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### HW3 Q11
### Competing risks, no censoring: CIF_k(t) = P(T <= t, cause = k) = (# cause-k events by t) / N.
### N = 550; renal failure 158; death 82; t = 5 years.
### ! Rscript "/mnt/c/Users/kirch/OneDrive/Documents/dev/ut-11-hdi/docs/part2/hw3_q11.R"
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N = 550; renal = 158; death = 82
cif.renal = renal / N
cif.death = death / N
cat("CIF_renal(5)  = 158/550 :", cif.renal, "\n")
cat("CIF_death(5)  =  82/550 :", cif.death, "\n")
cat("event-free at 5         :", 1 - cif.renal - cif.death, " (", N - renal - death, "patients )\n")
cat("difference              :", cif.renal - cif.death, "  ( = 76/550 )\n")
cat("ANSWER (2 dp)           :", round(cif.renal - cif.death, 2), "\n")

# cross-check with survfit multi-state (Aalen-Johansen) on constructed data, all events at t=5
suppressMessages(library(survival))
st = factor(c(rep("renal", renal), rep("death", death), rep("censor", N - renal - death)),
            levels = c("censor", "renal", "death"))
fit = survfit(Surv(rep(5, N), st) ~ 1)
p = summary(fit, times = 5)$pstate; colnames(p) = fit$states
cat("survfit cross-check P(state) at t=5:\n"); print(round(p, 4))