Selective inference for pruned interaction trees with known unequal variances in randomized trials
Abstract
Interaction trees reuse outcomes to discover treatment-effect heterogeneity, complicating inference after growth and pruning. We develop selective inference for generalized least-squares (GLS) interaction trees with a common covariate basis and known unequal variances. Under a conditional Gaussian model with positive diagonal covariance, weighted orthogonality reduces survival under additive fixed-penalty pruning to one quadratic inequality supplementing the growth event. This yields exact finite-sample conditional tests and confidence intervals, with retained-path and complete-tree inference agreeing on compatible sections. Under causal identification and a correct reference prognosis, the pruning-invariant GLS target is a signed finite-design weighted contrast of conditional average treatment effects. Simulations at n=100,200,400,800 and maximum depths one to three search all adjacent-observation midpoints, support calibration and demonstrate over-rejection when pruning survival is omitted. Compared with a 50:50 honest procedure, full-data learning improves reference-split recovery in some small-sample settings. Root-level median intervals can be shorter, while deep-node intervals and upper tails can be much wider; these comparisons concern each procedure's selected targets. Estimating a common scale with the variance ratio fixed produces modest changes in Selective coverage in the settings examined, without extending the exact guarantee. An exploratory ACTG 175 analysis provides a working-model illustration with estimated arm variances.
Related
- RECaST-Surv: A Calibrated Borrowing Method for Survival Endpoints in Unequal Randomized Trials
- More Data, Worse Inference: How the Imputation Model Decides an Interaction Effect
- Selective Randomization Inference for Interference
- Distributed Selective Inference for Quantile Regression
- Selective Inference in Growth Curve Models
BibTeX
@misc{nakamura2026selective,
title = {{Selective inference for pruned interaction trees with known unequal variances in randomized trials}},
author = {Tomoshige Nakamura},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01134},
eprint = {2611.01134},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01134},
}
RIS
TY - UNPB
TI - Selective inference for pruned interaction trees with known unequal variances in randomized trials
AU - Tomoshige Nakamura
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01134
UR - https://arxiv.org/abs/2611.01134
AB - Interaction trees reuse outcomes to discover treatment-effect heterogeneity, complicating inference after growth and pruning. We develop selective inference for generalized least-squares (GLS) interaction trees with a common covariate basis and known unequal variances. Under a conditional Gaussian model with positive diagonal covariance, weighted orthogonality reduces survival under additive fixed-penalty pruning to one quadratic inequality supplementing the growth event. This yields exact finite-sample conditional tests and confidence intervals, with retained-path and complete-tree inference agreeing on compatible sections. Under causal identification and a correct reference prognosis, the pruning-invariant GLS target is a signed finite-design weighted contrast of conditional average treatment effects. Simulations at n=100,200,400,800 and maximum depths one to three search all adjacent-observation midpoints, support calibration and demonstrate over-rejection when pruning survival is omitted. Compared with a 50:50 honest procedure, full-data learning improves reference-split recovery in some small-sample settings. Root-level median intervals can be shorter, while deep-node intervals and upper tails can be much wider; these comparisons concern each procedure's selected targets. Estimating a common scale with the variance ratio fixed produces modest changes in Selective coverage in the settings examined, without extending the exact guarantee. An exploratory ACTG 175 analysis provides a working-model illustration with estimated arm variances.
ER -