epiR (version 2.0.78)

epi.insthaz: Event instantaneous hazard based on Kaplan-Meier survival estimates

Description

Compute event instantaneous hazard on the basis of a Kaplan-Meier survival function.

Usage

epi.insthaz(survfit.obj, conf.level = 0.95)

Value

A data frame with the following variables: strata the strata identifier, time the observed event times, n.risk the number of individuals at risk at the start of the event time, n.event the number of individuals that experienced the event of interest at the event time, n.censor the number of individuals censored at the event time, sest the observed Kaplan-Meier survival estimate at the event time, slow the lower bound of the confidence interval for the observed Kaplan-Meier survival estimate at the event time, supp the upper bound of the confidence interval for the observed Kaplan-Meier survival estimate at the event time, hest the observed instantaneous hazard at the event time, hlow the lower bound of the confidence interval for the observed instantaneous hazard at the event time, and hupp the upper bound of the confidence interval for the observed instantaneous hazard at the event time.

Arguments

survfit.obj

a survfit object, computed using the survival package.

conf.level

magnitude of the returned confidence interval. Must be a single number between 0 and 1.

Details

Computes the instantaneous hazard of the event of interest, equivalent to the proportion of the group at risk failing per unit time.

References

Venables W, Ripley B (2002). Modern Applied Statistics with S, fourth edition. Springer, New York, pp. 353 - 385.

Singer J, Willett J (2003). Applied Longitudinal Data Analysis Modeling Change and Event Occurrence. Oxford University Press, London, pp. 348.

Examples

## EXAMPLE 1:
library(survival)
lung.df01 <- lung

lung.df01$status <- ifelse(lung.df01$status == 1, 0, lung.df01$status)
lung.df01$status <- ifelse(lung.df01$status == 2, 1, lung.df01$status)
lung.df01$sex <- factor(lung.df01$sex, levels = c(1,2), 
   labels = c("Male","Female"))

lung.km01 <- survfit(Surv(time = time, event = status) ~ 1, data = lung.df01)
lung.haz01 <- epi.insthaz(survfit.obj = lung.km01, conf.level = 0.95)

lung.shaz01 <- data.frame(
  time = lowess(lung.haz01$time, lung.haz01$hlow, f = 0.20)$x,
  shest =  lowess(lung.haz01$time, lung.haz01$hest, f = 0.20)$y,
  shlow =  lowess(lung.haz01$time, lung.haz01$hlow, f = 0.20)$y,
  shupp =  lowess(lung.haz01$time, lung.haz01$hupp, f = 0.20)$y)

## What was the maximum follow-up time? Use this to guide limits for the
## horizontal axis:
summary(lung.haz01$time)

## Maximum follow up time 883 days, so set horizontal axis limit to a 
## bit less, say 800 days. This will avoid instability in the smoothed results
## at the extremes of the data. 

plot(x = lung.haz01$time, y = lung.haz01$hest, xlab = "Time (days)", 
   ylab = "Daily probability of event", type = "s", 
   col = "grey", xlim = c(0,800), ylim = c(0, 0.05))
lines(x = lung.shaz01$time, y = lung.shaz01$shest, 
      lty = 1, lwd = 2, col = "black")
lines(x = lung.shaz01$time, y = lung.shaz01$shlow, 
      lty = 2, lwd = 1, col = "black")
lines(x = lung.shaz01$time, y = lung.shaz01$shupp, 
      lty = 2, lwd = 1, col = "black")

if (FALSE) { 
library(ggplot2)

ggplot() +
  theme_bw() +
  geom_step(data = lung.haz01, aes(x = time, y = hest), colour = "grey") + 
  geom_line(data = lung.shaz01, aes(x = time, y = shest), colour = "black", 
     linewidth = 0.75, linetype = "solid") +
  geom_line(data = lung.shaz01, aes(x = time, y = shlow), colour = "black", 
     linewidth = 0.50, linetype = "dashed") +
  geom_line(data = lung.shaz01, aes(x = time, y = shupp), colour = "black", 
     linewidth = 0.50, linetype = "dashed") +
  scale_x_continuous(limits = c(0,800), name = "Time (days)") +
  scale_y_continuous(limits = c(0,0.10), name = "Daily probability of event") 
}


## EXAMPLE 2:
## Stratify the analyses by sex:
lung.km02 <- survfit(Surv(time = time, event = status) ~ sex, data = lung.df01)
lung.haz02 <- epi.insthaz(survfit.obj = lung.km02, conf.level = 0.95)

## Split the data by sex:
lung.split02 <- split(x = lung.haz02, f = lung.haz02$strata)

## Loess smooth teh data for each group using lapply:
lung.loess02 <- lapply(X = lung.split02, FUN = function(dat, span = 0.4) {
   hest <- loess(hest ~ time, data = dat, span = span)$fit
   hlow <- loess(hlow ~ time, data = dat, span = span)$fit
   hupp <- loess(hupp ~ time, data = dat, span = span)$fit
  data.frame(strata = dat$strata, time = dat$time, hest = hest, 
   hlow = hlow, hupp = hupp)
})

## Combine the loess smoothed results into a single data frame:
lung.shaz02 <- do.call(rbind, lung.loess02)
row.names(lung.shaz02) <- NULL

if (FALSE) { 
library(ggplot2)

## Use the same horizontal axis limits calculated above:
ggplot() +
  theme_bw() +
  geom_step(data = lung.haz02, aes(x = time, y = hest), colour = "grey") + 
  facet_grid(strata ~ .) +
  geom_ribbon(data = lung.shaz02, aes(x = time, ymin = hlow, ymax = hupp), 
     alpha = 0.25) +
  scale_x_continuous(limits = c(0,800), name = "Time (days)") +
  scale_y_continuous(limits = c(0,0.10), name = "Daily probability of event")
}