Antisense Transcript Level The basic biology says genes on the DNA, get transcribed to mRNA (sense transcription), and the RNA will be translated to proteins. but sometimes, a gene can have transcription from the opposite strand, that sometimes impede RNA translation to protein, or sometimes help the translation by stabilizing the sense RNA
We designed an experiment with strand specific transcriptome and proteomics. To avoid the jargon, for each gene (in blue), we have the levels of sense (green) and antisense (red) transcription, as well as how much protein it produced (not shown in the figure below).

Additionally, since the sequencing is not an exact measurement and the resulting data, specially with low coverage, can be noisy, we have ran the experiments 3 times (replicates).
Therefore, for each gene $g$ we have $S_r(g)$ (its sense transcription at replicate $r$), $A_r(g)$ (its antisense transcription at replicate $r$) and its protein level $P(g)$ (no replicates there)
I have shown that Antisense levels are generally much lower, and independent of Sense levels:

Additionally, antisense ratio (${A_r(g) \over S_r(g)}$) follows a bell-curve distribution:

What I'm seeing is that the correlation between Sense and Protein levels diminishes when ratio of ${A_r(g) \over S_r(g)}$ gets larger and larger:

The problem is when transcription levels are low, the ${A_r(g) \over S_r(g)}$ ratio could be thrown off very easily. 
The QUESTIONs are:


*

*How can I use the replicates that I have to power my analysis?

*What sort of statistical test can I use to show loss of this correlation is significant or not?

 A: For a start, a simple linear regression (with log-transformed variables) might work for you.
A model you could try would be based on:
$$log P(g) = \beta_0 + \beta_S log{S(g)} + \beta_{A/S} log{A(g) \over S(g)}$$
which is the same as:
$$ log P(g)= \beta_0 + (\beta_S - \beta_{A/S}) log{S(g)} + \beta_{A/S} log{A(g)}.$$
In this model you assume that, for each gene $g$, $log P$ (protein) is linearly related to $log S$ (sense transcript), corrected by the log of the ratio $A/S$ (antisense/sense), in the same way for each gene. 
If you perform a linear regression of $log P$ against $log S$ plus $log A$ and the usual assumptions of linear regression hold, a test for significance of the coefficient for $log A$, $\beta_{A/S}$, would test whether and how much the ratio $A/S$ affects levels of $P$. The coefficient for $log S$ would be the indicated combination of the direct relation to $log S$ with the correction for $log A$.
With so many counts at or close to 0 and only one measure of $P$ per gene, it might be best to add the transcript counts among all 3 technical replicates for each gene first (perhaps after correction for any overall systematic technical differences among the replicates). If you still have 0 transcript counts in some instances, you could try adding 1 count to all counts. You probably want to remove from consideration all genes whose proteins that were undetected (value of 0), or add to the protein values some small number representing the limit of protein detection.
For readers who want to learn more about the underlying biology, see the Wikipedia page on antisense RNA, which is well known to affect protein production from individual genes.
