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I'm trying to implement a system to identify regions of high signal content in the presence of a noisy landscape. By high signal content, I simply mean intensity values significantly above background intensity values.

Intensity readings are taken at $T$ contiguous locations; at each location, $t, \text{ for } t \in [1,T]$, the intensity count, $f(t) \in [0,\infty)$, is recorded.

My current strategy is this:

Mean-correct---or, simply, subtract the mean intensity---at each observed intensity with a view to removing background noise.

  1. Move a sliding window along the landscape, such that:

  2. For each position $i \in [1,T]$ and window interval $w_{i,i+s-1}$:

  3. compute a test statistic from the $s$ observations within the current interval, $w_{i,i+s-1}$.

  4. compare this test statistic to a preselected null distribution centred on $0$.

  5. compute p-value corresponding to interval $w_{i,i+s-1}$; where the p-value corresponds to the probability of committing a type I error: assuming the region characterises high-signal content when,in fact, it doesn't.

  6. Implement correction for multiple testing, say Benjamini and Hochberg FDR control.

  7. If two overlapping window intervals, $w_{j+s-1},w_{k+s-1}: j+s-1 \geq k$, are both within the FDR threshold, concatenate regions to form one larger region-complex.

The figure given below illustrates this concept. In this figure, two regions, say $A$ and $B$, of the given landscape are covered by the sliding window. In each region, the window is depicted at $t_{A}$ and $t_{B}$ different coverage points respectively (hence the blurring effect). I'm looking for a procedure which which will determine whether the intensity levels at $A$ and $B$ are significantly different from background. The horizontal salmon line represents the mean intensity; upon mean-correction, anything below this line will be removed.

Landscape Signal Plot

I should also mention that I am working with several landscapes, say $L$; hence, the number of window positions---and, further hence, the number of tests---will be $\sum_{l=1}^{L}pos_{l}$, where $pos_{l}$ is the number of window positions in landscape $l$.

For this approach to work, I need to define the test statistic and corresponding null and alternative hypotheses. Given the nature of the problem, I'm not sure what form an appropriate statistic/hypotheses scenario should assume.

Could somebody provide some assistance on how to define an appropriate hypotheses scenario or perhaps suggest a more robust approach to identifying high-signal content regions?

(P.S. I'm not sure that Poisson-based approaches will work as the data seem to be over-dispersed; perhaps a negative binomial assumption would work, but I'm guessing that a non-parametric/resampling/simulation based approach might be best. Having said that, if somebody believes that a Poisson approach is appropriate, please do suggest it!)

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This sounds an awful lot like peak calling in *seq (ChIP-seq, clip-seq, etc) experiments.

A peak is called where either the number of reads exceeds a pre-determined threshold value or where there is a minimum enrichment compared to background signal, often in a sliding window across the genome. Some tools apply both methods.

from peak calling guide for chip-seq.

There are lots of different models which can be applied (after suitable bias correction)

Models used for the statistical assessment of enriched regions (peaks) range from Poisson (CSAR [85]), local Poisson (MACS), negative binomial (CisGenome [56]) to zero-inflated negative binomial (ZINBA [86]), or even extend to more sophisticated machine learning modeling techniques such as Hidden Markov Model (HPeak [87] and BayesPeak [88]).

From Practical guidelines for the comprehensive analysis of ChIP-seq

The discussion of the modeling assumptions and comparisons to other models present in each of these papers is probably far more informative than I could be.

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