A machine learning based approach towards high-dimensional mediation analysis

Fig. 1.. (A) An overview of the standard three-variable mediation model. The variables x, m, and y are all scalars along with the associated path coefficients, α, β, and γ. (B) Schematic representation of the proposed mediation analysis framework using deep learning. Here a deep learning model links the high-dimensional mediators (brain activation maps) to a standard path analysis model used to access mediation. The output of the deep learning model is a latent intermediate mediating variable between in the input stimulus intensity(x) and the reported pain (y). The goal is to evaluate whether there is a significant indirect effect αβ.

Fig. 2.. (A) Overview of Pain data. Studies 1 – 7, which comprise of 209 subjects and 13,372 trials, are used to train the deep learning model. The model is tested independently on Study 8 which consists of 75 subjects and 2,296 trials. Additionally, Study 8 not only includes the type of thermal pain stimuli used to train the model, but also aversive sounds. We tested our model and hypothesized that the estimated brain mediators of pain should generalize to the new pain dataset, but not to the sound dataset. (B) Overview of the HCP dataset. We used rs-fMRI data with LR polarity (rfMRI_REST1−LR) from the HCP 900 release to investigate the relationship between working memory accuracy, measured using performance on an N-back task, and fluid intelligence. We excluded subjects with missing time points. We used 70% of the selected subjects for training and 30% for testing the model.

Fig. 3.. Results of Simulation 1, where we varied the number of observations (subjects) while keeping the dimensions of mediator constant. Each violin plot shows the estimated model parameters for the training dataset using deep learning model, shallow learning model and support vector regression. The red dotted line represents the ground truth data.

Fig. 4.. Results of Simulation 2, where we varied the dimension of mediator while keeping the number of observation constant (n=1000). Similar to simulation 1, each violin plot shows the estimated model parameters for the training dataset using deep learning model, shallow learning model and support vector regression. The red dotted line represents the ground truth data.

Fig. 5.. Results of Simulation 3, where we varied the number of observations (subjects) and removed the effect of mediation. Similar to simulation 1, each violin plot shows the estimated model parameters for the training dataset using the deep learning model, shallow learning model and support vector regression. The red dotted line represents the ground truth data.

Fig. 6.. Validation on independent data (n=75). (A) Scatter plots show the relationship between the low-dimensional mediator and input temperature, pain ratings and mediator, and pain ratings and temperature of input stimuli, respectively. Lines show the least-squares fit between variables for each independent validation subject. (B) The estimated α, β, and αβ values obtained when applying the fitted machine learning model to the independent validation dataset, both for the pain and sound trials. These reflect the brain increases as a function of stimulus intensity, the relationship between brain and pain controlling for stimulus intensity, and the mediation effect, respectively. Error bars indicate SEM. ∗ ∗ ∗ p<0.001. All coefficients were strongly significant for heat pain but non-significant for sound, indicating specificity to pain when compared with aversive sounds. (C) Voxel maps representing the 5% largest (in absolute value) Shapley values, indicating the regions involved in mediating the relationship between stimulus intensity and pain in the independent validation dataset. The majority of identified regions are targets of pain-related ascending pathways (e.g., somatosensory…

Fig. 7.. Results on test data (n=240). (A) The high dimensional functional connectivity matrix which serves as a mediator (M) of the relationship between fluid intelligence (X) and the accuracy on the working memory task (Y). (B) Scatter plots show the relationship between the low-dimensional mediator z and fluid intelligence, accuracy and the mediator, and accuracy and fluid intelligence, respectively. Lines show the least-squares fit between variables for each test subject (n=240). (C) Shapley values averaged over voxels connecting each pair of large-scale networks. High connectivity within the Frontoparietal (FPN) and Default Mode Networks (DMN), and low/negative connectivity between FPN and DMN and between FPN and subcortical regions (among other connections) mediated the relationship between fluid intelligence and accuracy of working memory task. This demonstrates links between brain connectivity and both working memory performance and fluid intelligence. MF: Medial frontal, FP: Frontoparietal, DMN: Default model network, SCC: Subcortical-cerebellum, V1: Visual I, V2: Visual II, VA: Visual association. ∗ ∗ ∗ p<0.001 and ∗ ∗ p<0.01.