Statistics and Its Interface

Volume 2 (2009)

Number 4

A latent model approach to define event onset time in the presence of measurement error

Pages: 425 – 435



Ming-Hui Chen (Department of Statistics, University of Connecticut, Storrs, Conn., U.S.A.)

Peng Huang (SKCCC Oncology Biostatistics Division, School of Medicine, Johns Hopkins University, Baltimore, Maryland, U.S.A.)

Debajyoti Sinha (Department of Statistics, Florida State University, Tallahassee, Fl., U.S.A.)


For progressive diseases, it is often not so straightforward to define an onset time of certain disease condition due to disease fluctuation and clinical measurement variation. When a disease onset is claimed through the first presence of some clinical event which is subject to large measurement error, such onset time could be difficult to interpret if patients can often be seen to “recover” from the disease condition automatically.We generalize the traditional event onset time concept to control the recovery probability through the use of a stochastic process model. A simulation algorithm is provided to evaluate the recovery probability numerically. Bayesian latent residuals are developed for model assessment. This methodology is applied to define a new postural instability onset time measure using data from a Parkinson’s disease clinical trial. We show that our latent model not only captures the essential clinical features of a postural instability process, but also outperforms independent probit model and random effects model. A table of estimated recovery probabilities is provided for patients under various baseline disease conditions. This table can help physicians to determine the new postural instability onset time when different thresholds of estimated recovery probability are used in clinical practice.


binary process, Brownian motion, event onset time, latent model, probit model, random effects model

2010 Mathematics Subject Classification

Primary 62P10. Secondary 62M05.

Published 1 January 2009