Let's say that I have 8 proteins: A-H and I have protein expression data for each gene.
For each gene, the expression number is based on the average of 20 cell lines expressing that gene.
I also have drug sensitivity data for each of the cell lines. So let's say I have 5 drugs and AUC data. I averaged the AUC for each drug to include all of the cell lines.
I want to find out if there is a correlation between protein expression data and drug sensitivity. So, how does protein A correlate with drugs 1-5? I want 5 separate R and p-values.
Is this possible?
If so, what's the best way to represent these numbers graphically?
You can express drug sensitivity as IC50 and protein expression for example as µg per million cells per h, or as copies produced per cell per hour. Then both data are on the rational scale and you can use Pearson’s product moment correlation coefficient rp. There are also correlation coefficients for other scales:
nominal binary ordinal cardinal
nominal λ λ θ η2
binary λ e rj
ordinal e rs
cardinal rp
where
Goodman & Kruskal’s coefficient of relative predictability λ: J. Am. Stat. Assoc. 49:268 (1954), 732–764
point biserial correlation rj
Wilson’s e and related coefficients: J. Math. Sociol. 12:1 (1986), 49–69
Freeman’s measure of association θ: Elementary applied statistics. New York, London, Sidney: John Wiley & Sons, 1965; Psychometrica 41:2 (1976), 273–275
η2: https://de.wikipedia.org/wiki/Fehlerreduktionsma%C3%9Fe#.CE.B72
Pearson’s product moment correlation coefficient rp: Proc. Royal Soc. Lond. 58 (1895), 240–242
Spearman’s rank correlation coefficient rs: J. Math. Sociol. 12:1 (1986), 49–69
Except for rs, all these coefficients have PRE interpretation (proportional reduction of error), but only rp also has angle interpretation. All but η2 are symmetrical.
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