Fitting parametric frailty and mixture models under biased sampling

Economou, P; Caroni, C

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.publisher	ROUTLEDGE JOURNALS, TAYLOR & FRANCIS LTD	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