recursive sampling in r

Question

I´m trying to simulate death over 7 years with the cumulative probability as follows:

tab <- data.frame(id=1:1000,char=rnorm(1000,7,4))

cum.prob <- c(0.05,0.07,0.08,0.09,0.1,0.11,0.12)

How can I sample from tab$id without replacement in a vectorized fashion according to the cumulative probability in cum.prob ? The ids sampled from yr 1 can necessarily not be sampled again in yr 2. Hence the lapply(cum.prob,function(x) sample(tab$id,x*1000)) will not work. Is it possible to vectorize this?

//M

Prasad Chalasani · Accepted Answer · 2011-05-24 20:27:40Z

7

Here's one way: First get the probability of a given individual's dying in a given year as probYrDeath, i.e. probYrDeath[i] = Prob( individual dies in year i ), where i=1,2,...,7.

probYrDeath <- c(diff(c(0,cum.prob)).

Now generate a random sample of 1000 "Death Years", with replacement, from the sequence 1:8, according to the probabilities in probYrDeath, augmented by the probability of not dying by year 7:

set.seed(1) ## for reproducibility
tab$DeathYr <- sample( 8, 1000, replace = TRUE, 
                       prob = c(probYrDeath, 1-sum(probYrDeath)))

We interpret "'DeathYr = 8'" as "not dying within 7 years", and extract the subset of tab where DeathYr != 8:

tab_sample <- subset(tab, DeathYr != 8 )

You can verify that the cumulative proportions of deaths in each year approximate the values in cum.prob:

> cumsum(table(tab_sample$DeathYr)/1000)
    1     2     3     4     5     6     7 
0.045 0.071 0.080 0.094 0.105 0.115 0.124

edited May 24, 2011 at 20:27

answered May 24, 2011 at 20:21

Prasad Chalasani

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4 Comments

IRTFM Over a year ago

Nice work. Very direct approach. Sidesteps all the complications I was adding.

Nick Sabbe Over a year ago

Ooh. Way better than mine! I didn't realize you can pass probabilities to sample. And the diff is also groovy! You could set the 8 based on the length(cum.prob) + 1 though.

Misha Over a year ago

Very intuitive. Appreciate it. Thx. //M

Henry Over a year ago

You can also avoid the c(probYrDeath, 1-sum(probYrDeath)) instead of probYrDeath complication by using probYrDeath <- diff(c(0, cum.prob, 1)) in the earlier line

Nick Sabbe · Accepted Answer · 2011-05-24 19:27:14Z

0

Does this work for you:

prob.death.per.year<-c(1-cum.prob[length(cum.prob)], cum.prob - c(0, cum.prob[-length(cum.prob)]))
dead.in.years<-as.vector(rmultinom(1, length(tab$id),prob.death.per.year))[-1]
totsamp<-sum(dead.in.years)
data.frame(id=sample(tab$id, totsamp), dead.after=rep(seq_along(dead.in.years), dead.in.years))

Depending upon which form you want the result in, you can change the last step.

answered May 24, 2011 at 19:27

Nick Sabbe

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