The Price of Anatomical Precision: What Stands in the Way of Finding the Right Hippocampal Subfield bioRxiv

Original: "Sample size buys detection, not localisation: an identifiability limit for hippocampal subfield morphometry"
· R Debona, R Walz
b42w:2608.90046 · the paper's page · 2026-08-24 · CC BY 4.0 · 6 min
Correlations between hippocampal subfields make them hard to tell apart, and even perfect data cannot save you at typical effect sizes.

Context

Automated segmentation has made measuring the internal structure of the hippocampus routine: a standard scan yields volumes for a dozen or more subfields, and studies of aging, memory, and disease now report which specific subfield is linked to an outcome. Yet the results of these studies contradict one another: meta-analyses disagree even on the sign of the effect, and individual papers name different structures with no apparent link to sample size or protocol. A common explanation for these contradictions is insufficient statistical power, but debates about reproducibility only address whether an association replicates, not whether its anatomical localization can be recovered at all. This work stands apart: nearby in the archive are studies on tissue-response diagnostics, growing organoids, cell division with memory retention, living organs in a Petri dish, miniature brain habituation, speech compression, cell atlases, and precise stimulation, but none of them tested whether a real subfield design can name the correct subfield when a true effect exists.

Methods

The authors used data from 638 participants in the Cam-CAN cohort (age 18.6–89.0 years, mean 55.2). Volumes of 36 hippocampal subfields (18 per hemisphere) were obtained with FreeSurfer 8.2.0 using the Iglesias probabilistic atlas; volumes were log-transformed, residualized for intracranial volume, age (spline), sex, and education, then standardized. They extracted a global factor (the mean across all subfields) and local contrasts orthogonal to it. The primary model was a regularized horseshoe with a prior expectation of four significant predictors. To test recoverability, they injected artificial effects of known location and magnitude (2% or 5% of explained variance) into the real data and into a 'whitened' copy of the same design in which correlations between subfields were removed via ZCA whitening. In each repetition, both versions received identical subsamples, columns, true predictors, signs, and noise vector; only the scale of the coefficients differed. They compared three estimators: ridge regression, the lasso path, and the regularized horseshoe. The grid included 4 sample sizes (100, 200, 400, 638), 2 effect sizes, and 80 paired repetitions per cell; they additionally varied parcel granularity (6, 12, 18, 36 subfields) and the effect injection scheme.

Results

In the observed data, none of the 36 local coefficients was distinguishable from zero: not a single 89% interval excluded zero, and the posterior mean of the effective number of nonzero coefficients was 1.89 against a prior expectation of 4. The global factor had a coefficient of +0.067 (89% interval [0.004, 0.130]) and explained 0.6% of the outcome variance. The local block added only 0.005 to the Bayesian R², and the difference in expected log predictive density did not exceed 4 units for any model. Split-half stability was extremely low: the correlation of coefficient vectors averaged +0.12, the top-6 selection overlap was 0.08, while repeated runs on the same data gave perfect agreement (overlap 1.00). In the injection experiment, recovery of the full set of three subfields at a 5% effect was 20.8% at n=100 and 69.2% at n=638 for the real design, versus 30.0% and 85.0% for the whitened one. At a 2% effect, the corresponding values were 15.4% and 38.3% versus 15.4% and 53.3%. Fitting a saturation curve gave a recovery ceiling of 0.944 (real) and 1.05 (whitened) at a 5% effect; at a 2% effect the ceilings were 0.544 and 0.738. The sample size required to reach a criterion of 0.8 at a 5% effect was 1752–2803 participants for the real design and 893–1151 for the whitened one, meaning correlation multiplies the required sample size by 1.5–3.1. At a 2% effect, no design reached the criterion at any sample size. Coarsening the parcelation to 6 subfields gave recovery of only 0.750 (real) and 0.783 (whitened) at a 2% effect. The choice of estimator proved more important than correlation: at n=638 and a 5% effect, recovery was 24.6% for ridge, 69.2% for the horseshoe, and 76.7% for the lasso. 58.6% of subfield pairs were interchangeable (difference in leave-one-out R² less than 0.002).

Implications

This work brings to hippocampal research something that neighboring studies of cell atlases and organoids lack: a direct empirical assessment of whether a real subfield design can name the correct subfield when a true effect exists. Unlike studies that merely report associations or measure segmentation reliability, this is the first counterfactual experiment with paired 'whitened' data, allowing the contribution of correlation structure to be separated from that of sample size. It is not just another association study but a calibration surface on which the realism of a planned study can be assessed in advance. The main takeaway for science: standard conclusions about effect localization in a specific subfield often have no statistical basis, and the practice of naming a 'winner' among highly correlated subfields should give way to reporting equivalence classes.

Future development

The topic could evolve toward open tools for pre-calibrating study designs: a researcher could specify their parcelation, expected effect size, and available sample size to get a realistic estimate of the probability of correct localization. Reporting standards may emerge that require stating an equivalence class instead of a single subfield, along with recommendations for choosing an estimator, since the difference between methods turned out to be larger than the effect of correlation. Extending the 'injected effects' approach to other brain regions and other modalities where multicollinearity is also high is a promising direction.

Impact

The results will directly affect the planning and interpretation of studies in cognitive neuroscience, neuropsychology, and psychiatry that use hippocampal subfield volumes. They are also important for genetic studies, where adjusting for total hippocampal volume is already standard practice, and for the development of clinical biomarkers based on fine-grained anatomy.

Next steps

Immediate next steps include recalculating calibration curves for other segmentation tools (such as ASHS) and for other cohorts to assess the transferability of the results. It is also necessary to check whether the conclusions hold with other cognitive outcomes and in longitudinal designs.

Key open problems

This work is directly tied to the fundamental problem of irreproducibility in neuroimaging: it shows that contradictions in the hippocampal subfield literature may stem not only from low power but also from a fundamental non-identifiability of localization at typical effect sizes. This casts doubt on the interpretation of many published results and calls for a revision of evidentiary standards in structure-behavior research.

The condition number of the design matrix was 1727, and the median variance inflation factor was 7.3, meaning that information about many subfields is almost entirely duplicated by their neighbors. At the same time, 32 of the 36 bivariate correlations with the cognitive factor were positive, so a negative coefficient in a multivariate model would have to be interpreted as suppression rather than an inverse relationship.

A(n) = a - b n^{-1/2}
Probability of recovering the full set of subfields as a function of sample size: parameter a is the asymptotic ceiling, b is the rate of approach to it.

Key numbers

  • Participants: 638
  • Hippocampal subfields: 36
  • Condition number of the design matrix: 1727
  • Median variance inflation factor: 7.3
  • Share of interchangeable subfield pairs: 58.6%
  • Multiplier of required sample size due to correlation: 1.5–3.1

Take the whole work

Not published on arXiv. Here are its page, the PDF and the formalization: you can check it yourself, not only read our account.

Concepts
sample size hippocampus