prostate triage

Can this patient avoid the invasive diagnostic test?
512 draws (Python, shipped) · recomputed in 133 ms
headline

Informative molecules from tumour luminal

461 (58.1–2,720) informative molecules of tumour luminal reach the detector, against 3,000 needed.

  • Detection at the operating tumour fraction of 0.5%, tumour-informed aggregate readout: 77.8% (60.5%–97.1%).
  • Limit of detection at 95%: 2.19% (0.382%–17.8%).
  • Feasibility ratio, achieved over required molecules: 0.154 (0.0194–0.907).
  • The median draw carries fewer informative molecules than the assay class needs (3,000), so this is an architectural failure: no optimisation of depth fixes it.
requiredurothelium1,444 (207–7,097)renal tubule143 (20.5–704)leukocyte0.0187 (8.3e-4–0.294)hepatocyte0.00801 (3.7e-4–0.133)tumour luminal461 (58.1–2,720)tumour transrenal0.0263 (9.8e-4–0.386)0.0010.010.11101001,00010,000informative molecules in the tube (GE)
Median, 25–75% box and 5–95% whisker over 512 draws. The target source is drawn solid.
funnel

From shedding to the detector

1.8e6 genome equivalents of tumour luminal shed a day become 461 informative in the tube: 3.6 decades lost, the steepest drop at M1 in the collected urine, which keeps 1.3%.

under 60 bp60–100 bp100–170 bp170–300 bp300 bp and longer10010,0001e6genome equivalents of the target source, log scaleunder 60 bp: 2.3e5 GE at M0 to 2,795 GE at M160–100 bp: 4.4e5 GE at M0 to 5,498 GE at M1100–170 bp: 5.8e5 GE at M0 to 7,211 GE at M1170–300 bp: 4.0e5 GE at M0 to 4,964 GE at M1300 bp and longer: 1.4e5 GE at M0 to 1,760 GE at M1−98.7%dilution: 20 mL of the day's urinekept 1.3% (0.739%–2.38%)under 60 bp: 2,795 GE at M1 to 2,795 GE at M260–100 bp: 5,498 GE at M1 to 5,498 GE at M2100–170 bp: 7,211 GE at M1 to 7,211 GE at M2170–300 bp: 4,964 GE at M1 to 4,964 GE at M2300 bp and longer: 1,760 GE at M1 to 1,760 GE at M20%no sieve on the luminal routekept 100% (100%–100%)under 60 bp: 2,795 GE at M2 to 11,938 GE at M360–100 bp: 5,498 GE at M2 to 7,323 GE at M3100–170 bp: 7,211 GE at M2 to 2,564 GE at M3170–300 bp: 4,964 GE at M2 to 381 GE at M3300 bp and longer: 1,760 GE at M2 to 20.3 GE at M3−<0.01%the nuclease: the leak below the gridkept 100% (99.9%–100%)under 60 bp: 11,938 GE at M3 to 4,669 GE at M460–100 bp: 7,323 GE at M3 to 4,270 GE at M4100–170 bp: 2,564 GE at M3 to 1,783 GE at M4170–300 bp: 381 GE at M3 to 285 GE at M4−50%void capture and the kit's recoverykept 50% (17.4%–126%)under 60 bp: 4,669 GE at M4 to 42.4 GE at M560–100 bp: 4,270 GE at M4 to 172 GE at M5100–170 bp: 1,783 GE at M4 to 198 GE at M5170–300 bp: 285 GE at M4 to 45.9 GE at M5300 bp and longer: 15.5 GE at M4 to 3.26 GE at M5−96.2%library conversion and the footprint gatekept 3.84% (1.05%–9.83%)M0 shed1.8e6 GE a dayM0 shed · under 60 bp: 12.6%, 2.3e5 GE a dayM0 shed · 60–100 bp: 24.7%, 4.4e5 GE a dayM0 shed · 100–170 bp: 32.4%, 5.8e5 GE a dayM0 shed · 170–300 bp: 22.3%, 4.0e5 GE a dayM0 shed · 300 bp and longer: 7.92%, 1.4e5 GE a dayM1 in the collected urine22,227 GEM1 in the collected urine · under 60 bp: 12.6%, 2,795 GEM1 in the collected urine · 60–100 bp: 24.7%, 5,498 GEM1 in the collected urine · 100–170 bp: 32.4%, 7,211 GEM1 in the collected urine · 170–300 bp: 22.3%, 4,964 GEM1 in the collected urine · 300 bp and longer: 7.92%, 1,760 GEM2 past the sieve22,227 GEM2 past the sieve · under 60 bp: 12.6%, 2,795 GEM2 past the sieve · 60–100 bp: 24.7%, 5,498 GEM2 past the sieve · 100–170 bp: 32.4%, 7,211 GEM2 past the sieve · 170–300 bp: 22.3%, 4,964 GEM2 past the sieve · 300 bp and longer: 7.92%, 1,760 GEM3 after the nuclease22,227 GEM3 after the nuclease · under 60 bp: 53.7%, 11,938 GEM3 after the nuclease · 60–100 bp: 32.9%, 7,323 GEM3 after the nuclease · 100–170 bp: 11.5%, 2,564 GEM3 after the nuclease · 170–300 bp: 1.72%, 381 GEM4 collected and extracted11,023 GEM4 collected and extracted · under 60 bp: 42.4%, 4,669 GEM4 collected and extracted · 60–100 bp: 38.7%, 4,270 GEM4 collected and extracted · 100–170 bp: 16.2%, 1,783 GEM4 collected and extracted · 170–300 bp: 2.59%, 285 GEM5 informative461 GEM5 informative · under 60 bp: 9.2%, 42.4 GEM5 informative · 60–100 bp: 37.3%, 172 GEM5 informative · 100–170 bp: 42.8%, 198 GEM5 informative · 170–300 bp: 9.97%, 45.9 GEM5 informative · 300 bp and longer: 0.707%, 3.26 GErequired 3,000
Each stop is the median over draws of the target source's genome equivalents, its width on a log scale, so equal tapers are equal factors wherever they happen. The whisker at each stop is the 5–95% spread. The ribbons carry the length classes through; the grey behind them is what the stage removed. Hover a ribbon or a stop for its numbers.
  • What gets through at M5: 46.5% shorter than 100 bp, 42.8% between 100 and 170 bp, 10.7% longer.
  • The neck against the requirement: 461 informative against 3,000 needed, the neck does not reach it at the median.
detection

