arXiv subjects

Margaret Hoch

Publications and source records attributed to Margaret Hoch.

2 recordsLinked to original sources

arXiv2026

A Review of Methods and Practices for Missing Data in Sequential Multiple Assignment Randomized Trials (SMARTs): An Ancillary Study of a Scoping Review

Background: Missing data poses an acute threat to sequential multiple assignment randomized trial (SMART) analyses because of the sequential treatment structure and response-dependent re-randomization. Objectives: This study aimed to (1) review the current statistical methods for handling missing data in SMARTs, and (2) characterize how missing data is reported and handled in published SMARTs. Methods: We conducted a narrative review of statistical methods developed for missing data in SMARTs. Additionally, we conducted a pre-specified secondary extraction of a previously published scoping review of SMARTs focused on missing data. Extraction captured attrition rates, methods for handling missingness, and planned versus performed missing data analyses. Results: Seven methodological papers were identified; nearly all assume missing at random (MAR), and only one addresses the full set of SMART-specific missingness types. Across 30 published SMARTs, median overall attrition was 18.1% (range 0.6%-56.5%). Methods used to address missing data were described in 80% of the manuscripts; mixed-model methods were most common (30%). Among 14 studies with paired protocols, sensitivity analyses were pre-specified in 2 (14%). Conclusions: SMART-specific methodology for missing data is limited, and a substantial gap exists between available methodology and current SMART practice.

stat.ME↗

arXiv2026

Linear Regression Using Principal Components from General Hilbert-Space-Valued Covariates

We introduce Adaptive Subspace PCA (AS-PCA), a framework for principal component analysis of random elements in a general separable Hilbert space. AS-PCA projects the covariance operator onto a data-adaptive finite-dimensional subspace prior to eigendecomposition, requiring no kernel specification and accommodating multi-dimensional functional objects including images and surfaces. Under the second-moment condition, we prove a Donsker theorem for Hilbert-space-valued empirical processes and use it to establish uniform consistency and joint Gaussian limits for the leading eigenpairs. A data-driven diagnostic verifies projection accuracy, and a consistent proportion-of-variance-explained rule selects the number of components. Building on AS-PCA, we construct Hilbert-Space Principal Component Regression (HS-PCR) for models combining Euclidean and Hilbert-space-valued covariates. The HS-PCR estimator is root-$n$ consistent and asymptotically normal, with an explicit influence function decomposition accounting for eigenfunction estimation uncertainty. Both nonparametric and wild bootstrap procedures are shown to be asymptotically valid. Simulations with two- and three-dimensional imaging predictors confirm accurate eigenstructure recovery and nominal bootstrap coverage. HS-PCR is applied to Alzheimer's Disease Neuroimaging Initiative data in regression and precision-medicine settings.

math.ST↗