# Event instantaneous hazard based on Kaplan-Meier survival estimates Compute event instantaneous hazard on the basis of a Kaplan-Meier survival function. ```r epi.insthaz(survfit.obj, conf.level = 0.95) ``` ## 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. ## Returns 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. ## 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 ```r ## 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$shupp, lty = 2, lwd = 1, col = "black") ## Not run: library(ggplot2) ggplot() + theme_bw() + geom_step(data = lung.haz01, aes(x = time, y = hest), colour = "grey") + geom_line(data = lung.shaz01, aes(x = time, y = shest), colour = "black", linewidth = 0.75, linetype = "solid") + geom_line(data = lung.shaz01, aes(x = time, y = shlow), colour = "black", linewidth = 0.50, linetype = "dashed") + geom_line(data = lung.shaz01, aes(x = time, y = shupp), colour = "black", linewidth = 0.50, linetype = "dashed") + scale_x_continuous(limits = c(0,800), name = "Time (days)") + scale_y_continuous(limits = c(0,0.10), name = "Daily probability of event") ## End(Not run) ## EXAMPLE 2: ## Stratify the analyses by sex: lung.km02 <- survfit(Surv(time = time, event = status) ~ sex, data = lung.df01) lung.haz02 <- epi.insthaz(survfit.obj = lung.km02, conf.level = 0.95) ## Split the data by sex: lung.split02 <- split(x = lung.haz02, f = lung.haz02$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 ## Not run: 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") ## End(Not run) ```

epi.insthaz function