High dimensional biomedical data often exhibit nonlinear, heterogeneous, and manifold driven structures that challenge global parametric and tree-based models. We propose MAPLE (mapper-based Adaptive Prediction via Local Estimation), a localized prediction framework grounded in topological data analysis. The method is formulated as a nonparametric estimator of conditional class probabilities that adapts to the intrinsic geometry of the predictor space. Neighborhoods are defined through connectivity in a data-adaptive Mapper graph, enabling localized averaging within graph induced regions that capture complex structures such as branching and multi-scale heterogeneity. We introduce a statistically principled, data driven procedure for cover selection based on a bias-variance trade off, yielding optimal asymptotic scaling for interval widths and overlaps. The framework accommodates binary, nominal, and ordinal outcomes and incorporates a permutation-based variable importance measure to quantify covariate contributions in prediction. We establish theoretical guarantees, including pointwise consistency and Bayes risk consistency under standard regularity conditions. Simulations show that MAPLE consistently outperforms or matches multinomial regression, ordinal regression, and random forest, with the largest gains observed under heterogeneous and high-noise settings. Applications to Parkinson's disease progression (PPMI) and glioma classification (TCGA RNA sequencing) demonstrate strong predictive accuracy and interpretable, topology-aware summaries of underlying data structure.
Muhammad Ahsan, Priyam Das, Nitai D. Mukhopadhyay· 0 citations
Abstract Background Parkinson's disease (PD) is clinically heterogeneous, with variable progression rates that complicate clinical trial design. The data‐driven diffuse malignant (DM), intermediate (IM), and mild‐motor predominant (MMP) subtyping model has prognostic value but lacks disease duration–specific thresholds for prospective use in disease‐modifying trials. Objective To define year‐specific percentile thresholds for key motor and non‐motor measures within the first 5 years after diagnosis to enable real‐time PD subtyping and assess progression patterns across subtypes. Methods We analyzed de‐identified PPMI data (downloaded April 22, 2026) from 1030 individuals with idiopathic PD. For each disease year, we computed percentiles for a composite motor score (MDS‐UPDRS II + III + PIGD) and non‐motor measures (MoCA, RBDSQ, SCOPA‐AUT). Thresholds were set at the 75th percentile for motor, RBDSQ, and SCOPA‐AUT, and the 25th percentile for MoCA, and applied annually to classify DM‐, IM‐, and MMP‐PD. Subtype stability (years 1–5) and progression were assessed using 25 predefined PPMI milestones. Kaplan–Meier and Cox regression models evaluated time to first milestone. Results Percentile thresholds worsened progressively over time, paralleling cohort‐level decline. DM‐PD prevalence ranged from 19.2–20.5% (IM 41.8–44.4%; MMP 35.1–38.8%). At baseline, clinical measures differed significantly across subtypes. Compared to MMP‐PD, DM‐PD (HR 3.03; 95% CI: 2.30–3.97) and IM‐PD (HR 1.48; 95% CI: 1.19–1.84) showed faster progression. Conclusions We establish disease duration–specific percentiles for prospective application of the DM/IM/MMP subtyping model, supporting patient stratification and enrichment in disease‐modifying trials.
Ahmed Negida, Nitai D. Mukhopadhyay, Brian D Berman et al.· Movement Disorders Clinical...· 0 citations