QALY Problem 1 ======================================================== ```{r echo=FALSE,results="hide",label="options",echo=FALSE} require(knitr, quietly=TRUE) opts_chunk\$set(fig.width=5,fig.height=5,out.width="60%",dev='svg') ``` ```{r warning=FALSE,error=FALSE,message=FALSE,results="hide",echo=FALSE} library(mosaic,quietly=TRUE) trellis.par.set(theme=col.mosaic()) ``` In epidemiology, a QALY ([quality-adjusted life year](http://en.wikipedia.org/wiki/Quality-adjusted_life_year)) is a measure of duration of life adjusted for the health condition of the person --- a year of a person in good health is 1 QALY, but a year in a person in very poor health is less than 1 QALY. The point of using QALYs is to count the extent to which a health intervention improves health. Interventions that improve the quality of life at the same time as they extend it are more valued than interventions that do not. The graph shows the number of Quality Adjusted Life Years added by three different interventions --- A, B, C --- as a function of the amount of money spent on each. ```{r label="qaly",echo=FALSE} money = seq(0,1000,length=1000) A = 500*pnorm(money, mean=300, sd=150) + .05*money A = A - min(A) B = 350*pnorm(money,mean=0, sd=100) + .05*money B = B - min(B) C = money/1.6 plot( money, A, ylim=c(0,700),type="l",lwd=3, xlab="Expenditure (\$1000)", ylab="QALYs added") lines( money, B, lwd=3,col="red" ) lines( money, C, lwd=3,col="blue" ) text( 1000, max(A), "A", xpd=TRUE,pos=4) text( 1000, max(B), "B", xpd=TRUE,pos=4,col="red") text( 1000, max(C), "C", xpd=TRUE,pos=4, col="blue") ``` You have \\$1,000,000 to allocate among the three interventions. How much will you spend on each of A, B, and C in order to maximize the number of QALYs produced by the expenditure? ### Background: The graphs are fictitious, but let's pretend they are: * [A] Surgical treatment of congenital heart defects in newborns. * [B] Treatment for hemophilia. * [C] In-home health assistance for the disabled.