Mixed graphical models for integrative causal analysis with application to chronic lung disease diagnosis and prognosis.

MOTIVATION: Integration of data from different modalities is a necessary step for multi-scale data analysis in many fields, including biomedical research and systems biology. Directed graphical models offer an attractive tool for this problem because they can represent both the complex, multivariate probability distributions and the causal pathways influencing the system. Graphical models learned from biomedical data can be used for classification, biomarker selection and functional analysis, while revealing the underlying network structure and thus allowing for arbitrary likelihood queries over the data. RESULTS: In this paper, we present and test new methods for finding directed graphs over mixed data types (continuous and discrete variables). We used this new algorithm, CausalMGM, to identify variables directly linked to disease diagnosis and progression in various multi-modal datasets, including clinical datasets from chronic obstructive pulmonary disease (COPD). COPD is the third leading cause of death and a major cause of disability and thus determining the factors that cause longitudinal lung function decline is very important. Applied on a COPD dataset, mixed graphical models were able to confirm and extend previously described causal effects and provide new insights on the factors that potentially affect the longitudinal lung function decline of COPD patients. AVAILABILITY AND IMPLEMENTATION: The CausalMGM package is available on http://www.causalmgm.org. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Bayesian networks for fMRI: a primer.

Bayesian network analysis is an attractive approach for studying the functional integration of brain networks, as it includes both the locations of connections between regions of the brain (functional connectivity) and more importantly the direction of the causal relationship between the regions (directed functional connectivity). Further, these approaches are more attractive than other functional connectivity analyses in that they can often operate on larger sets of nodes and run searches over a wide range of candidate networks. An important study by Smith et al. (2011) illustrated that many Bayesian network approaches did not perform well in identifying the directionality of connections in simulated single-subject data. Since then, new Bayesian network approaches have been developed that have overcome the failures in the Smith work. Additionally, an important discovery was made that shows a preprocessing step used in the Smith data puts some of the Bayesian network methods at a disadvantage. This work provides a review of Bayesian network analyses, focusing on the methods used in the Smith work as well as methods developed since 2011 that have improved estimation performance. Importantly, only approaches that have been specifically designed for fMRI data perform well, as they have been tailored to meet the challenges of fMRI data. Although this work does not suggest a single best model, it describes the class of models that perform best and highlights the features of these models that allow them to perform well on fMRI data. Specifically, methods that rely on non-Gaussianity to direct causal relationships in the network perform well.

Non-Gaussian methods and high-pass filters in the estimation of effective connections.

We consider several alternative ways of exploiting non-Gaussian distributional features, including some that can in principle identify direct, positive feedback relations (graphically, 2-cycles) and combinations of methods that can identify high dimensional graphs. All of the procedures are implemented in the TETRAD freeware (Ramsey et al., 2013). We show that in most cases the limited accuracy of the several non-Gaussian methods in the Smith et al. (2011) simulations can be attributed to the high-pass Butterworth filter used in that study. Without that filter, or with the filter in the widely used FSL program (Jenkinson et al., 2012), the directional accuracies of several of the non-Gaussian methods are at or near ceiling in many conditions of the Smith et al. simulation. We show that the improvement of an apparently Gaussian method (Patel et al., 2006) when filtering is removed is due to non-Gaussian features of that method introduced by the Smith et al. implementation. We also investigate some conditions in which multi-subject data help with causal structure identification using higher moments, notably with non-stationary time series or with 2-cycles. We illustrate the accuracy of the methods with more complex graphs with and without 2-cycles, and with a 500 node graph; to illustrate applicability and provide a further test we apply the methods to an empirical case for which aspects of the causal structure are known. Finally, we note a number of cautions and issues that remain to be investigated, and some outstanding problems for determining the structure of effective connections from fMRI data.

Py-Tetrad and RPy-Tetrad: A New Python Interface with R Support for Tetrad Causal Search.

We give novel Python and R interfaces for the (Java) Tetrad project for causal modeling, search, and estimation. The Tetrad project is a mainstay in the literature, having been under consistent development for over 30 years. Some of its algorithms are now classics, like PC and FCI; others are recent developments. It is increasingly the case, however, that researchers need to access the underlying Java code from Python or R. Existing methods for doing this are inadequate. We provide new, up-to-date methods using the JPype Python-Java interface and the Reticulate Python-R interface, directly solving these issues. With the addition of some simple tools and the provision of working examples for both Python and R, using JPype and Reticulate to interface Python and R with Tetrad is straightforward and intuitive.

Multi-subject search correctly identifies causal connections and most causal directions in the DCM models of the Smith et al. simulation study.

Smith et al. report a large study of the accuracy of 38 search procedures for recovering effective connections in simulations of DCM models under 28 different conditions. Their results are disappointing: no method reliably finds and directs connections without large false negatives, large false positives, or both. Using multiple subject inputs, we apply a previously published search algorithm, IMaGES, and novel orientation algorithms, LOFS, in tandem to all of the simulations of DCM models described by Smith et al. (2011). We find that the procedures accurately identify effective connections in almost all of the conditions that Smith et al. simulated and, in most conditions, direct causal connections with precision greater than 90% and recall greater than 80%.

Network modelling methods for FMRI.

