Bayesian borrowing: how many infants a prior is worth, and when it lies
also called MAP prior · meta-analytic-predictive prior · information borrowing · extrapolation to infants
Statisticians can let data from adults or from related leukemias count partly towards the answer in babies, which shrinks the number of babies needed. The catch is that it only works if the babies really are similar to the borrowed patients, and in this disease there is good reason to think they are not.
The same thing, for a scientist
Borrowing formalises what regulators already do informally when they extrapolate an adult result to children. A meta-analytic-predictive prior summarises external data into a prior whose effective sample size states exactly how many patients' worth of information is being contributed, and a robust mixture version adds a weakly-informative component so that a discordant current trial down-weights the prior automatically. Applied to infant KMT2A-rearranged leukemia the technique could plausibly halve the required infant sample, turning a two-year accrual into one. Whether it should be used is a biological question, and this graph's own content argues for caution: infant disease arises from a fetal cell of origin, carries a different partner distribution and a near-silent co-mutational landscape, and behaves differently from adult KMT2A-rearranged disease.
The mechanism, stated plainly3 deeper
A meta-analytic-predictive (MAP) prior takes historical or external cohorts, models between-trial heterogeneity, and produces a prior distribution for the current trial's parameter. Its effective sample size is the number of additional patients the prior is worth. Because between-trial heterogeneity is estimated rather than assumed zero, the prior is automatically discounted when the external studies disagree with each other 1.
The robust extension adds a weakly-informative mixture component. If the current trial's data conflict with the prior, the posterior weight shifts to the vague component and the borrowing quietly switches itself off. This is the property that makes borrowing acceptable to regulators: it fails safe.
A Bayesian hierarchical basket is the same idea applied across concurrent strata rather than across time, shrinking each stratum towards a common mean by an amount the data choose 2.
Three axes this project could borrow along, ranked by defensibility
| Axis | Borrow from | Defensibility | Why |
|---|---|---|---|
| Across KMT2A partners within infants | KMT2A::MLLT3, MLLT1, MLLT10 infants | Highest | Same age, same cell of origin, same interface; only the 3' partner differs, and all partners require menin |
| Across fusion families with a shared dependency | NPM1-mutant, NUP98-rearranged | Medium | Shared menin or shared HOXA output, but different cell of origin and very different age distribution |
| Across age within KMT2A | adults with KMT2A-rearranged disease | Lowest | Fetal versus adult cell of origin, different partner mix, near-silent versus mutation-rich genome, fifty-year age gap |
The intuitive move is the third one, because that is where the data are. It is the least defensible. The first one is the most defensible and the least used, and it is the one this project could actually justify from the mechanism it studies.
What would make borrowing from adults defensible, and how to test it
Exchangeability is testable, not merely assertable. Three concrete checks, in increasing order of strength.
- Pharmacological. Show that exposure-response for menin inhibition is the same in children and adults. Paediatric pharmacokinetic data exist from the AUGMENT-101 paediatric strata; the exposure-response comparison has not been published.
- Transcriptional. Show that the menin-dependent target-gene program, measured on treatment, is the same in infant and adult blasts. This is a sample-access question rather than a technical one, and the graph flags that on-treatment infant material is scarce (
strategy-data-and-sample-access-map). - Clinical. Show that the historical response rate of infant KMT2A-rearranged disease to a shared-mechanism agent tracks the adult rate. There is currently no such agent with both datasets.
Until at least one of these is satisfied, a borrowing design should use a robust mixture with a deliberately modest prior weight, and should pre-specify the amount of borrowing rather than letting it be chosen after seeing the data.
The number that matters to a reviewer
State the effective sample size of the prior in the protocol, in patients. A reviewer can then ask the only question that matters: would you be willing to enrol that many fewer infants on the strength of adult data?
For illustration, in the feasibility arithmetic (ana-infant-trial-feasibility-arithmetic) a design needing 93 infants for a hazard ratio of 0.47 would need roughly 60 with a prior worth 30 patients. Thirty infants is more than the entire blinatumomab study. Framing it that way makes the size of the assumption visible instead of hiding it in a hyperparameter.
| design class | Bayesian borrowing |
|---|---|
| illustrative effect | a prior worth 30 patients reduces a 93-infant design to ~60 infants |
| recommendation | pre-specify effective sample size in patients; use a robust mixture; prefer the partner axis over the age axis |
methods
[ "meta-analytic-predictive prior", "robust MAP mixture", "Bayesian hierarchical basket" ]
borrowing axes ranked
[
{
"axis": "across KMT2A partners within infants",
"defensibility": "highest"
},
{
"axis": "across fusion families with shared menin dependency",
"defensibility": "medium"
},
{
"axis": "across age within KMT2A",
"defensibility": "lowest"
}
]exchangeability tests proposed
[ "paediatric versus adult exposure-response", "on-treatment menin target-gene program", "historical cross-age response concordance for a shared-mechanism agent" ]
- Borrowing makes an underpowered infant trial look adequately powered. If exchangeability fails, the design delivers a narrow credible interval around the wrong number, and the false precision is more dangerous than the original uncertainty.
- The axis with the most data (age) is the axis with the weakest biological justification, and the temptation to use it will be strongest exactly when accrual is worst. Pre-specifying the axis before accrual difficulties appear is the only real protection.
