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Comparing drug-binding affinity of different drugs to different transcription factors

I am trying to analyze 5 different drug candidates on >1000 candidate genes as therapeutic targets. My raw data has a few columns: Gene, Annotation Sequence, Binding Intensity (3 replicates, so I have 3 columns for this value per each drug and gene), Average Binding Intensity. I'm not really sure where the best place to start is. I am thinking about doing basic one-way ANOVA across the 3 different drugs and getting the p-value, but I'm not sure how to do this in R given that I have 3 technical replicates for each drug. Additionally, do you have any suggestions on which direction I should take this analysis?

e.g.

Gene.          Annotation Sequence.          Drug 1 (replicate 1).    Drug 1 (replicate 2).      Drug 1 (replicate 3).  ....
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proteomics genes

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