Exercise 11. Cox regression with all-cause mortality as the outcome
Now fit a model to the localised melanoma data where the outcome is observed survival (i.e. all deaths are considered to be events).
You may have to install the required packages the first time you use them. You can install a package by install.packages("package_of_interest") for each package you require.
Load the melanoma data and explore it.
## Read melanoma data
## and select subcohorts
melanoma.l <- biostat3::melanoma %>%
filter(stage=="Localised") %>%
mutate(
## Create a death indicator
death_cancer = as.numeric(status=="Dead: cancer"),
death_any = as.numeric(status=="Dead: cancer" | status=="Dead: other") )
## Truncate follow-up time
melanoma.l2 <-
mutate(melanoma.l,
## Create new death indicators (only count deaths within 120 months)
death_cancer = death_cancer * as.numeric( surv_mm <= 120),
death_any = death_any * as.numeric( surv_mm <= 120),
## Create a new time variable
surv_mm = pmin(surv_mm, 120))(a)
Interpret the estimated hazard ratio for the parameter labelled agegrp60-74, including a comment on statistical significance.
summary( coxfit11a <- coxph(Surv(surv_mm, death_any) ~ sex + year8594 + agegrp,
data = melanoma.l2) )Write out the regression equation. Using the regression equation, write out a formula for the hazard ratio for a male aged 60–74 years compared with a female aged 75 years or over.
(b)
On comparing the estimates between the observed and cause-specific survival models it appears that only the parameters for age have changed substantially. Can you explain why the estimates for the effect of age would be expected to change more than the estimates of the effect of sex and period?