- If an infant result is obtained by borrowing from adults, a later finding that infant biology differs invalidates the infant conclusion retrospectively, and there will be no independent infant dataset left to fall back on.
- What effective sample size would a properly fitted robust MAP prior on adult KMT2A-rearranged menin-inhibitor data contribute to an infant analysis, and has anyone computed it?
- Is the exposure-response relationship for revumenib the same in the paediatric strata of AUGMENT-101 as in adults? This is the cheapest available test of exchangeability and the data already exist.
- Can borrowing across KMT2A partners within infants be validated retrospectively using Interfant partner-stratified outcomes, which would establish the defensible axis before it is needed?
- E1established confidence 5 of 5: Multiple independent lines of evidence; treated as settled in the field.paper
Historical control information can be summarised into a meta-analytic-predictive prior whose effective sample size quantifies the information borrowed, with between-trial heterogeneity estimated from the data and robust mixture formulations limiting the consequences when the historical and current populations differ.
Summarizing historical information on controls in clinical trials · Neuenschwander B, Capkun-Niggli G, Branson M, Spiegelhalter DJ · Clinical Trials 2010What this evidence cannot show
A general methods paper; the behaviour of a MAP prior depends heavily on the prior placed on the between-trial heterogeneity parameter, which is weakly identified when few external trials exist. Infant leukemia has few external trials.
Evidence that argues against this (1)
- A meta-analytic-predictive prior quantifies what is borrowed and does not make the borrowing safe. Its effective sample size is only meaningful if the historical trials are exchangeable with the new one, and for infant KMT2A-rearranged leukaemia the candidate historical controls come from earlier protocols with different supportive care and different transplant practice. Robust mixtures limit the damage from prior-data conflict rather than preventing it. Leukemia 2021
- E2established confidence 5 of 5: Multiple independent lines of evidence; treated as settled in the field.paper
Bayesian hierarchical modelling across patient subpopulations lets a phase 2 oncology trial borrow strength between strata with the degree of borrowing adapting to observed heterogeneity.
Bayesian hierarchical modeling of patient subpopulations: efficient designs of Phase II oncology clinical trials · Berry SM, Broglio KR, Groshen S, Berry DA · Clinical Trials 2013What this evidence cannot show
Simulated operating characteristics only; frequentist error rates are not controlled by construction and must be established by simulation for each specific design.
Evidence that argues against this (1)
- Borrowing across subgroups assumes exchangeability, and infant KMT2A-rearranged disease is where that assumption is least safe: it differs from older-child disease in cell of origin, in HOXA output, in mutation burden and in outcome. Adaptive borrowing shrinks the amount borrowed when heterogeneity is OBSERVED, which requires enough patients per stratum to observe it — and the small strata are exactly the ones the method is being invoked to rescue. Statistics in Medicine 2006
- E3moderate confidence 3 of 5: One strong study, or several smaller consistent ones.paper
Infant KMT2A-rearranged ALL differs from adult KMT2A-rearranged disease in cell of origin, partner distribution and co-mutational burden, and had 3-year event-free survival below 40% with most relapses on treatment, a pattern not shared with the adult disease.
Blinatumomab Added to Chemotherapy in Infant Lymphoblastic Leukemia · van der Sluis IM, de Lorenzo P, Kotecha RS, et al. · New England Journal of Medicine 2023What this evidence cannot show
This citation supports the infant outcome pattern; the cell-of-origin and co-mutational claims rest on the mechanism and comutation entries elsewhere in this graph (`cell-type-fetal-liver-hsc`, `comut-low-mutation-burden-infant-kmt2a-r`) rather than on this paper, and should be cited from those primary sources when used. **Regraded strong -> moderate on 2026-09-20** under `concept-the-confidence-grading-rule`: this is background epidemiology quoted in the paper's introduction, not a result of this trial, so it is an inference from sources the paper cites rather than from its own data.
Evidence that argues against this (1)
- Heterogeneity within infant KMT2A-rearranged ALL is itself large enough to break borrowing between infant subgroups, not only between infants and adults. Multi-omics clustering of 84 infants resolved five integrative clusters with different master transcription factors and fusion partners - two IRX-type and three HOXA-type - and the most refractory cluster (IRX-type undifferentiated) carried RAS-pathway mutations at 100% frequency. A hierarchical model that pools KMT2A-rearranged infants as one stratum will therefore shrink estimates towards a mean that describes no actual subgroup, and the exchangeability assumption fails at the level the design treats as homogeneous. Isobe T et al. 2022
- ← related toNUP98::KDM5A (NUP98-JARID1A), t(11;12)(p15;p13)
Comparator decomposition (de Rooij 2017, PMID 28112737): RNA and exome sequencing of 99 non-DS-AMKL specimens resolved seven genomic subgroups with varying outcomes, so 'not an independent prognostic factor' against a pooled AMKL block is a power-and-comparator statement.
- ← related toTCF3::PBX1 (E2A-PBX1), t(1;19)(q23;p13.3)
Counter-evidence: Ribera 2021 (PMID 34549416) found significantly higher relapse incidence in adult TCF3-PBX1 on MRD-oriented protocols, so the paediatric intensification result does not transfer across age bands
borrowing reduces the required infant sample
fetal cell of origin is the main threat to exchangeability with adults
a second biological argument against borrowing across age
the statistical engine of a hierarchical basket