# Bootstrap-based comparison of gene values in two independent experiments

I have a matrix of N gene-based observations (between 0 and 1) from 2 experiments like the following (The actual matrix is much bigger). \begin{array} {|r|r|r|} \hline GeneName & Exp1 & Exp2 \\ \hline Gene1 & 0.721& 0.733 \\ \hline Gene2 & 0.072& 0.325 \\ \hline Gene3& 0.66& 0.16 \\ \hline Gene4& 0.244& 0.279 \\ \hline Gene5& 0.613& 0.9 \\ \hline Gene6& 0.76& 0.753 \\ \hline Gene7& 0.101& 0.863 \\ \hline \end{array}

The experiments are independent and the goal is to look for variation in gene-based observations between the two experiments using non-parameteric bootstrapping.

I believe that, according to the bootstrapping theory, one will repeatedly take N samples (7 in case of above) with replacement from input matrix of N gene-based observations. Since, in my case, the experiments are independent, I was thinking to take 2 independent samples (of size N each) each time, merge them by gene name and compute the difference in corresponding gene-based observations. However, while merging by gene name, I observed that the resulting matrix size (in terms of rows) may be greater than the original matrix size.

Will the above sampling algorithm be incorrect according to bootstrapping strategy? In case it is incorrect, how can I take bootstrap samples in a problem like above?

• 1. I take it the Exp1 and Exp2 are two instances of the same experiment? 2. What do the results of the experiments mean? 3. It is not clear what your goal is. – Yair Daon Jun 26 '17 at 18:04
• It is a disease model where the cancer affects multiple tissues (e.g. liver, lung). This effect is demonstrated by differential expression (number of active copies) of the same gene(s) in those tissues. The idea is to study this across possible pairs of tissues. Since the estimates of gene expression are not perfect (can be due to a number of reasons), I want to address this uncertainty by bootstrapping... Was I able to clarify it? I can discuss it in more detail if that would help – Ikram Jun 28 '17 at 14:13
• so you do two experiments to get better estimates? But if these experiments are on different organs, how do you relate them? I'm still confused about your strategy, your assumptions and your goal. – Yair Daon Jun 29 '17 at 22:40