Outline

• Background
• Methodology–iDEG
• Numerical studies
• Real data analysis

Background

• Precision Medicine
• Single-subject analysis
• Example RNA-Seq quantified mRNA expression data (Single-Subject)
• Our goal
• Main Challenges
• Our solution (iDEG)

Precision Medicine

Single-subject analysis

Single-subject analysis studies one patient at a time, with the purpose of revealing the patient-specific disease mechanism for highly heterogeneous diseases.

Single-subject analysis

Example RNA-Seq quantified mRNA expression data (Single-Subject)

Our goal

• How differentially expressed is a gene?
  • A meaningful effect size of differential expression
• What is the uncertainty of the measurement?
  • A probability of gene differential expression.

Main Challenges

Main Challenges

Our solution (iDEG)

• Bypass gene-level variance estimation: Transform RNA-Seq data such that, under null hypothesis, all genes have the same variance.
• Borrow strength across genes: model all genes in a single model

Methodology–iDEG

• Data transformation
• Two-group mixture model

Data transformation

Data transformation

Data transformation

Under null hypothesis:

Two-group mixture model

Suppose \(G\) genes are measured in the RNA-Seq experiment, each of the genes is either null or differentially expressed with prior probabilities \(\pi_{0}\) or \(\pi_{1} = 1-\pi_{0}\). And the density function of \(z_{g}\) is either \(f_{0}(z)\) or \(f_{1}(z)\).

The marginal mixture density is:

Two-group mixture model

The local false positive rate, \(fdr\), is the Bayes posterior probability that a gene \(g\) is a null gene given \(z_{g}\):

Two-group mixture model

\(f_{0}\) corresponds to an empirical null distribution.

In large-scale simultaneous hypothesis testing, the theoretical null may be deficient due to various reasons:

• correlation across genes
• unobserved covariates (e.g. gender, age, smoking status, etc.)
• or failed mathematical assumptions (e.g. asymptotic approximation).

Fortunately, in large-scale simultaneous testing, the parallel structure allows the estimation of an empirical null distribution, via empirical Bayes, from the own data of the study.

Numerical studies

• Simulate a single-subject dataset
• Procedure
• Method evaluation
• Sensitivity Analysis

Simulate a single-subject dataset

Simulate a pair of transcriptomes:

Simulate a single-subject dataset

Procedure

• Step 1: Simulate one single-subject dataset, which contains \(p \%\) DEG.
• Step 2: Conduct iDEG, edgeR¹, DESeq², and DEGseq³.
• Step 3: Compute an F1 score for each method,

• Step 4: Repeat Step1-Step3 for 1000 times
• Step 5: Calculate the arithmetic mean and standard deviation of the 1000 \(F_{1}\) resulted from each method.
• Step 6: Change the value of \(p\), repeat Step 1-Step 5

Method evaluation

Method evaluation

Although the Recall/TPR and number of precisions of iDEG are lower than edgeR, iDEG has high precision and low FPR across all percentages of DEG. These operating characteristics of iDEG may be preferable in large-scale inference, like RNA-Seq analysis, where investigators examine tens of thousands of genes in a high-throughput manner.

Sensitivity Analysis

Our experience indicates that without making assumptions on RNA-Seq data, it is difficult to construct suitable statistical inferences for a single-subject dataset. Nonetheless we test the two main assumptions we make:

• The value of dispersion parameter is a function of expression mean.
• The majority of the genes are null genes.

Sensitivity Analysis

• Draw dispersion parameter \(\delta_{g}\) from a uniform distribution \(\text{unif}(0.001, 0.1)\).

Sensitivity Analysis

• Simulate single-subject datasets with a series of percentages of DEG.

Real data analysis

• Data
• iDEG result
• Some interesting genes

Data

A transcriptome of tumor sample and a transcriptome of surrounding healthy sample of an African American woman with Triple negative breast cancer (TNBC).

TNBC is a subtype of breast cancer that has poor prognosis and considerable heterogeneity. It disproportionately affects women with African origin (Dietze et al., 2015). Personalized treatment may be successful for an African American TNBC patient if one could discover a set of her specific DEG and match some of these DEG to the targets of a therapeutic drug.

iDEG result

Some interesting genes

• ADIPOQ & LEP: Adiponectin (gene product of gene ADIPOQ) and leptin (gene product of LEP) are considered as mediators for the association of breast cancer with obesity, which is a major risk factor for breast cancer (Nalabolu et al., 2014; Grossmann et al., 2010).
• PLA2G2A: Although PLA2G2A has not been extensively studied for breast cancer, many studies have shown that it inhibits invasion and metastasis of gastric and colon cancer (Ganesan et al., 2008; Movahedian et al., 2016; Fijneman et al., 2009) and may predict survival (Xing et al., 2011).
• TUSC5: Bubnov et al. (2012) has demonstrated the down-regulation of TUSC5 induced by DNA methylation in breast cancer. In contrast to mutated genes, DNA methylation is reversible.

Take home message

We developed a new and effective method to identify differentially expressed genes from two transcriptomes of a single patient.

Acknowledgements

Helen Hao Zhang

Yves A. Lussier

• Haiquan Li
• Joanne Berghout
• Grant Schissler
• Yuan Shang

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