Testing for differentially expressed genetic pathways with single-subject N-of-1 data in the presence of inter-gene correlation

Abstract

Modern precision medicine increasingly relies on molecular data analytics, wherein development of interpretable single-subject ("N-of-1") signals is a challenging goal. A previously developed global framework, N-of-1- pathways, employs single-subject gene expression data to identify differentially expressed gene set pathways in an individual patient. Unfortunately, the limited amount of data within the single-subject, N-of-1 setting makes construction of suitable statistical inferences for identifying differentially expressed gene set pathways difficult, especially when non-trivial inter-gene correlation is present. We propose a method that exploits external information on gene expression correlations to cluster positively co-expressed genes within pathways, then assesses differential expression across the clusters within a pathway. A simulation study illustrates that the cluster-based approach exhibits satisfactory false-positive error control and reasonable power to detect differentially expressed gene set pathways. An example with a single N-of-1 patient's triple negative breast cancer data illustrates use of the methodology.

Keywords: Gene expression data; N-of-1; RNA-seq; affinity propagation clustering; exemplar learning; gene set; inter-gene correlation; precision medicine; single-subject inference; triple negative breast cancer.

Figure 1

Empirical false-positive rates (dots) based on 2000 simulated N-of-1-pathways data sets for three competing testing procedures (lower horizontal axis: Clustered-T = proposed test, naïve t = standard t test, Wilcoxon = signed-rank test), cross-classified by correlation structure (top: Independent = uncorrelated mRNA expression, Block = cluster-correlated expression, All = unconstrained inter-gene correlation) and pathway size G (left). The corresponding cluster numbers, m, for each pathway are also listed; see Table 2. Nominal significance level is set to α = 0.05 (dotted horizontal lines). Results reported for ψ = 1.5 (see text). Horizontal bars are pointwise 95% Agresti-Coull confidence intervals for the underlying false-positive rate based on each set of 2000 simulated samples.

Figure 2

Empirical rejection probabilities (‘power’) for the AP-based cluster approach using (7), based on 2000 simulated N-of-1-pathways data sets. Results are presented as a function of DEG proportion π (lower horizontal axis). Displays are cross-classified by correlation structure (top: Independent = uncorrelated mRNA expression, Block = cluster-correlated expression, All = unconstrained inter-gene correlation) and pathway size G (left). The corresponding cluster numbers, m, for each pathway are also listed; see Table 2. Simulated fold change is indicated by line styling: ψ = 4 (solid lines), ψ = 2 (dashes), and ψ = 1.5 (dot-dashes). Nominal significance level is set to α = 0.05. Horizontal bars are pointwise 95% Agresti-Coull confidence intervals for the underlying rejection rate based on each set of 2000 simulated samples.

Figure 3

Comparison of −log{p} values from Spectral Clustering (SC) vs. AP clustering in the clustered-T test of (7) when applied to TNBC data from Sec. 4. Dot color indicates p-value overlap status: (i) dark gray dots for significant p-value overlaps (both below 5% cutoff), (ii) white dots for insignificant p-value overlaps (both above 5% cutoff), (iii) light gray dots for p-value discords with ITS match (high informatic similarity), and (iv) black dots for p-value discords with no ITS match. See text for details.