Oncofusion

start / graph / concept-q147-a-bounded-absence-across-five-partners-is-a-rule-of-three-bound

Explainerestablished confidence 5 of 5: Multiple independent lines of evidence; treated as settled in the field.Q147-hoxa-irx1-across-partners

A cross-partner absence is a rule-of-three bound, and the denominator must be the samples that could have shown it

Finding nothing in eighteen samples does not mean it never happens. It means the rate is below about one in six - and that bound gets weaker if some of those eighteen were too poorly measured to count.

The same thing, for a scientist

Zero of eighteen is not zero. **Rule of three:** with 0 successes in n trials the true rate is below 3/n with roughly 95% confidence. For this beat's headline: | denominator | what it is | bound on non-AFF1 IRX1 occupancy | |---:|---|---:| | 18 | all untreated non-AFF1 samples | **< 16.7%** | | 12 | depth-ADEQUATE and readable only | **< 25.0%** | | 16 | independent patients (three pairs collapse) | < 18.8% | **Both the 16.7% and the 25.0% are reported in the headline entry**, because the choice of denominator is a judgement and the weaker bound is the one a sceptical reader should use [E1]. Four of the 18 have IRX1 **UNMEASURED** - exact zero in both antibodies at inadequate depth - and an unmeasured sample cannot contribute to an absence, which is exactly why the 12-sample bound exists. **The rule that generalises:** for a bounded absence, the denominator is *the samples in which the thing could have been detected had it been there* - not the samples you downloaded. Depth, readability and locus mappability each remove samples from that denominator, and each removal makes the bound weaker. **A beat that reports the larger denominator without the smaller one is reporting the more flattering of two defensible numbers.**

Go deeper
Why the bound is the result and the zero is not

A zero reads as 'never' and it is not. At n = 18 the bound is 16.7% - which means an occupancy rate of one in seven non-AFF1 patients is entirely compatible with this beat's data. That is a clinically meaningful rate. The result is genuinely strong (0 of 18, with a positive control at 17 of 18 in the same libraries), and the honest statement of its strength is the bound, not the zero.

It also tells the next beat what to do: to push the bound under 5% you need 60 samples, which no single deposit currently has. The way forward is not more analysis of GSE252378.

Contrast with the proportion the deposit cannot bound

Three of eight KMT2A::AFF1 samples are IRX1-occupied, i.e. 37.5% with a Wilson 95% interval of roughly 13.7-69.4% - a 56-point interval that spans everything from 'uncommon' to 'most patients'. At these n the zero is far more informative than the mid-range proportion, which is the same asymmetry this corpus already records: a value near 50% at small n is the least informative result available, and a zero is the most.

Facts and figures
rule0 of n gives a 95% upper bound of 3/n
bound all18 PCT16.7
bound adequate12 PCT25
bound patients16 PCT18.8
n unmeasured4
aff1 positive3/8
n needed for 5pct bound60
aff1 wilson95
[
  13.7,
  69.4
]
analyses
[
  "ana-q147-irx1-fusion-occupancy-is-confined-to-kmt2a-aff1"
]
How this could bite us back
  • A 16.7% upper bound means up to one in six non-AFF1 KMT2A-r patients could have a fusion-occupied IRX1 locus. Treating this beat's zero as 'never' in a stratification scheme would be an over-reading of its own result.
Still open
  1. Is there a second independent KMT2A-r chromatin deposit with non-AFF1 partners at adequate depth? Pushing the bound below 5% needs about 60 samples and no single deposit has them.
Every source behind this entry (1)
  1. E1established confidence 5 of 5: Multiple independent lines of evidence; treated as settled in the field.dataset

    IRX1 fusion occupancy is 0 of 18 untreated non-AFF1 GSE252378 samples, giving a rule-of-three 95% upper bound of 16.7%; restricted to the 12 samples that are both depth-ADEQUATE and pass the MEIS1/CDK6 readability gate the bound is 25.0%; collapsed to 16 independent patients it is 18.8%. Four of the 18 have IRX1 UNMEASURED (exact zero in both KMT2A-N antibodies at inadequate depth). By contrast 3 of 8 KMT2A::AFF1 samples are IRX1-occupied, a Wilson 95% interval of about 13.7-69.4%.

    What this evidence cannot show

    The rule of three is an approximation to the exact binomial upper bound and is accurate to within a percentage point at these n. It assumes the samples are independent draws from the population the bound is about; three of the 18 are pair members and all 18 come from four referral centres, so the effective n is smaller than 18 and the true bound is correspondingly weaker than any figure quoted here. Every number is a WITHIN-SAMPLE share: an interval's mean coverage divided by that same library's mean coverage over all 19,404 hg38 RefSeq promoters, so 1.0 = an average promoter in that library. GSE252378 has no spike-in, so no between-library absolute statement is licensed; the only cross-sample quantity used is a ratio of two loci measured inside one library, where the unknown per-library scale cancels.

    Evidence that argues against this (1)
    • The population the bound describes is 'KMT2A-rearranged leukaemia samples banked at four North American paediatric centres and selected into one chromatin-profiling study', which over-represents lineage-switch and relapse cases by design. The bound does not transfer to unselected KMT2A-r disease without that caveat. Janssens DH et al. 2024
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