A Bayesian analysis of multiple interval-censored failure time events with application to AIDS data

[摘要] English: The measure of time to event (failure) for units on longitudinal clinical visitscannot always be ascertained exactly. Instead only time intervals within which theevent occurred may be recorded. That being the case, each unit's failure will bedescribed 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 byendpoints within which the event has occurred. These endpoints may encompassseveral intervals, hence overlapping intervals across units. Furthermore, someunits 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 asingle unit resulting in several failure times that inevitably are dependent. Allthese prescribe an interval-censored survival data with multiple-failure times.Three models of analysing interval-censored survival data with two failure timeswere applied to four sets of data. For the distribution free methods, Cox's hazardwith either a log-log transform or logit transform on the baseline conditionalsurvival probabilities was used to derive the likelihood. The Independenceassumption model (lW) work under the assumption that the lifetimes areindependent and any dependence exists through the use of common covariates.The second model that do not necessarily assume independence, computes thejoint failure probabilities for two lifetimes by Bayes' rule of conditioning on theinterval of failure for one lifetime, hence Conditional Bivariate model (CB). The useof Clayton and Farley-Morgenstern bivariate Copulas (CC) with inbuiltdependence parameter was the other model. For parametric models the IW and CCmethods were applied to the data sets on the assumption that the marginaldistribution of the lifetimes is Weibull.The traditional classical estimation method of Newton-Raphson was used to findoptimum parameter estimates and their variances stabilized using a sandwichestimator, where possible. Bayesian methods combine the data with priorinformation. Thus for either transforms, two proper priors were derived, of whichtheir combination with the likelihood resulted in a posterior function. To estimatethe entire distribution of a parameter from non-standard posterior functions, twoMarkov Chain Monte Carlo (MCMC) methods were used. The Gibbs Samplermethod samples in turn observations from the conditional distribution of aparameter in question, while holding other parameters constant. For intractablycomplex posterior functions, the Metropolis-Hastings method of sampling vectorsof parameter values in blocks from a Multivariate Normal proposal density wasused.The analysis of ACTG175data revealed that increase in levels of HIV RNA precededecline in CD4 cell counts. There is a strong dependence between the two failuretimes, hence restricting the use of the independence model. The most preferredmodels are using copulas and the conditional bivariate model. It was shown thatARV's actually improves a patient's lifetime at varying rates, with combinationtreatment performing better. The worrying issue is the resistance that HIV virusdevelops against the drugs. This is evidenced by the adverse effect the previoususe 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 patientsdisplaying signs of AIDS at entry respond negatively to drugs.

[发布机构] University of the Free State