bioinf 527 lecture 14 (last on exam 1)

beware of interpretational thresholding

Researchers often fall into the trap of interpretational thresholding

● We assign some meaningful discontinuity to the p-value threshold

● Anything on one side of the cutoff is ‘real’ and everything on the other side is a true negative

● P-values provide a gradient of evidence not a binary verdict on the result

If my p-value is above the chosen threshold for significance, often 0.05, how do I interpret that result?

1. The null hypothesis could be true i.e. It’s a true negative

2. You may not have had enough statistical power to detect a significant result (e.g. too small of a sample size)

3. Random sampling error may have prevented you from detecting a significant result (you got unlucky)

Real ChIP-Seq data presents two major problems

○ Highly accessible regions have a high read counts in both input control and ChIP data

○ Many windows have very low input control counts (even zero!) which provides an unreliable estimate for lambda in those windows

null lambda for rna-seq poisson

Data from healthy samples can be used to select a 𝞴 value representing the expected count under the null hypothesis

● Setting the null Poisson distribution allows us to determine how surprising counts observed in disease samples are

what went wrong applying poisson to rna-seq data

A Poisson distribution assumes that the mean and variance are equal

● In real RNA-Seq data, as shown here, the variance is observed to be greater than the mean

● As the mean increases, the variance increases faster than the mean

● There is more variance than expected in real RNA-Seq data`

overdispersion

extra variability beyond what the Poisson distribution predictsw

where does overdispersion come from

In a perfect world, expression of gene A in each control cell would be exactly the same

● Similarly, expression of a gene would be exactly the same in each treated cell

In the real world, replicate cells even under the same conditions will display some variability so expression of a gene will be ~ in control cells

● Similarly, expression of gene A in treated cells under the same conditions will display some variability so expression of a gene will be ~ in treated cells

underestimating variance

increases false positives

Using Poisson on the overdispersed RNA-Seq data will lead to false positives

negative binomial distrivution

models count data

adds an additional parameter that allows the variance and mean to be different

Variance can be adjusted to account for the observed overdispersion in real RNA-Seq data

Permutation Tests

Unlike many traditional statistical tests, a permutation test does not rely on assumptions about how the underlying data are distributed

● There is no mathematical model needed for generating the null distribution

● The null distribution is generated directly from the data itself

● Permutation tests give us incredible flexibility in what feature of the data we want to interrogate

We can even generate a p-value from this permutation test

rough steps of permutation test

To perform a permutation test we treat the labels as if they are arbitrary

● Under the null hypothesis it shouldn’t matter which samples get which label because the groups are the same

● After shuffling (aka perumuting) the labels, we calculate any statistic we want e.g. difference in the means

● Repeat this process many times to and calculate our test statistic for each shuffling (aka permutation) of the labelsl

log transformation

The skewness of the data can make it difficult to visualize patterns and trends

can reveal structure in the data that was obscured on a linear scaleb

bayes theorum

provides a mathematical approach for updating our beliefs about something unknown based on new evidence

Bayesian approaches give us probabilities for our hypothesis given the data

Bayes’ lets us use the probability when there is no evidence to calculate a new probability once we have evidence

our prior can be a distribution of possible values

reasons to love bayes

You can use more than one piece of evidence

● And if you have enough evidence, you don’t need a good prior

● The more evidence you gather (i.e. data) the more you can update your belief in a meaningful way