Transcript Dia 1
Semantics and History of the term frailty Luc Duchateau Ghent University, Belgium Semantics of term frailty Medical field: gerontology Frail people higher morbidity/mortality risk Determine frailty of a person (e.g. Get-up and Go test) Frailty: fixed effect, time varying, surrogate Modelling: statistics Frailty often at higher aggregation level (e.g. hospital in multicenter clinical trial) Frailty: random effect, time constant, estimable History of term frailty - Beard (1) Introduced by Beard (1959) in univariate setting to improve population mortality modelling by allowing heterogeneity Beard (1959) starts from Makeham’s law (1868) with the constant hazard and with the hazard increases with time Longevity factor is added to model History of term frailty- Beard (2) Beard’s model Population survival function Population hazard function Hazard at time t for subject with frailty u Survival at time t for subject with frailty u History of term frailty - Vaupel (1) Term frailty first introduced by Vaupel (1979) in univariate setting to obtain individual mortality curve from population mortality curve For the case of no covariates Frailty – two subpopulations (1) Vaupel and Yashin (1985) studied heterogeneity due to two subpopulations Population 1: Population 2: Frailty – two subpopulations (2) Smokers:high and low recidivism rate R program age<-seq(0,75) mu1.1<-rep(0.06,76);mu1.2<-rep(0.08,76) pi1.0<-0.8 pi1<-(pi1.0*exp(-age*mu1.1))/(pi1.0*exp(-age*mu1.1)+(1-pi1.0)*exp(age*mu1.2)) mu1<-pi1*mu1.1+(1-pi1)*mu1.2 plot(age,mu1,type="n",xlab="Time(years)",ylab="Hazard",axes=F,ylim=c(0. 05,0.09)) box();axis(1,lwd=0.5);axis(2,lwd=0.5) lines(age,mu1);lines(age,mu1.1,lty=2);lines(age,mu1.2,lty=2) Frailty – two subpopulations (3) Reliability engineering Frailty – two subpopulations (4) Two hazards increasing at different rates Frailty – two subpopulations (5) Two parallel hazards (at log scale) Exercise Assume that the population of heroine addicts consists of two subpopulations. The first subpopulation (80%) has a constant monthly hazard of quitting drug use of 0.10, whereas the second subpopulation (20%) has a constant monthly hazard of quitting drug use of 0.20. What is the hazard of the population after 2 years? Make a picture of the hazard function of the population as a function of time Hazard after two years R programme time<-seq(0,4,0.1) mu1.1<-rep(0.1,length(time));mu1.2<-rep(0.2, length(time)) pi1.0<-0.8 pi1<-(pi1.0*exp(-time*mu1.1))/(pi1.0*exp(-time*mu1.1)+(1-pi1.0)*exp(time*mu1.2)) mu1<-pi1*mu1.1+(1-pi1)*mu1.2 plot(time,mu1,type="n",xlab="Time(years)",ylab="Hazard",axes=F,ylim=c(0. 09,0.21)) box();axis(1,lwd=0.5);axis(2,lwd=0.5) lines(time,mu1);lines(time,mu1.1,lty=2);lines(time,mu1.2,lty=2)