Text A.

Description of synthetic data generation. <b>Fig A</b>. Directed acyclic graph of the Bayesian hierarchical linear regression model. Inferred parameters are shown in circles, and known parameters are shown within boxes. Boxes highlighted in blue are informed by the control data, and the boxes highlighted in yellow are chosen by us. The functions <i>m</i> ( ⋅ ) and <i>v</i> ( ⋅ ) indicate the mode and variance for a parameter. The dotted boxes enclosing parameters indicate which parameters occur for every sample (the outer box) and which occur for every myofibre in a sample (the inner box). For simplicity, a new variable is introduced, , the precision used to model the <i>j</i>^th myofibre in the <i>i</i>^th sample. It is defined as <i>τ</i>, if <i>i</i> is a control or , and <i>γ</i> otherwise. <b>Fig B–D</b>. Posterior myofibre classifications and posterior 95% predictive interval for all OXPHOS proteins and patients. Protein abundances from all control subjects are shown in black. The patient myofibres are coloured on a scale from red to blue, red being not-like-control and blue being healthy, based on their posterior expected marginal probability of being not-like-control. The posterior expected value and 95% predictive interval for the linear model fit to the healthy patient cells are shown as solid and dashed green lines. <b>Fig E</b>. Posterior beliefs of the proportion of myofibres with are not-like-controls for all patients and OXPHOS proteins. Twenty thousand draws from their posterior distributions represent the beliefs. <b>Fig F</b>. Wide and narrow prior distributions used to inspect the impact of parameter uncertainty. The two sets of prior distributions for all patients and OXPHOS protein NDUFB8, used in Sect <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1012770#sec015" target="_blank">3.2</a> to assess hyperparameter uncertainty, which we chose and not informed from the control data. <b>Fig G</b>. No difference in the not-like-control proportion from models with varying amounts of prior uncertainty. The difference in the <i>π</i> posterior between the original priors and the narrow/wider ones. The prior variance for the precisions, and <i>τ</i>, were increased or decreased by a factor of 5.0 for the wide and narrow priors, respectively. The prior variance for the expected slope and intercept, and , were increased and decreased by a factor of 5.0. <b>Fig H</b>. Synthetic data generated for patient P12, D01. OXPHOS protein abundances for control data are shown by black points and synthetic patient data is shown in coloured points. Synthetic patient myofibres are coloured blue if their ground-truth state is like-control and red with a yellow dot if their ground-truth state is not-like-control. <b>Fig I</b>. The Bayesian hierarchical model able to find ground-truth parameter values in synthetic dataset D01. Posterior beliefs and model fit for OXPHOS protein in patient P09, of the synthetic dataset D01. Ground-truth parameter values, used to generate the data, are shown with vertical dotted lines. Prior and posterior beliefs are shown in pink and green respectively for all parameters except the slope and intercept for control subjects. Each subject was given a different colour to distinguish between ground-truth values for each control subject. The 2Dmito plot shows the 95% posterior predictive interval and expected value for the linear model fitted to the patient subject. <b>Fig J</b>. The Bayesian hierarchical model more accurately estimates the not-like-control proportion compared to the frequentist model in synthetic data D01. The posterior difference between the ground-truth not-like-control proportion and the Bayesian hierarchy’s beliefs. Also shown are the differences between the frequentist estimates and the ground-truth. Stars indicate the probability of observing the frequentist linear model’s estimate, given the Bayesian posterior, is greater than 1%. <b>Fig K</b>. Misclassifications of synthetic data D01 are due to data overlap. Synthetic OXPHOS data and the posterior predictive of the Bayesian hierarchical model. Posterior Bayesian classifications are simplified to be whether the expected marginal posterior probability of being not-like-control is above 0.5. Misclassifications are highlighted with a yellow square or diamond, depending on the misclassification type, see legend. <b>Fig L</b>. Synthetic data generate for patient P12, D01. OXPHOS protein abundances for control data are shown by black points and synthetic patient data is shown in coloured points. Synthetic patient myofibres are coloured blue if their ground-truth state is like-control and red with a yellow dot if their ground-truth state is not-like-control. <b>Fig M</b>. The Bayesian hierarchical model able to find ground-truth parameter values in synthetic dataset D02. Posterior beliefs and model fit for OXPHOS protein in patient P12, of the synthetic dataset D02. Ground-truth parameter values, used to generate the data, are shown with vertical dotted lines. Prior and posterior beliefs are shown in pink and green respectively for all parameters except the slope and intercept for control subjects. Each subject was given a different colour to distinguish between ground-truth values for each control subject. The 2Dmito plot shows the 95% posterior predictive interval and expected value for the linear model fitted to the patient subject. <b>Fig N</b>. The Bayesian hierarchical model more accurately estimates the not-like-control proportion compared to the frequentist model with synthetic data D02. The posterior difference between the ground-truth not-like-control proportion and the Bayesian hierarchy’s beliefs. Also shown are the differences between the frequentist estimates and the ground-truth. Stars indicate the probability of observing the frequentist linear model’s estimate, given the Bayesian posterior, is greater than 1%, showing a lack of significance between the two methods. <b>Fig O</b>. Misclassifications of synthetic data D02 are due to data overlap. Synthetic OXPHOS data and the posterior predictive of the Bayesian hierarchical model. Posterior Bayesian classifications are simplified to be whether the posterior expected marginal probability of being not-like-control is above 0.5. Misclassifications are highlighted with a yellow square or diamond, depending on the misclassification type, see legend. (PDF)