Thesis (MCom)--Stellenbosch University, 2014. / 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 aangeheg. Die
longitudinale datastel bestaan uit herhaalde metings van die toestand waarin ’n subjek verkeer
en die tydsverloop tussen waarnemings. Waarnemings van die longitudinale datastel word met
gereelde of ongereelde tussenposes onderneem totdat die subjek sterf, wanneer die studie dan
ook ten einde loop.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/95994 |
| Date | 12 1900 |
| Creators | Mafu, Thandile John |
| Contributors | Muller, Christoffel Joseph Brand, Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | Unknown |
| Type | Thesis |
| Format | 89 p. : ill. |
| Rights | Stellenbosch University |
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