Fitting parametric frailty and mixture models under biased sampling

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dc.contributor.author Economou, P en
dc.contributor.author Caroni, C en
dc.date.accessioned 2014-03-01T01:30:43Z
dc.date.available 2014-03-01T01:30:43Z
dc.date.issued 2009 en
dc.identifier.issn 0266-4763 en
dc.identifier.uri https://dspace.lib.ntua.gr/xmlui/handle/123456789/19617
dc.subject Burr distribution en
dc.subject EM algorithm en
dc.subject Finite mixture en
dc.subject Frailty en
dc.subject Type I right censoring en
dc.subject Viased sampling en
dc.subject Weibull distribution en
dc.subject Weighted distribution en
dc.subject.classification Statistics & Probability en
dc.subject.other WEIBULL-DISTRIBUTIONS en
dc.subject.other RELIABILITY-MEASURES en
dc.subject.other HETEROGENEITY en
dc.subject.other DURATION en
dc.title Fitting parametric frailty and mixture models under biased sampling en
heal.type journalArticle en
heal.identifier.primary 10.1080/02664760802382525 en
heal.identifier.secondary http://dx.doi.org/10.1080/02664760802382525 en
heal.language English en
heal.publicationDate 2009 en
heal.abstract Biased sampling from an underlying distribution with p.d.f. f(t), t>0, implies that observations follow the weighted distribution with p.d.f. fw(t)=w(t)f(t)/E[w(T)] for a known weight function w. In particular, the function w(t)=tα has important applications, including length-biased sampling (α=1) and area-biased sampling (α=2). We first consider here the maximum likelihood estimation of the parameters of a distribution f(t) under biased sampling from a censored population in a proportional hazards frailty model where a baseline distribution (e.g. Weibull) is mixed with a continuous frailty distribution (e.g. Gamma). A right-censored observation contributes a term proportional to w(t)S(t) to the likelihood; this is not the same as Sw(t), so the problem of fitting the model does not simply reduce to fitting the weighted distribution. We present results on the distribution of frailty in the weighted distribution and develop an EM algorithm for estimating the parameters of the model in the important Weibull-Gamma case. We also give results for the case where f(t) is a finite mixture distribution. Results are presented for uncensored data and for Type I right censoring. Simulation results are presented, and the methods are illustrated on a set of lifetime data. en
heal.journalName Journal of Applied Statistics en
dc.identifier.doi 10.1080/02664760802382525 en
dc.identifier.isi ISI:000260573200006 en
dc.identifier.volume 36 en
dc.identifier.issue 1 en
dc.identifier.spage 53 en
dc.identifier.epage 66 en

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