Detection probability against tumour fraction

The curve says where the assay starts to work; the band says how sure the priors are of it.

00.20.40.60.81tumour-informed aggregate readout (median, 5–95%)single-locus counting (median, 5–95%)operating pointprobability of detection1e-43e-40.0010.0030.010.030.10.3tumour fraction
Median with the 5–95% band over draws, at the current collection and assay.
00.250.50.751tumour-informed aggregate readoutsingle-locus countingoperating pointshare of draws0.0010.0030.010.030.10.31limit of detection at 95% (tumour fraction)
Cumulative share of draws whose 95% limit of detection lies below each tumour fraction. Draws that never reach 95% are counted as unreachable.
cascade

Where the molecules of tumour luminal go

The largest single loss at the medians is M5 informative (post-footprint), which removes 95.8% of what reaches it.

M1 shed and diluted1,111 (457–3,104)M2 past the sieve1,111 (457–3,104)M3 after the nuclease1,111 (456–3,103)M4 collected and extracted551 (135–2,618)M5 informative (post-footprint)23 (2.9–136)310301003001,0003,000genome equivalents per mL of urine
Each stage's total for the target source, in GE/mL. M3 only redistributes mass over length, so its loss is the sub-detectable leak; the footprint gate at M5 is where a long amplicon costs the most.
  • Extracted DNA yield, all sources: 8.83 (2.74–31.9) ng/mL.
  • Median fragment length of the extracted population: 55 (40–70) bp.
length

What the nuclease and the footprint leave

The population after M3 sits far below the footprint for most of its molecules; the informative population is the tail the assay can still read.

00.050.10.15after the nuclease (M3) (median, 5–95%)informative (M5) (median, 5–95%)footprintshare of molecules per bin2004006008001,000fragment length (bp)
Weighted mean over draws of each draw's normalised molecule-count profile for the target source.
design

Collected volume against assay footprint

Each cell replays the same draws through one design; the comparison is between designs, not between samplings.

volume \ footprint30 bp45 bp60 bp90 bp
10 mL79.1%
61.6%–97.7%
478 mol.		73.9%
58%–95.3%
309 mol.		69.2%
54.8%–92.5%
194 mol.		62.3%
51.4%–85.7%
77.3 mol.
25 mL84.5%
65.8%–98.9%
800 mol.		79%
61.2%–97.7%
507 mol.		73.9%
56.5%–95.2%
319 mol.		65.4%
51.9%–88.7%
126 mol.
50 mL88.9%
69.5%–99.6%
1,096 mol.		83.6%
63.4%–98.9%
704 mol.		77.5%
58.1%–97.1%
442 mol.		68%
52.3%–91.3%
172 mol.
100 mL92.4%
73.8%–99.8%
1,572 mol.		87.4%
66.5%–99.4%
1,001 mol.		81.7%
59.7%–98.3%
604 mol.		71.2%
53%–94.5%
228 mol.

Detection at the operating point: median, 5–95% range, and the median informative molecules. Green clears the target at the 5% quantile, amber clears it only at the median, red has too few molecules for the assay class. The current design is outlined. Every other control applies to every cell.

method

How this page computes

  • The chain M0 to M6 runs in this page in JavaScript, checked against the Python model on fixed draws to a relative 1e-8 on every stage and readout.
  • The 512 shipped draws are Python's, seeds 0 to 511, with their post-nuclease states solved at build time. Volume, kit, footprint, chemistry, platform, tumour volume, injury and urine output are downstream or linear, so they recompute in the page.
  • Hold, temperature, preservative, pH, filtration and proteinuria change the nuclease input, so the page re-solves the fragmentation master equation for every draw in a pool of workers, by the action of the matrix exponential on each draw's own profiles.
  • A prior edit reweights the draws by the ratio of the new density to the old, which is exact but thins the sample; the effective sample size says by how much. Fresh draws sample the edited priors in the page and re-solve.