LINKING LUNG AIRWAY STRUCTURE TO PULMONARY FUNCTION VIA COMPOSITE BRIDGE REGRESSION

Abstract

The human lung airway is a complex inverted tree-like structure. Detailed airway measurements can be extracted from MDCT-scanned lung images, such as segmental wall thickness, airway diameter, parent-child branch angles, etc. The wealth of lung airway data provides a unique opportunity for advancing our understanding of the fundamental structure-function relationships within the lung. An important problem is to construct and identify important lung airway features in normal subjects and connect these to standardized pulmonary function test results such as FEV1%. Among other things, the problem is complicated by the fact that a particular airway feature may be an important (relevant) predictor only when it pertains to segments of certain generations. Thus, the key is an efficient, consistent method for simultaneously conducting group selection (lung airway feature types) and within-group variable selection (airway generations), i.e., bi-level selection. Here we streamline a comprehensive procedure to process the lung airway data via imputation, normalization, transformation and groupwise principal component analysis, and then adopt a new composite penalized regression approach for conducting bi-level feature selection. As a prototype of composite penalization, the proposed composite bridge regression method is shown to admit an efficient algorithm, enjoy bi-level oracle properties, and outperform several existing methods. We analyze the MDCT lung image data from a cohort of 132 subjects with normal lung function. Our results show that, lung function in terms of FEV1% is promoted by having a less dense and more homogeneous lung comprising an airway whose segments enjoy more heterogeneity in wall thicknesses, larger mean diameters, lumen areas and branch angles. These data hold the potential of defining more accurately the "normal" subject population with borderline atypical lung functions that are clearly influenced by many genetic and environmental factors.

Keywords: bi-level variable selection; composite penalization; feature extraction; lung airway data; pulmonary function tests.

Fig 1

Airway trees of two normal subjects; subject of the left (right) diagram has the lowest (highest) standardized FEV1%.

Fig 2

Heatmap of FEV1% and the lung features used in the analysis. Each subject is represented by a column, and the columns are sorted by their FEV1% value. The topmost row gives the FEV1% values, followed by a block of variables selected by either CoB, CoMCP or GrB, and another block of unselected variables.

Fig 3

A diagram showing the selected features by various methods. Dark grey means the coefficient estimate of a selected variable is positive, light grey means the coefficient estimate of a selected variable is negative, and white means a variable is not selected.

Fig 4

Left diagram: scatter plot of the observed FEV1% values vs the fitted values. Right Diagram: the normal Q-Q plot for the residuals.

Fig 5

Relative frequency plot of each covariate not been selected in Examples 1–2. The vertical lines indicate the group structure. As neither of the methods yields false negative in the two examples, the four types of symbols at the bottom of each figure are overlaid.