A Bayesian analysis of multiple interval-censored failure time events with application to AIDS data
| dc.contributor.advisor | Groenewald, C. N. | |
| dc.contributor.advisor | De Waal, Daniel J. | |
| dc.contributor.author | Mokgatlhe, Lucky | |
| dc.date.accessioned | 2017-05-10T06:19:17Z | |
| dc.date.available | 2017-05-10T06:19:17Z | |
| dc.date.issued | 2003-05 | |
| dc.description.abstract | English: The measure of time to event (failure) for units on longitudinal clinical visits cannot always be ascertained exactly. Instead only time intervals within which the event occurred may be recorded. That being the case, each unit's failure will be described by a single interval resulting in grouped interval data over the sample. Yet, due to non-compliance to visits by some units, failure will be described by endpoints within which the event has occurred. These endpoints may encompass several intervals, hence overlapping intervals across units. Furthermore, some units may not realize the event of interest within the preset duration of study, hence are censored. Finally, several events of interest can be investigated on a single unit resulting in several failure times that inevitably are dependent. All these prescribe an interval-censored survival data with multiple-failure times. Three models of analysing interval-censored survival data with two failure times were applied to four sets of data. For the distribution free methods, Cox's hazard with either a log-log transform or logit transform on the baseline conditional survival probabilities was used to derive the likelihood. The Independence assumption model (lW) work under the assumption that the lifetimes are independent and any dependence exists through the use of common covariates. The second model that do not necessarily assume independence, computes the joint failure probabilities for two lifetimes by Bayes' rule of conditioning on the interval of failure for one lifetime, hence Conditional Bivariate model (CB). The use of Clayton and Farley-Morgenstern bivariate Copulas (CC) with inbuilt dependence parameter was the other model. For parametric models the IW and CC methods were applied to the data sets on the assumption that the marginal distribution of the lifetimes is Weibull. The traditional classical estimation method of Newton-Raphson was used to find optimum parameter estimates and their variances stabilized using a sandwich estimator, where possible. Bayesian methods combine the data with prior information. Thus for either transforms, two proper priors were derived, of which their combination with the likelihood resulted in a posterior function. To estimate the entire distribution of a parameter from non-standard posterior functions, two Markov Chain Monte Carlo (MCMC) methods were used. The Gibbs Sampler method samples in turn observations from the conditional distribution of a parameter in question, while holding other parameters constant. For intractably complex posterior functions, the Metropolis-Hastings method of sampling vectors of parameter values in blocks from a Multivariate Normal proposal density was used. The analysis of ACTG175data revealed that increase in levels of HIV RNA precede decline in CD4 cell counts. There is a strong dependence between the two failure times, hence restricting the use of the independence model. The most preferred models are using copulas and the conditional bivariate model. It was shown that ARV's actually improves a patient's lifetime at varying rates, with combination treatment performing better. The worrying issue is the resistance that HIV virus develops against the drugs. This is evidenced by the adverse effect the previous use of ARV's has on patients, in that a new drug used on them has less effect. Finally it is important that patients start therapy at early stages since patients displaying signs of AIDS at entry respond negatively to drugs. | en_ZA |
