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

Abstract

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.

Fig. 1.

Schematic view of CausalMGM and its applications

Fig. 2.

Precision-Recall curves of edge direction recovery on high-dimensional dataset. (A) Full range of algorithms and edge types. (B) Detail view of CPC-stable and MGM-CPC-stable performance averaged over all edge types. Parameter range: 0.2 ≤ λ ≤ 0.8; 0.01 ≤ α ≤ 0.1. Bars correspond to one standard error

Fig. 3.

Structural Hamming Distance on high dimensional dataset for CPC-stable and MGM-CPCS. The lower the SHD, the closer the predicted graph is to the true graph. Parameter range: 0.2 ≤ λ ≤ 0.8 and 0.01 ≤ α ≤ 0.1

Fig. 4.

Average running times with 95% confidence interval error bars of search algorithms on high dimensional data. Each row of columns corresponds to a different setting of $\alpha$ and each column corresponds to a different setting of λ. Directed search steps were run in parallel on a 4-core laptop

Fig. 5.

First and second neighbors of 2-year lung function decline, measured as FEV₁ Progression. The variables that most influence the FEV₁ progression are smoking status, creatinine and TNFα blood levels, pulmonary artery enlargement, history of GERD, systolic BP after exercise and four spirometry variables (% change in FEV₁ before and after bronchodilators, best percent predicted FVC, best percent predicted FRC, and PIF)