How to calculate this by vector? - r

Question

Updated: Now it's working, but still don't konw how the other way work.
cuts <- seq(from=3, to=36, by=0.01)
for (i in cuts) {
cut_off<- i
set.seed(666)
samp_h <-rnorm(1000,mean=12,sd=3)
samp_d <-rnorm(1000,mean=18,sd=6)
a <- sum(samp_h <= cut_off)
c <- sum(samp_h > cut_off)
b <- sum(samp_d <= cut_off)
d <- sum(samp_d > cut_off)
sens <- a / (a+c)
spci <- d / (d+b)
assign(paste("ss",as.character(cut_off),sep = ""), sens)
assign(paste("sp",as.character(cut_off),sep = ""), spci)}
ss_v<- unlist(
lapply(
paste0("ss",cuts),
get)
)
sp_v<- unlist(
lapply(
paste0("sp",cuts),
get)
)
plot(1-sp_v, ss_v)
Hi all:
I was trying to use different 'cut_off' to get different 'sens' (sensitive) and 'spci' (spcificity). The problem for code above is that for 34 'cuts', i can get the result. but if i change the cuts to:
cuts <- seq(from=3, to=36, by=0.01)
This method can't return the results. The problem is that I calculate the number in each vector, so I am asking how to use the vector to calculate the "ss_v" and "ss_p" directly. Thank you very much.
Background information:
Suppose that in ‘healthy’ patients antibody levels are distributed Normal(12,32) and in ‘diseased’ patients antibodies are distributed Normal(18,62). Note that these are ‘made up’ numbers and not intended to be realistic.
Simulate antibody counts for a large number of diseased and healthy patients (e.g. 1000 of each) – using the ‘rnorm’ function in R. What would the sensitivity and specificity be if a cutoff of 15 was chosen?
Record the sensitivity and specificity for a range of cutoffs between 3 and 36 (e.g. 3, 3.01, 3.02, …, 35.98, 35.99, 36). Hint: generate the cutoffs using the ‘seq’ function in R and then calculate the sensitivity and specificity using a ‘for’ loop or a vectorised calculation.
Produce a plot with ‘1-Specificity’ in the x-axis and ‘Sensitivity’ in the y-axis.

Answer 1

Your code is an example of trying to use R as a macro language. Better would be learning how to use R vectors properly. Since you used a for-loop, you should pre-allocate sens and spci and instead assign to sens and spci as indexed vectors. (So I am endorsing your request for a vector of results as teh sensible way to go.) Then give the vectors names, rather than littering your workspace with a profusion of individual, disconnected named objects. Try this instead:
cuts <- seq(from=3, to=36, by=1)
sens <- numeric(length(cuts)); spci=numeric(length(cuts))
for (i in cuts) {
cut_off<- i
set.seed(666)
samp_h <-rnorm(1000,mean=12,sd=3)
samp_d <-rnorm(1000,mean=18,sd=6)
hth <- table(samp_h)
dis <-table(samp_d)
a<-length(hth[names(hth) <= cut_off])
c<-length(hth[names(hth) > cut_off])
b <-length(dis[names(dis) <= cut_off])
d <-length(dis[names(dis) > cut_off])
sens[i] <- a / (a+c)
spci[1] <- d / (d+b)
}
names(sens) <- paste0("ss",cuts)
names(spci) <- paste0("sp",cuts)
I don't think the notion of working on a new simulated dataset with every loop iteration really impresses me with its efficiency, but it might be if you simulating something with a diff. I'm also not sure you have constructed sens and spci as sensitivity and specificity correctly, but at least you now can see what the results look like. There are several packages that will construct ROC curves.
This is the reason I'm doubtful that your algorithm inside the loop is correct:
> sens
ss3 ss4 ss5 ss6 ss7 ss8 ss9 ss10 ss11 ss12 ss13
0.000 0.000 0.745 0.747 0.752 0.764 0.792 0.836 0.895 0.000 0.123
ss14 ss15 ss16 ss17 ss18 ss19 ss20 ss21 ss22 ss23 ss24
0.239 0.374 0.485 0.593 0.661 0.700 0.721 0.736 0.744 0.745 0.745
ss25 ss26 ss27 ss28 ss29 ss30 ss31 ss32 ss33 ss34 ss35
0.745 0.745 0.745 0.745 0.745 0.745 0.745 0.747 0.747 0.747 0.747
ss36 <NA> <NA>
0.747 0.747 0.747
It just doesn't look like a sensitivity result that I would expect. I might have used code like abcd <-table( samp_h >= cut_off, samp_d >= cutoff) to generate the values you have for a,b,c,d. You can then use matrix indexing with that table result. Another option might be to skip your table efforts and use this code block:
a <- sum(samp_h <= cut_off)
c <- sum(samp_h > cut_off)
b <- sum(samp_d <= cut_off)
d <- sum(samp_d > cut_off)
The sens-itivity results now look more sensible, but not so the spci results.` ( because I had the indexing wrong, now fixed in code below.)
cuts <- seq(from=3, to=36, by=1)
sens <- numeric(length(cuts)); spci=numeric(length(cuts))
set.seed(666)
samp_h <-rnorm(1000,mean=12,sd=3)
samp_d <-rnorm(1000,mean=18,sd=6)
#Only need to make the test data.frame once
dfrm <- data.frame( vals = c(samp_h, samp_d),
grp = c( rep("H", 1000), rep("D",1000) ) )
for (i in seq_along(cuts) ) {
cut_off<- i
abcd <- with(dfrm,
table(Test_res = vals > cut_off,
status=grp ) )
sens[i] <- abcd["TRUE","D"] / sum( abcd[, "D"])
spci[i] <- abcd["FALSE", "H"] / sum( abcd[, "H"])
}
names(sens) <- paste0("ss",cuts)
names(spci) <- paste0("sp",cuts)
plot( 1-spci, sens, type="b")
text( 1-spci[c(TRUE,FALSE,FALSE,FALSE,FALSE)]+.05,
# hack to print every 5th cutoff value
sens[c(TRUE,FALSE,FALSE,FALSE,FALSE)],
label=(3:36)[ c(TRUE,FALSE,FALSE,FALSE,FALSE)] )