Estimating disease onset from change points of markers measured with error

Huntington disease is an autosomal dominant, neurodegenerative disease without clearly identified biomarkers for when motor-onset occurs. Current standards to determine motor-onset rely on a clinician's subjective judgment that a patient's extrapyramidal signs are unequivocally associated with Huntington disease. This subjectivity can lead to error which could be overcome using an objective, data-driven metric that determines motor-onset. Recent studies of motor-sign decline-the longitudinal degeneration of motor-ability in patients-have revealed that motor-onset is closely related to an inflection point in its longitudinal trajectory. We propose a nonlinear location-shift marker model that captures this motor-sign decline and assesses how its inflection point is linked to other markers of Huntington disease progression. We propose two estimating procedures to estimate this model and its inflection point: one is a parametric method using nonlinear mixed effects model and the other one is a multi-stage nonparametric approach, which we developed. In an empirical study, the parametric approach was sensitive to correct specification of the mean structure of the longitudinal data. In contrast, our multi-stage nonparametric procedure consistently produced unbiased estimates regardless of the true mean structure. Applying our multi-stage nonparametric estimator to Neurobiological Predictors of Huntington Disease, a large observational study of Huntington disease, leads to earlier prediction of motor-onset compared to the clinician's subjective judgment.