to the flexibility of the prior, as shown by the empirical Beta prior defined for the normalized maximal inhibition. Through experiments on large combination screenings and comparison against benchmark methods, we show that SynBa provides improved accuracy of dose-response predictions and better-calibrated uncertainty estimation for the parameters and the predictions. AVAILABILITY AND IMPLEMENTATION: The code for SynBa is available at https://github.com/HaotingZhang1/SynBa. The datasets are publicly available (DOI of DREAM: 10.7303/syn4231880; DOI of the NCI-ALMANAC subset: 10.5281/zenodo.4135059).

BACKGROUND: Most analyses of microarray data are based on point estimates of expression levels and ignore the uncertainty of such estimates. By determining uncertainties from Affymetrix GeneChip data and propagating these uncertainties to downstream analyses it has been shown that we can improve results of differential expression detection, principal component analysis and clustering. Previously, implementations of these uncertainty propagation methods have only been available as separate packages, written in different languages. Previous implementations have also suffered from being very costly to compute, and in the case of differential expression detection, have been limited in the experimental designs to which they can be applied. RESULTS: puma is a Bioconductor package incorporating a suite of analysis methods for use on Affymetrix GeneChip data. puma extends the differential expression detection methods of previous work from the 2-class case to the multi-factorial case. puma can be used to automatically create design and contrast matrices for typical experimental designs, which can be used both within the package itself but also in other Bioconductor packages. The implementation of differential expression detection methods has been parallelised leading to significant decreases in processing time on a range of computer architectures. puma incorporates the first R implementation of an uncertainty propagation version of principal component analysis, and an implementation of a clustering method based on uncertainty propagation. All of these techniques are brought together in a single, easy-to-use package with clear, task-based documentation. CONCLUSION: For the first time, the puma package makes a suite of uncertainty propagation methods available to a general audience. These methods can be used to improve results from more traditional analyses of microarray data. puma also offers improvements in terms of scope and speed of execution over previously available methods. puma is recommended for anyone working with the Affymetrix GeneChip platform for gene expression analysis and can also be applied more generally.

Microarray technology is associated with many sources of experimental uncertainty. In this review we discuss a number of approaches for dealing with this uncertainty in the processing of data from microarray experiments. We focus here on the analysis of high-density oligonucleotide arrays, such as the popular Affymetrix GeneChip array, which contain multiple probes for each target. This set of probes can be used to determine an estimate for the target concentration and can also be used to determine the experimental uncertainty associated with this measurement. This measurement uncertainty can then be propagated through the downstream analysis using probabilistic methods. We give examples showing how these credibility intervals can be used to help identify differential expression, to combine information from replicated experiments and to improve the performance of principal component analysis.

MOTIVATION: Finding differentially expressed genes is a fundamental objective of a microarray experiment. Numerous methods have been proposed to perform this task. Existing methods are based on point estimates of gene expression level obtained from each microarray experiment. This approach discards potentially useful information about measurement error that can be obtained from an appropriate probe-level analysis. Probabilistic probe-level models can be used to measure gene expression and also provide a level of uncertainty in this measurement. This probe-level measurement error provides useful information which can help in the identification of differentially expressed genes. RESULTS: We propose a Bayesian method to include probe-level measurement error into the detection of differentially expressed genes from replicated experiments. A variational approximation is used for efficient parameter estimation. We compare this approximation with MAP and MCMC parameter estimation in terms of computational efficiency and accuracy. The method is used to calculate the probability of positive log-ratio (PPLR) of expression levels between conditions. Using the measurements from a recently developed Affymetrix probe-level model, multi-mgMOS, we test PPLR on a spike-in dataset and a mouse time-course dataset. Results show that the inclusion of probe-level measurement error improves accuracy in detecting differential gene expression. AVAILABILITY: The MAP approximation and variational inference described in this paper have been implemented in an R package pplr. The MCMC method is implemented in Matlab. Both software are available from http://umber.sbs.man.ac.uk/resources/puma.

MOTIVATION: Affymetrix GeneChip arrays are currently the most widely used microarray technology. Many summarization methods have been developed to provide gene expression levels from Affymetrix probe-level data. Most of the currently popular methods do not provide a measure of uncertainty for the expression level of each gene. The use of probabilistic models can overcome this limitation. A full hierarchical Bayesian approach requires the use of computationally intensive MCMC methods that are impractical for large datasets. An alternative computationally efficient probabilistic model, mgMOS, uses Gamma distributions to model specific and non-specific binding with a latent variable to capture variations in probe affinity. Although promising, the main limitations of this model are that it does not use information from multiple chips and does not account for specific binding to the mismatch (MM) probes. RESULTS: We extend mgMOS to model the binding affinity of probe-pairs across multiple chips and to capture the effect of specific binding to MM probes. The new model, multi-mgMOS, provides improved accuracy, as demonstrated on some bench-mark datasets and a real time-course dataset, and is much more computationally efficient than a competing hierarchical Bayesian approach that requires MCMC sampling. We demonstrate how the probabilistic model can be used to estimate credibility intervals for expression levels and their log-ratios between conditions. AVAILABILITY: Both mgMOS and the new model multi-mgMOS have been implemented in an R package, which is available at http://www.bioinf.man.ac.uk/resources/puma.

MOTIVATION: Principal Component Analysis (PCA) is one of the most popular dimensionality reduction techniques for the analysis of high-dimensional datasets. However, in its standard form, it does not take into account any error measures associated with the data points beyond a standard spherical noise. This indiscriminate nature provides one of its main weaknesses when applied to biological data with inherently large variability, such as expression levels measured with microarrays. Methods now exist for extracting credibility intervals from the probe-level analysis of cDNA and oligonucleotide microarray experiments. These credibility intervals are gene and experiment specific, and can be propagated through an appropriate probabilistic downstream analysis. RESULTS: We propose a new model-based approach to PCA that takes into account the variances associated with each gene in each experiment. We develop an efficient EM-algorithm to estimate the parameters of our new model. The model provides significantly better results than standard PCA, while remaining computationally reasonable. We show how the model can be used to 'denoise' a microarray dataset leading to improved expression profiles and tighter clustering across profiles. The probabilistic nature of the model means that the correct number of principal components is automatically obtained.

Abstract Motivation: Gene expression levels are obtained from microarray experiments through the extraction of pixel intensities from a scanned image of the slide. It is widely acknowledged that variabilities can occur in expression levels extracted from the same images by different users with the same software packages. These inconsistencies arise due to differences in the refinement of the placement of the microarray ‘grids’. We introduce a novel automated approach to the refinement of grid placements that is based upon the use of Bayesian inference for determining the size, shape and positioning of the microarray ‘spots’, capturing uncertainty that can be passed to downstream analysis. Results: Our experiments demonstrate that variability between users can be significantly reduced using the approach. The automated nature of the approach also saves hours of researchers’ time normally spent in refining the grid placement. Availability: A MATLAB implementation of the algorithm and tiff images of the slides used in our experiments, as well as the code necessary to recreate them are available for non-commercial use from http://www.dcs.shef.ac.uk/~neil/VIS

Sequence learning has a variety of different approaches. We can distinguish two fundamental approaches: general-regularity learning and specific sequence learning. Although some studies suggest that it is possible for a single subsystem underlying both general-regularity and specific-sequence learning, it is proved that relatively independent subsystems may execute the two types of learning more efficiently than a single subsystem. In this paper we propose to implement specific sequence learning in a neural network with no memory and with an implicit representation of time.