Leveraging vibration of effects analysis for robust discovery in observational biomedical data science

Fig 1. Overview of the algorithmic approach and its place in the hypothesis generation toolkit. (A) The process/paradigm of “data-driven” discovery. First, high-dimensional data are collected on a set of individuals with a given phenotype (i.e., a disease) as well as controls (individuals without the phenotype). The researcher selects a modeling strategy, most often just one, and computes associations between the phenotype of interest (a “Y”) and a particular feature (an “X,” like coffee in the example). The resultant associations yield associational “hypotheses” regarding the relationship between the X and the Y, but only fitting one model specification can yield nonrobust results. Quantvoe replaces this middle step of choosing one model, instead attempting to fit up to every possible model specification, thereby charting a course to robust hypothesis generation. (B) Quantvoe takes 3 types of input data, all in the form of pairs of data frames (tables), either at the command line or in an interactive R session: (1) a single dependent variable and multiple independent variables; (2) multiple dependent variables, or (3) multiple datasets. (C) There are 4 main steps—checking the input…

Fig 2. Examples of VoE for prominent associations. Each point in the density plots represent at least one model. x-Axes are estimate size for beta-coefficients of interest (e.g., for panel A, the coefficient on the calcium intake variable). Quantiles show the range of estimate sizes for each above relationship. The y-axis is the −log10(p.value) of that association. The solid line is nominal (p < 0.05) significance. Data underlying these plots are available at https://figshare.com/account/home#/projects/120969 and S2 Table. VoE, vibration of effects.

Fig 3. VoE output for 10 exposures and their relationship with common indicators of cardiovascular health in the form of density plots. Each point represents output from different model specifications. The x-axis is the beta-coefficient on the primary independent variable of interest (e.g., physical activity), and the y-axis the −log10(p.value) of that association. The solid line is nominal (p < 0.05) significance. Data underlying these plots are available at https://figshare.com/account/home#/projects/120969 and S2 Table. BMI, body mass index; LDL, low-density lipoprotein; VoE, vibration of effects.

Fig 4. Examples of adjusters that appear to drive VoE for highly confounded associations. Rows: associations with particularly high JEs for each dependent variable. Left column: established variables known to confound cardiovascular risk factors. Middle column: top 10 adjusters (not found in the left most column) whose presence is correlated to changes in the associations reported on the rows. Right columns: vibration plots from Fig 3 (rescaled on the axes) colored by if the adjuster in the plot title was present in models represented by a given point. The solid line is nominal (p < 0.05) significance. Data underlying these plots are available at https://figshare.com/account/home#/projects/120969 and S2 Table. JE, Janus effect; LDL, low-density lipoprotein; MFA, Monounsaturated Fatty Acids; OGTT, oral glucose tolerance test; PIR, poverty income ratio; SFA, Saturated Fatty Acids; VoE, vibration of effects; WIC, Women, Infants, Children.

Fig 5. Software performance statistics. (A) Runtime for different numbers of vibrations, (B) memory usage for different numbers of vibrations, and (C) consistency of results across the number of vibration associations (n). Heatmap color depicts the correlations between the coefficients in the nonmixed effects version of Eq (10). Data underlying these plots are available at https://figshare.com/account/home#/projects/120969. BMI, body mass index; LDL, low-density lipoprotein.