title: Self-modeling ordinal regression with time invariant covariates - An application to prostate cancer data.
abstract: In a prostate cancer study, the severity of genito-urinary (bladder) toxicity is assessed for patients who were given different doses of radiation. The ordinal responses (severity of side effects) are recorded longitudinally along with the cancer stage of a patient. Differences among the patients due to time-invariant covariates are captured by the parameters. To build up a suitable framework for an analysis of such data, we propose the use of self-modeling ordinal longitudinal model where the conditional cumulative probabilities for a category of an outcome have a relation with shape-invariant model. Since patients suffering from a common disease usually exhibit a similar pattern, it is natural to build up a nonlinear model that is shape invariant. The model is essentially semi-parametric where the population time curve is modeled with penalized regression spline. Monte Carlo expectation maximization technique is used to estimate the parameters of the model. A simulation study is also carried out to justify the methodology used.
authors.affiliation: 1 Department of Statistics, IMECC, University of Campinas, SP, Brazil.
authors.forename: Aliakbar Mastani
authors.initials: AM
authors.lastname: Shirazi
authors.affiliation: 2 Department of Statistics, University of Calcutta, India.
authors.forename: Kalyan
authors.initials: K
authors.lastname: Das
authors.affiliation: 1 Department of Statistics, IMECC, University of Campinas, SP, Brazil.
authors.forename: Aluisio
authors.initials: A
authors.lastname: Pinheiro
mesh_terms: D003627:Data Interpretation, Statistical; D018450:Disease Progression; D006801:Humans; D008297:Male; D015233:Models, Statistical; D011471:Prostatic Neoplasms / Q000532:radiotherapy*; D012044:Regression Analysis; D012720:Severity of Illness Index; D013997:Time Factors; D016896:Treatment Outcome
keywords: Longitudinal data; nonparametric; penalized spline; self-modeling