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I'm doing biological gene expression data. For the genes I analysed, each gene can produce two isoforms, one dominant (Gene isoform 1) one minus can be treated as a by-product (Gene isoform 2).

I'm actually interested in is the expression change of the by-product following time series (Gene isoform 2). However, the problem is, the expression of "Gene isoform 1" is a confounder here. i.e. I want the variance of "isoform 2" expression is driven by itself, not driven by the variance of the dominant "isoform 1".

Two graph to explain my problem:

Situation one:

"Gene isoform 1" and "Gene isoform 2" both increase their expression over time, however they vary synchronously, it is likely the variation of Gene isoform 2 is due to the caused by the variation of "Gene isoform 1". This is not what I want!

Situation 2:

"Gene isoform 1" and "Gene isoform 2" both increase their expression over time, the increase of "Gene isoform 2" is much faster than "Gene isoform 1", this means at least partially "Gene isoform 2" vary independent of "Gene isoform 1", and this independent part of variance is exactly what I'm interested in.

The question is, how do I test the change of "Gene isoform 2" without the influence of "Gene isoform 1".

Thanks a tons for any answer!

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You could detrend isoform 2 by isoform 1 or test for isoform 1 as a covariate. So, a) can regress 1 vs 2, take the residual and regress it against time. This will look for a linear relationship of detrended data; b) here is an example of ANCOVA with repeated measures ANCOVA with repeated measures in R and time-series analysis with covariates https://www.researchgate.net/publication/239802706_Covariate-Adjusted_Regression_for_Tim%E2%80%8C%E2%80%8Be_Series ; Assessing Seasonal Covariates in a Seasonal ARIMA Time Series Model‌​nal-arima-time-series-model

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