There is great interest in estimating brain "networks" from FMRI data. This is often attempted by identifying a set of functional "nodes" (e.g., spatial ROIs or ICA maps) and then conducting a connectivity analysis between the nodes, based on the FMRI timeseries associated with the nodes. Analysis methods range from very simple measures that consider just two nodes at a time (e.g., correlation between two nodes' timeseries) to sophisticated approaches that consider all nodes simultaneously and estimate one global network model (e.g., Bayes net models). Many different methods are being used in the literature, but almost none has been carefully validated or compared for use on FMRI timeseries data. In this work we generate rich, realistic simulated FMRI data for a wide range of underlying networks, experimental protocols and problematic confounds in the data, in order to compare different connectivity estimation approaches. Our results show that in general correlation-based approaches can be quite successful, methods based on higher-order statistics are less sensitive, and lag-based approaches perform very poorly. More specifically: there are several methods that can give high sensitivity to network connection detection on good quality FMRI data, in particular, partial correlation, regularised inverse covariance estimation and several Bayes net methods; however, accurate estimation of connection directionality is more difficult to achieve, though Patel's τ can be reasonably successful. With respect to the various confounds added to the data, the most striking result was that the use of functionally inaccurate ROIs (when defining the network nodes and extracting their associated timeseries) is extremely damaging to network estimation; hence, results derived from inappropriate ROI definition (such as via structural atlases) should be regarded with great caution.

Estimating feedforward and feedback effective connections from fMRI time series: Assessments of statistical methods.

We test the adequacies of several proposed and two new statistical methods for recovering the causal structure of systems with feedback from synthetic BOLD time series. We compare an adaptation of the first correct method for recovering cyclic linear systems; Granger causal regression; a multivariate autoregressive model with a permutation test; the Group Iterative Multiple Model Estimation (GIMME) algorithm; the Ramsey et al. non-Gaussian methods; two non-Gaussian methods by Hyvärinen and Smith; a method due to Patel et al.; and the GlobalMIT algorithm. We introduce and also compare two new methods, Fast Adjacency Skewness (FASK) and Two-Step, both of which exploit non-Gaussian features of the BOLD signal. We give theoretical justifications for the latter two algorithms. Our test models include feedback structures with and without direct feedback (2-cycles), excitatory and inhibitory feedback, models using experimentally determined structural connectivities of macaques, and empirical human resting-state and task data. We find that averaged over all of our simulations, including those with 2-cycles, several of these methods have a better than 80% orientation precision (i.e., the probability of a directed edge is in the true structure given that a procedure estimates it to be so) and the two new methods also have better than 80% recall (probability of recovering an orientation in the true structure).

Comparison of strategies for scalable causal discovery of latent variable models from mixed data.

Modern technologies allow large, complex biomedical datasets to be collected from patient cohorts. These datasets are comprised of both continuous and categorical data ("Mixed Data"), and essential variables may be unobserved in this data due to the complex nature of biomedical phenomena. Causal inference algorithms can identify important relationships from biomedical data; however, handling the challenges of causal inference over mixed data with unmeasured confounders in a scalable way is still an open problem. Despite recent advances into causal discovery strategies that could potentially handle these challenges; individually, no study currently exists that comprehensively compares these approaches in this setting. In this paper, we present a comparative study that addresses this problem by comparing the accuracy and efficiency of different strategies in large, mixed datasets with latent confounders. We experiment with two extensions of the Fast Causal Inference algorithm: a maximum probability search procedure we recently developed to identify causal orientations more accurately, and a strategy which quickly eliminates unlikely adjacencies in order to achieve scalability to high-dimensional data. We demonstrate that these methods significantly outperform the state of the art in the field by achieving both accurate edge orientations and tractable running time in simulation experiments on datasets with up to 500 variables. Finally, we demonstrate the usability of the best performing approach on real data by applying it to a biomedical dataset of HIV-infected individuals.

Optical coherence tomography machine learning classifiers for glaucoma detection: a preliminary study.

PURPOSE: Machine-learning classifiers are trained computerized systems with the ability to detect the relationship between multiple input parameters and a diagnosis. The present study investigated whether the use of machine-learning classifiers improves optical coherence tomography (OCT) glaucoma detection. METHODS: Forty-seven patients with glaucoma (47 eyes) and 42 healthy subjects (42 eyes) were included in this cross-sectional study. Of the glaucoma patients, 27 had early disease (visual field mean deviation [MD] > or = -6 dB) and 20 had advanced glaucoma (MD < -6 dB). Machine-learning classifiers were trained to discriminate between glaucomatous and healthy eyes using parameters derived from OCT output. The classifiers were trained with all 38 parameters as well as with only 8 parameters that correlated best with the visual field MD. Five classifiers were tested: linear discriminant analysis, support vector machine, recursive partitioning and regression tree, generalized linear model, and generalized additive model. For the last two classifiers, a backward feature selection was used to find the minimal number of parameters that resulted in the best and most simple prediction. The cross-validated receiver operating characteristic (ROC) curve and accuracies were calculated. RESULTS: The largest area under the ROC curve (AROC) for glaucoma detection was achieved with the support vector machine using eight parameters (0.981). The sensitivity at 80% and 95% specificity was 97.9% and 92.5%, respectively. This classifier also performed best when judged by cross-validated accuracy (0.966). The best classification between early glaucoma and advanced glaucoma was obtained with the generalized additive model using only three parameters (AROC = 0.854). CONCLUSIONS: Automated machine classifiers of OCT data might be useful for enhancing the utility of this technology for detecting glaucomatous abnormality.