Survival analysis in Spinocerebellar Ataxia type 7 using Random Forests

Abstract

Introduction: Spinocerebellar ataxia type 7 (SCA7) is a neurodegenerative disorder caused by a CAG repeat expansion in the ATXN7 gene. Modeling its natural history is highly relevant for genetic counseling and for establishing historical control cohorts for future clinical trials. Given that classical survival analysis methods (parametric and semi-parametric) fail to capture complex interactions, we propose the use of the Random Survival Forests (RSF) algorithm to overcome this limitation.

Objective: To evaluate survival in patients with SCA7 using RSF to rank mortality risk factors and determine their biological effect.

Methodology: Retrospective cohort study with 117 patients diagnosed with SCA7, including cases with motor onset <40 years and a short allele in normal ranges (mean age 35.8 years; 33 events, 84 censored). Baseline variables included: age at motor onset (AAO, mean 23.4 years), CAG repeats (mean 53.5), short allele (mean 10.4), sex (60 males, 57 females), parental origin of the mutation (58 paternal, 53 maternal, 6 unknown), and location. An RSF model was trained using cross-validation (5-folds). Predictive accuracy was measured with Uno's IPCW C-index and the Out-of-Bag (OOB) metric. Clinical interpretation was performed using permutation variable importance (VIMP) and SHAP dependence plots.

Results: The estimated median overall survival (Kaplan-Meier) was 21.97 years (95% CI: 19.15-29.51). The RSF model demonstrated high discrimination capacity (OOB=0.89, Uno's C-index=0.85). Only the CAG expansion, AAO, and parental origin maintained predictive value. The CAG expansion was the main determinant of mortality (VIMP=0.155), followed by AAO (VIMP=0.087). The SHAP plot for CAG showed that the risk remains stable up to 45 repeats, at which point it increases abruptly. Furthermore, it revealed a strong synergistic interaction; at the same triplet length, an earlier AAO significantly worsens the risk.

Conclusions: The RSF algorithm effectively captures the non-linear genetic interactions of SCA7. It was demonstrated that the CAG expansion and age at onset interact to define survival in this classic and early-onset cohort. This objective prognostic assessment allows for personalized interventions and lays the foundation for a historical cohort, which is essential as a control group to evaluate the efficacy of future clinical and therapeutic trials.