I have a question dealing with statistical approach to use for treating biological and technical replicates in an in vitro screening of a 349 inhibitor library.
We have at our disposal a collection of 11 cancer stem cell lines isolated from different patients, thus genetically independent, that constitute our biological replicates.The cell suspension is spotted on a plate and treated with vehicle, 20nM and 200 nM of each of 349 inhibitors, and viability is measured for each spot. The inhibitors are distributed in 4 plates and each plate contains 86 to 91 inhibitor treatments (either 20 nM or 200 nM) and 3 to 6 vehicle treatments as internal controls, since each plate can have different baseline signal due to technical conditions. The design was a complete block design, each cell line subjected to vehicle, 20 nM and 200 nM of each inhibitor. Each plate is reproduced identically three times, thus generating three technical replicates for each cell line/treatment dose combination.
At first I chose to take an inferential approach to determine which inhibitors exert a significant effect at any dosage. Having internal controls for each plate, I could not use multiple group testing and adopted pairwise comparisons (control-20nM, control 200nM for each inhibitor/cell line) with multiple testing correction. Row data have shown to be non-gaussian and non-omoschedastic, hence I chose to use Wilcoxon rank sum (Mann-Whitney) paired test with Benjamini Hochberg multiple testing correction.
The problem is: how should I treat technical replicates? In previous experiments a colleague included the 3 to 6 controls for each plate and the three technical replicates of each spot in the test, but I think this is definitely incorrect for it makes technical replicates, which are all associated measures, at the same level of biological replicates. In this case I simply averaged the technical replicates to increase the measure accuracy, I guess this is correct but I think there could be a better way to use this information. I would be grateful if anyone would give me an insight on how to deal with this, and maybe to suggest other possible statistical approaches. Thanks a lot in advance.