| dc.description.abstract | Afrikaans: Tyd tot 'n gebeurtenis (faling) van eenhede op 'n regiment van longitudinale kliniese besoeke kan nie altyd presies bepaal word nie. Gewoonlik kan net 'n interval waarin 'n gebeurtenis plaasgevind het bepaal word. In so 'n geval word elke eenheid se faling beskryf deur 'n enkele interval wat lei tot gegroepeerde data oor die hele steekproef. Verder, as gevolg van nie-nakornings van besoeke deur sommige eenhede, kan die falings slegs beskryf word deur die eindpunte van die tydperk waarin die gebeurtenis plaasgevind het. Hierdie eindpunte mag verskeie intervalle insluit, en kryons dus oorvleuende tydperke oor eenhede. Verder mag die gebeurtenis van belang by sekere eenhede nie plaasvind binne die voorafbepaalde tydperk van studie nie, en is dus gesensoreerd. Laastens, verskeie gebeurtenisse van belang kan ondersoek word op In enkele eenheid. Die resultaat is dan meervoudige falingstye wat uiteraard dan afhanklik is. Bogenoemde situasie word dan beskryf as interval-gesensoreerde oorlewingsdata met meervoudige falingstye. Drie modelle vir die analise van interval-gesensoreerde oorlewingsdata met twee' falingstye is toegepas op vier data stele. Vir verdelingsvrye metodes is Cox se gevaarfunksie met of 'n log-log transformasie of 'n logit transformasie op die basislyn voorwaardelike oorlewingswaarskynlikhede gebruik om die aanneemlikheidsfunksie af te lei. Die Onafhanklikheidsaanname model (IW) neem aan dat die leeftye inherent onafhanklik is en dat afhanklikheid slegs ingebring word deur gemeenskaplike koveranderlikes. Die tweede model aanvaar nie onafhanklikheid nie, maar bereken die gesamentlike falingswaarskynlikhede deur die voorwaardelike waarskynlikheid vir die interval van een leeftyd gegee die ander leeftyd se interval, te bereken. Dit is die Voorwaardelike tweeveranderlike model (CB). Die Clayton en Farley-Morgenstern tweeveranderlike Copulas (CC) met ingeboude afhanklikheidsparameters is die derde model. Vir parametriese modelle is die lW en CC metodes toegepas op die data onder die aanname dat die randverdelings van die leeftye Weibull is. Die traditionele klassieke beramingsmetode van Newton-Raphson is gebruik om die optimale beramers of modus van die afgeleide aanneernlikheidsfunksie te vind waar moontlik. Bayes metodes kombineer die data met a priori informasie. Vir elk van die twee transformasies is twee nie-inligtende prior verdelings algelei, wat se kombinasie met die aanneemlikheidsfunksie lei tot 'n posterior funksie. Om die volledige verdeling van 'n parameter te beraam uit nie-standaard posterior funksies is twee Markov Ketting Monte Carlo (MCMC) metodes gebruik. Die Gibbs steekproefnemingsmetode neem waarnemings uit die voorwaardelike verdeling van 'n parameter, gegee die ander parameters. Vir nie-standaard komplekse posterior funksies is die Metropolis-Hastings metode gebruik deur In vector van moontlike parameter waardes in 'n blok uit 'n surrogaat verdeling te trek. Die analise van ACTG175 dui aan dat toename in vlakke van MIV RNS die afname van CD4 sell tellings voorafgaan. Daar is In sterk afhanklikheid tussen die twee falingstye. wat dus die gebruik van die onafhanklikheidsaanname model beperk. Die meer aanvaarbare modelle gebruik copulas en ook die voorwaardelike tweeveranderlike model. Dit is aangetoon dat die gebruik van ARV In pasiënt se leeftyd kan verleng, met kombinasie behandelings wat die beste resultate gee. In Sorgwekkende resultaat is dat die MIV virus In weerstand teen die middels ontwikkel. Dit blyk uit die nadelige effek wat vorige gebruik van ARV op In pasiënt het, deurdat In nuwe middel dan minder effek het. Laastens is dit belangrik dat In pasiënt op In vroë stadium behandeling begin aangesien pasiënte wat al tekens van VIGS wys negatief kan reageer op behandeling. | af |
| dc.identifier.uri | http://hdl.handle.net/11660/6202 | |
| dc.language.iso | en | en_ZA |
| dc.publisher | University of the Free State | en_ZA |
| dc.rights.holder | University of the Free State | en_ZA |
| dc.subject | AIDS data | en_ZA |
| dc.subject | Bayes | en_ZA |
| dc.subject | Copula | en_ZA |
| dc.subject | Dependence | en_ZA |
| dc.subject | Hazard rate | en_ZA |
| dc.subject | Interval-censoring | en_ZA |
| dc.subject | Metropolis-Hastings Algorithm | en_ZA |
| dc.subject | Visiting-compliance | en_ZA |
| dc.subject | Weibull | en_ZA |
| dc.subject | Multiple-failure | en_ZA |
| dc.subject | Metropolis-Hastings algorithm | en_ZA |
| dc.subject | Bayesian statistical decision theory | en_ZA |
| dc.subject | Time-series analysis | en_ZA |
| dc.subject | Failure time data analysis | en_ZA |
| dc.subject | Thesis (Ph.D. (Mathematical Statistics))--University of the Free State, 2003 | en_ZA |
| dc.title | A Bayesian analysis of multiple interval-censored failure time events with application to AIDS data | en_ZA |
| dc.type | Thesis | en_ZA |