AbstractsStatistics

ENGLISH ABSTRACT: A multi-state model is a way of describing a process in which a subject moves through a series of states in continuous time. The series of states might be the measurement of a disease for example in state 1 we might have subjects that are free from disease, in state 2 we might have subjects that have a disease but the disease is mild, in state 3 we might have subjects having a severe disease and in last state 4 we have those that die because of the disease. So Markov models estimates the transition probabilities and transition intensity rates that describe the movement of subjects between these states. The transition might be for example a particular subject or patient might be slightly sick at age 30 but after 5 years he or she might be worse. So Markov model will estimate what probability will be for that patient for moving from state 2 to state 3. Markov multi-state models were studied in this thesis with the view of assessing the Markov models assumptions such as homogeneity of the transition rates through time, homogeneity of the transition rates across the subject population and Markov property or assumption. The assessments of these assumptions were based on simulated panel or longitudinal dataset which was simulated using the R package named msm package developed by Christopher Jackson (2014). The R code that was written using this package is attached as appendix. Longitudinal dataset consists of repeated measurements of the state of a subject and the time between observations. The period of time with observations in longitudinal dataset is being made on subject at regular or irregular time intervals until the subject dies then the study ends. AFRIKAANSE OPSOMMING: ’n Meertoestandmodel is ’n manier om ’n proses te beskryf waarin ’n subjek in ’n ononderbroke tydperk deur verskeie toestande beweeg. Die verskillende toestande kan byvoorbeeld vir die meting van siekte gebruik word, waar toestand 1 uit gesonde subjekte bestaan, toestand 2 uit subjekte wat siek is, dog slegs matig, toestand 3 uit subjekte wat ernstig siek is, en toestand 4 uit subjekte wat aan die siekte sterf. ’n Markov-model raam die oorgangswaarskynlikhede en -intensiteit wat die subjekte se vordering deur hierdie toestande beskryf. Die oorgang is byvoorbeeld wanneer ’n bepaalde subjek of pasiënt op 30-jarige ouderdom net lig aangetas is, maar na vyf jaar veel ernstiger siek is. Die Markov-model raam dus die waarskynlikheid dat so ’n pasiënt van toestand 2 tot toestand 3 sal vorder. Hierdie tesis het ondersoek ingestel na Markov-meertoestandmodelle ten einde die aannames van die modelle, soos die homogeniteit van oorgangstempo’s oor tyd, die homogeniteit van oorgangstempo’s oor die subjekpopulasie en tipiese Markov-eienskappe, te beoordeel. Die beoordeling van hierdie aannames was gegrond op ’n gesimuleerde paneel of longitudinale datastel wat met behulp van Christopher Jackson (2014) se R-pakket genaamd msm gesimuleer is. Die R-kode wat met behulp van hierdie pakket geskryf is, word as bylae…