An independence null OVERSTATES partner-exclusive recurrence 16-fold here - it is not a lower bound, and the brief that dispatched this beat said it was
also called q152 independence null direction
A standard shortcut is to pretend each gene switch behaves independently of the others, on the assumption that this under-counts how often a pattern appears by chance. In this dataset the shortcut over-counts by sixteen times, so using it would have made a real pattern look impressive when it is not.
The same thing, for a scientist
The dispatch brief for this beat stated that an independence calculation is a LOWER bound on expected recurrence because promoters cluster by activity and chromosome. Measured on this matrix it is the opposite. Poisson-binomial convolution over the 8 AFF1 samples' own pass rates gives P(occupied in >=3 of 8) = 0.05320; the product over the 19 non-AFF1 samples gives P(occupied in none) = 0.14622; 19,404 x 0.05320 x 0.14622 = 150.9 expected promoters. The label-permutation null on the same matrix gives 9.1 and the observation is 17. Independence overstates by 16.6x against the permutation null and by 8.9x against the observation.
Why the direction reverses
Positive correlation across samples is what breaks it, and it breaks the absence term, not the co-occurrence term. Occupancy is strongly shared: a promoter occupied in three AFF1 samples is very likely occupied in some non-AFF1 sample too, because the same promoters are active in all of these blasts. The independence product prod(1 - q_s) over 19 samples treats those 19 chances as independent coin flips and so hugely overestimates the chance that all 19 come up absent conditional on three of the eight index samples coming up present.
The co-occurrence term errs in the other direction (correlation makes >=3-of-8 more likely than independent), but the absence term dominates: 0.146 independent versus an implied conditional value roughly sixteen times smaller 1.
The general rule
For a pattern of the form present in >=k of A and absent in ALL of B, the independence null runs high, not low, whenever occupancy is positively correlated across samples - and it runs higher the larger B is, because the error is a product of |B| terms. The intuition that 'clustering makes chance co-occurrence more likely, so independence is conservative' is correct for the co-occurrence half and exactly wrong for the exclusion half.
A claim about your own instrument's conservatism is still a claim (queen brief, rule 78 corollary). This one was in the dispatch brief, in red, and was false.
| script | analyses/q152-the-aff1-only-recurrent-promoter-core/step2.py |
|---|---|
| status | run |
| result summary | Independence expectation 150.9 versus permutation null 9.1 and observation 17. Independence is a 16.6x OVER-estimate, not a lower bound. |
inputs
[ "C:/Temp/q147part/promoter_matrix.tsv" ]
measurements
[
{
"quantity": "ratio_independence_null_to_permutation_null",
"subject": "expected count of promoters occupied in >=3 of 8 AFF1 and 0 of 19 non-AFF1",
"value": 16.6,
"units": "fold",
"n": 19404,
"universe": "19,404 refGene 2 kb promoters x 27 GSE252378 samples under the two-antibody 2.0x plus floor rule",
"null": 1,
"note": "150.9 independence / 9.1 permutation; independence overstates, it does not understate"
},
{
"quantity": "p_absent_in_all_19_nonAFF1_under_independence",
"subject": "an arbitrary promoter being called unoccupied in all 19 non-AFF1 samples",
"value": 0.14622,
"units": "probability",
"n": 19,
"universe": "product over the 19 non-AFF1 samples' own pass rates",
"null": null,
"note": "the term that carries the error; occupancy is positively correlated across samples so the true conditional value is far smaller"
}
]- How large does |B| have to be before the independence error exceeds an order of magnitude? Here |B| = 19 and the error is 16.6x; the relationship should be roughly geometric in |B| and is cheap to chart.
- Does the same reversal hold for the gene-body-scale occupancy calls q147 used, or is it specific to the 2 kb promoter window?
- E1strong confidence 4 of 5: Replicated in peer-reviewed work by more than one group.dataset
On the 19,404 x 27 GSE252378 promoter occupancy matrix, Poisson-binomial convolution over the eight KMT2A::AFF1 per-sample pass rates gives P(>=3 of 8) = 0.05320 and the independent product over the nineteen non-AFF1 pass rates gives P(0 of 19) = 0.14622, so the independence expectation is 19,404 x 0.05320 x 0.14622 = 150.9 promoters, against a label-permutation null of 9.1 and an observation of 17.
Q152 independence versus label-permutation nulls on the same occupancy matrix · Iqbal Lab oncofusion knowledge graph, beat Q152 · this project 2026What this evidence cannot show
The Poisson-binomial uses each sample's marginal pass rate estimated from the same data, so it is a plug-in estimate; the ratio between the two nulls is what carries the point, not the absolute 150.9.
Evidence that argues against this (1)
- The 16.6x is a ratio of two nulls, not of a null to an observation, so it does not by itself establish that any published claim was inflated. If a claim was scored against no null at all - which is the usual case in this project - then the direction of this error is irrelevant to it, and the reason the claim was weak is different. Iqbal Lab oncofusion knowledge graph et al. 2026
- E2established confidence 5 of 5: Multiple independent lines of evidence; treated as settled in the field.dataset
This project already holds the general caveat that a set-overlap statistic is not a result until its null accounts for active promoters clustering, recorded from the q146 Jaccard work.
concept-q146-a-jaccard-is-not-a-result-until-its-null-knows-that-active-promoters-cluster (this graph) · Iqbal Lab oncofusion knowledge graph, beat Q152 · this project 2026What this evidence cannot show
That entry records the clustering caveat; it does not record the direction of the error for an exclusion-type pattern, which is what this analysis adds.
Evidence that argues against this (1)
- q146's clustering caveat was written about a Jaccard, which is a symmetric overlap statistic, and it is not obvious that a caveat about overlap transfers to a caveat about exclusion. The two failures share a cause but the q146 entry cannot be cited as having anticipated this one. Iqbal Lab oncofusion knowledge graph et al. 2026
why the primary null is a label permutation and not an independence calculation
the measured 16.6x error is the evidence for the concept
extends q146's clustering caveat by giving the direction of the error for an exclusion pattern