Using GEO

Series, Platform, Samples

Data to analyze

Using GEO2R

control vs treatment

Results

Expression and Log

Raw data is light intensity (luminescence) for Control and Treatment \[C, T\]

We work with the logarithm (base 2) of these values \[LC=\log_2(C)\\LT=\log_2(T)\]

Average Expression & Fold Change

Then Average expression is \[AvgExp = \frac{LT + LC}{2}\] and Fold change is \[logFC = LT - LC=\log_2\left(\frac{T}{C}\right)\]

Hypothesis test

Classical statistics. We have two scenarios, called hypothesis

• H₀: Nothing happens
• H₁: Something happens

But our experiment cannot tell us directly which one is true

What we measure

Every experiment has 4 contributions

• Biology (or Nature)
• Natural variability
• Instrument
• Noise

Experiments are random variables

We may have bad luck. Maybe black and white horses have the same average height, but

• we got only the small black horses and the tall white ones
• the horses move a lot and we cannot measure the correct values

Therefore, we cannot be 100% sure that our results correspond to reality

But we can have a degree of confidence that we are not far away

p-value and null hypothesis

In terms of hypothesis test, we have

• H₀: the real averages are the same. We only see variability and noise.
• H₁: the real averages are different. The measurements are too different to be only noise.

The p-value is the probability of observing the experimental data \(X\), assuming that H₀ is true \[ℙ(X|H_0)\]

Is this what we want?

Notice that \[ℙ(X|H_0)≠ℙ(H_0|X)\] In other words, the p-value is not the probability that the null hypothesis is true, given the experimental result

Ideally we will like to know this last probability, but it is hard to do so

When is it significant?

Traditionally, 5% and 1% are used as p-value thresholds

But there is nothing to decide that these are good values

Indeed, in Gene Expression, these value are usually too big

Multiple test correction

There are several approaches

• Family Wise Error Rate control (Bonferroni)
• False Discovery Rate control (Hochberg)
• Others

The basic difference is the trade-off between False Positives and False Negatives

Two ways of being wrong

In every hypothesis test, we can be wrong in two ways

• Type 1: False positive
  • putting innocents in the jail
• Type 2: False negatives
  • freeing criminals

Usually improving one means worsening of the other

How does FWER work

Family Wise Error Rate multiplies each p-value by the number of cases \[p.adj = p.value ⋅ N\]

It reduces False Positives and increases False Negatives

Sometimes we get nothing significant

How does FDR work

FDR sorts the p-values and multiplies each by an increasing value \[p.adj = p.value \cdot\frac{i}{N}\]

If we get \(p.adj<0.05\) then the probability that it is a false positive is 5%