Enrico GlaabLuxembourg Centre for Systems Biomedicine

Exploiting technical replicate variance in omics data analysis (RepExplore)

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Introduction: Variance and replicates

• Biomedical omics datasets may contain different types of variance:

Variance across samples from different individuals:- Between-group variance- Within-group variance

Variance across samples from the same individual:- Intra-individual variance- Technical variance

• Between- and within-group variance are covered via biological replicates, intra-individual variance via time-series measurements, and technical variance via technical replicates

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Motivation: Loss of technical variance information

• Typically, combinations of biological and summarized technical replicates are used for case-control analyses:

• Summarization of technical replicates into average measurements can provide more robust input data, but information on the variance across technical replicates is lost!

Mean/mediansummarization

Mean/mediansummarization

Statistical analysis

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Example: Relevance of technical variance information

Abundance of the top differential metabolite (L-valine) in the Arabidopsis data by

Andersen et al. (2014) without (a) and with technical error (b, see whiskers)

without technical error with technical errora) b)

mean-summarizedtechnical replicates

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Probability of positive likelihood ratio (PPLR)

• We assume the omics data on logarithmic scale has an approximate normal distribution

• Using mean (μ) and variance (s²) estimates derived from technical replicate measurements, differential expression can be scored using the probability of positive likelihood ratio (PPLR):

where P is the cumulative distribution function for the standard normal curve.

• For probe replicates on DNA microarray chips, Liu et al. propose a dedicated parameter estimation approach to incorporate the probe-level measurement error into variance estimates s² (Bioinformatics, 2006)

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Comparison: Classical vs. PPLR top-ranked result

Whisker plots of the top differential metabolite in the Arabidopsis data by

Andersen et al. (2014): (a) classical approach (L-valine), (b) PPLR (L-proline)

a) b)

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Application to Parkinson‘s disease transcriptome data

a) b)

a) Whisker plot of the top differential gene (NDUFB2) in the Parkinson’s diseasedataset by Simunovic et al. (2009); b) Heat map of the top 10 differentially expressed genes according to the PPLR statistic.

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Improved robustness of rankings across studies

• Evaluation: Compare the similarity of gene rankings across two Parkinson‘s disease datasets (Simunovic et al., 2009, and Zheng et al., 2010)

• Two gene ranking methods are compared: PPLR and limma/eBayes (note: duplicateCorrelation-function not generally applicable)

• Kendall‘s tau used as similarity measure for rankings

Significantly higher similarity of rankings with PPLR statistic (p < 2.2E-16 for both up- and down-regulated genes)

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Rankings improve with increasing numbers of replicates

• Apply method to simulated normal data with stddev. 1, 100 samples(two groups, 50 per group) and 1000 features/biomolecules (900 uncorrelated, irrelevant and 100 differential, fixed effect size of D = 1)

• Add simulated technical replicates with measurement noise (R function jitter) • Test enrichment of 100 differential features in the final PPLR ranking

Enrichment score increases with increasing numbers of replicates

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Using replicate variance information in PCA

• Principal Component Analysis (PCA) can be cast as a probabilistic model (Tipping & Bishop, 1999) where d-dimensional data points yn can be reconstructed from a q-dimensional latent point xn via a linear transformation (W) and a noise vector εn:

• The corresponding data distribution is:

• If each dimension is allowed to have a different noise variance:

• While the maximum likelihood solution for the original model is equivalent to PCA, Sanguinetti et al. presented an expectation maximization (EM) method for the model with feature-specific noise variance (Bioinformatics, 2005)

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Denoising property & results on Parkinson‘s disease data

• In the new probabilistic PCA, the noise estimate enables an evaluation of the significance of principal components (PCs) automated computation of the maximum number of retainable PCs

• By accounting for measurement error in the model, noisy values are down-

weighted pre-processing data via the modified PCA tends to provide tighter sample clusters (confirmed on Parkinson‘s disease transcriptome data)

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Summary

• Technical replicate variance in omics data is usally not constant across different biomolecules only summarizing replicates via averaging will result in loss of valuable information

• On Parkinson‘s disease transcriptomics data, accounting for technical replicate variance provided improved robustness of differential expression rankings across studies and gave tighter clusters in PCA visualizations

• All methods presented have been implemented on a public web-server (RepExplore: www.repexplore.tk, Bioinformatics, 2015), providing automated analyses with interactive visualizations and ranking tables

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