R Function for Handling Survival Data in intervals

Question

Hello I am learning about survival analysis and I was curious if I could use the survival package on survival data of this form:

Here is some code to genereate data in this form

start_interval <-  seq(0, 13)
end_interval <-  seq(1, 14)
living_at_start <- round(seq(1000, 0, length.out = 14))
dead_in_interval <- c(abs(diff(living_at_start)), 0)
df <- data.frame(start_interval, end_interval, living_at_start, dead_in_interval)

From my use of the survival package so far it seems to have each individual be a survival time but I might be misreading the documentation of the Surv function. If survival will not work what other packages are out there for this type of data. If there is not a package or function to easily to estimate the survival function I can easily calculate the survival times myself with the following equation.

Answer 1

Since the survival package need one observation per survival time we need to do some transformations. Using the simulated data.

Simulated Data:

library(survival)
start_interval <-  seq(0, 13)
end_interval <-  seq(1, 14)
living_at_start <- round(seq(1000, 0, length.out = 14))
dead_in_interval <- c(abs(diff(living_at_start)), 0)
df <- data.frame(start_interval, end_interval, living_at_start, dead_in_interval)

Transforming the data by duplicated by the number dead

duptimes <- df$dead_in_interval
rid <- rep(1:nrow(df), duptimes)
df.t <- df[rid,]

Using the Surv Function

test <- Surv(time = df.t$start_interval,
     time2 = df.t$end_interval,
     event = rep(1, nrow(df.t)), #Every Observation is a death
     type = "interval")

Fitting the survival curve

summary(survfit(test ~ 1))

Comparing with by hand calculation from original data

df$living_at_start/max(df$living_at_start)

They match.

Questions

When using the survfit function why is number of risk 1001 at time 0 when there is only 1000 people in the data?

length(test)