Self-modeling ordinal regression with time invariant covariates - An application to prostate cancer data

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.