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I have a data set with expression levels of a list of genes, measured in replicate at two different time points between two groups; a control group and a disease group.

I want to identify the changes in expression between the two groups, however I'm having some trouble on formulating how best to do this. For example, if I have $[C_0]$ and $[C_1]$ as the control group measured at $t=0$ and $t=1$ respectively, and $[D_0]$ and $[D_1]$ as the disease group, I had tried to do:

$$\frac{([D_1] - [D_0]) - ([C_1] - [C_0])}{[C_1] - [C_0]}$$

I feel like a fold change would be appropriate, however it doesn't seem to make any sense logically for the genes where $[C_0] = [C_1]$ or $[D_0] = [D_1]$.

Could anyone suggest an appropriate ratio or measurement? This is straightforward enough when it's simply comparing between C and D, (e.g. you just find $\frac{D}{C}$), however I'm not sure how to treat the different time points.

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The gene expression profile may change at different time points between the two groups; you should decide what you actually want to measure. If you want to see if the diseased group is different from the control then you should compare them at every time point. For most situations you would need to compare just their steady state behaviour.

Imagine a diseased individual who shows some physiological differences at certain developmental stages compared to the control but in the end turns out to be perfectly normal. So what matters in most cases is the steady state and not the transients.

However if you are interested in the change in expression then you should compare ([D1] - [D0]) with ([C1] - [C0]). This will tell you if the dynamics of the diseased and the control samples are similar or not.

There are issues with fold changes. Though they are decent measures, you cannot really apply a t-test with fold changes (normalizing to 1 is a different thing).

You can do another t-test between [C1] and [C0] (similarly for D). This would tell you if the diseased or control population changes its expression at time t=1 or not.

AFAIK you cannot compare the dynamics and the values simulatenously. What you should test depends on what you are interested in.

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