A multiple testing procedure for multi-dimensional pairwise comparisons with application to gene expression studies

Anjana Grandhi, Wenge Guo, Shyamal D. Peddada

Often researchers are interested in comparing multiple experimental groups (e.g. tumor size) with a reference group (e.g. normal tissue) on the basis of thousands of features (e.g. genes) and determine if a differentially expressed feature is up or down regulated in a pairwise comparison. There are two sources of false discoveries, one due to multiple testing involving several pairwise comparisons and the second due to falsely declaring a feature to be up (or down) regulated when it is not (known as directional error). Together, the total error rate is called the mixed directional false discovery rate (mdFDR). We develop a general powerful mdFDR controlling testing procedure and illustrate the methodology by analyzing uterine fibroid gene expression data (PLoS ONE 8:63909, 2013). We identify several differentially expressed genes (DEGs) and pathways that are specifically enriched according to the size of a uterine fibroid. The proposed general procedure strongly controls mdFDR. Several specific methodologies can be derived from this general methodology by using appropriate testing procedures at different steps of the general procedure. Thus we are providing a general framework for making multiple pairwise comparisons. Our analysis of the uterine fibroid growth gene expression data suggests that molecular characteristics of a fibroid changes with size. Our powerful methodology allowed us to draw several interesting conclusions regarding the molecular characteristics of uterine fibroids. For example, IL-1 signaling pathway (Sci STKE 2003:3, 2003), associated with inflammation and known to activate prostaglandins that are implicated in the progression of fibroids, is significantly enriched only in small tumors (volume < 5.7 cm (3)). It appears that the molecular apparatus necessary for fibroid growth and development is established during tumor development. A complete list of all DEGs and the corresponding enriched pathways according to tumor size is provided for researchers to mine these data. Identification of these DEGs and the pathways may potentially have clinical implications.