Applications of Different Weighting Schemes to Improve Pathway-Based Analysis

Table 1

A brief summary of the four proposed weighting schemes. The algorithms are expressed for the pathway of 𝑚 genes and 𝑛 samples. absT and Qdiff algorithms calculate the weight for the 𝑗_th gene in a pathway, and RWV selects an optimal random weight vector 𝑤 minimizing 𝑃-value or OOB error rate, and RWM selects an optimal weight matrix 𝑤 minimizing 𝑃-value or OOB error rate.

Name	Algorithm	Notes
absT	𝑊^|𝑇|(𝑗)=|𝑇(𝑗)|/∑^𝑚𝑗=1|𝑇(𝑗)|	Based on two-sample 𝑡 statistics of a gene, apply the same weight across all samples of a gene
Qdiff	𝑊^|𝑄𝑑𝑖𝑓𝑓|(𝑗)=|𝑄−𝑄(−𝑗)|/∑^𝑚𝑗=1|𝑄−𝑄(−𝑗)|	Based on the global test statistic 𝑄 for a pathway, apply the same weight across all samples for a gene
RWV (Random Weight Vector)	𝑤𝑋=^𝑤1𝑋1𝑤2𝑋2⋮𝑤𝑚𝑋𝑚	𝑚 number of random weights in predefined range that minimizes 𝑃-value in the global test, or OOB error rates in the random forests for a pathway
RWM (Random Weight Matrix)	𝑤𝑋=⎡⎢⎢⎣^𝑤1,1𝑋1,1𝑤1,2𝑋1,2...𝑤1,𝑚𝑋1,𝑚𝑤2,1𝑋2,1......𝑤2,𝑚𝑋2,𝑚𝑤............𝑛−1,1𝑋𝑛−1,1......𝑤𝑛−1,𝑚𝑋𝑛−1,𝑚𝑤𝑛,1𝑋𝑛,1𝑤𝑛,2𝑋𝑛,2...𝑤𝑛,𝑚𝑋𝑛,𝑚⎤⎥⎥⎦	𝑚×𝑛number of random weights in predefined range that minimizes 𝑃-value in the global test or error rates in the random forests for a pathway