@article {9349, title = {Switching nonparametric regression models for multi-curve data}, journal = {Canadian Journal of Statistics}, volume = {45}, year = {2017}, pages = {442{\textendash}460}, keywords = {EM algorithm, Functional data analysis, latent variables, machine learning, MSC 2010: Primary 62G08, nonparametric regression, power usage, secondary 62G05, switching nonparametric regression model}, issn = {1708-945X}, doi = {10.1002/cjs.11331}, url = {http://dx.doi.org/10.1002/cjs.11331}, author = {de Souza, Camila P. E. and Heckman, Nancy E. and Xu, Fan} } @article { ISI:000343808700001, title = {Switching nonparametric regression models}, journal = {JOURNAL OF NONPARAMETRIC STATISTICS}, volume = {26}, number = {4}, year = {2014}, month = {OCT 2}, pages = {617-637}, publisher = {TAYLOR \& FRANCIS LTD}, type = {Article}, address = {4 PARK SQUARE, MILTON PARK, ABINGDON OX14 4RN, OXON, ENGLAND}, abstract = {We propose a methodology to analyse data arising from a curve that, over its domain, switches among J states. We consider a sequence of response variables, where each response y depends on a covariate x according to an unobserved state z. The states form a stochastic process and their possible values are j=1, horizontal ellipsis , J. If z equals j the expected response of y is one of J unknown smooth functions evaluated at x. We call this model a switching nonparametric regression model. We develop an Expectation-Maximisation algorithm to estimate the parameters of the latent state process and the functions corresponding to the J states. We also obtain standard errors for the parameter estimates of the state process. We conduct simulation studies to analyse the frequentist properties of our estimates. We also apply the proposed methodology to the well-known motorcycle dataset treating the data as coming from more than one simulated accident run with unobserved run labels.}, keywords = {EM algorithm, latent variables, machine learning, mixture of Gaussian processes, motorcycle data, nonparametric regression}, issn = {1048-5252}, doi = {10.1080/10485252.2014.941364}, author = {de Souza, Camila P. E. and Heckman, Nancy E.} } @article {mackay_altman_longitudinal_2012, title = {A longitudinal model for magnetic resonance imaging lesion count data in multiple sclerosis patients}, journal = {Statistics in Medicine}, volume = {31}, number = {5}, year = {2012}, pages = {449{\textendash}469}, abstract = {

Magnetic resonance imaging (MRI) data are routinely collected at multiple time points during phase 2 clinical trials in multiple sclerosis. However, these data are typically summarized into a single response for each patient before analysis. Models based on these summary statistics do not allow the exploration of the trade-off between numbers of patients and numbers of scans per patient or the development of optimal schedules for MRI scanning. To address these limitations, in this paper, we develop a longitudinal model to describe one MRI outcome: the number of lesions observed on an individual MRI scan. We motivate our choice of a mixed hidden Markov model based both on novel graphical diagnostic methods applied to five real data sets and on conceptual considerations. Using this model, we compare the performance of a number of different tests of treatment effect. These include standard parametric and nonparametric tests, as well as tests based on the new model. We conduct an extensive simulation study using data generated from the longitudinal model to investigate the parameters that affect test performance and to assess size and power. We determine that the parameters of the hidden Markov chain do not substantially affect the performance of the tests. Furthermore, we describe conditions under which likelihood ratio tests based on the longitudinal model appreciably outperform the standard tests based on summary statistics. These results establish that the new model is a valuable practical tool for designing and analyzing multiple sclerosis clinical trials. Copyright {\textcopyright} 2011 John Wiley \& Sons, Ltd.

}, keywords = {clinical trials, hypothesis testing, latent variables, longitudinal count data, mixed hidden Markov model, model diagnostics}, doi = {10.1002/sim.4394}, url = {http://onlinelibrary.wiley.com/doi/10.1002/sim.4394/abstract}, author = {Altman, RM and Petkau, A.John and Vrecko, D and Smith, A} }