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### HW2 Q9
### Cox model: beta = (age 0.05, treatment -0.1, female 0.15, ulcer 0.12).
### Patient A: 35, female, ulcer, treated.  Patient B: 21, male, no ulcer, untreated.
### HR(A vs B) = exp{ beta^T (z_A - z_B) }  -- baseline hazard cancels.
### ! Rscript "/mnt/c/Users/kirch/OneDrive/Documents/dev/ut-11-hdi/docs/part1/hw2_q9.R"
################################

beta = c(age = 0.05, treatment = -0.1, female = 0.15, ulcer = 0.12)
zA   = c(age = 35, treatment = 1, female = 1, ulcer = 1)
zB   = c(age = 21, treatment = 0, female = 0, ulcer = 0)

cat("z_A - z_B                       :", zA - zB, "\n")
cat("per-term beta*(zA - zB)         :", beta * (zA - zB), "\n")
lp.diff = sum(beta * (zA - zB))
cat("beta^T (z_A - z_B)              :", lp.diff, "\n")
cat("HR = exp(0.87)                  :", exp(lp.diff), "\n")
cat("check: exp(lpA)/exp(lpB)        :", exp(sum(beta * zA)) / exp(sum(beta * zB)), "\n")
cat("ANSWER (2 dp)                   :", round(exp(lp.diff), 2), "\n")