Kaplan-Meier estimate Heidi Seibold Statistician at LMU Munich - - PowerPoint PPT Presentation

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Kaplan-Meier estimate Heidi Seibold Statistician at LMU Munich - - PowerPoint PPT Presentation

Oct 07, 2023 7 likes •240 views

DataCamp Survival Analysis in R SURVIVAL ANALYSIS IN R Kaplan-Meier estimate Heidi Seibold Statistician at LMU Munich DataCamp Survival Analysis in R Survival function THEORY ESTIMATION ^ n d S ( t ) = 1 F ( t ) = P ( T > t ) (

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DataCamp Survival Analysis in R

Kaplan-Meier estimate

SURVIVAL ANALYSIS IN R

Heidi Seibold

Statistician at LMU Munich

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DataCamp Survival Analysis in R

Survival function

THEORY

S(t) = 1 − F(t) = P(T > t)

ESTIMATION

(t) = S ^

i: t ≤t

i

∏

ni n −d

i i

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DataCamp Survival Analysis in R

Survival function estimation

DATA ESTIMATION

(t) = S ^

i: t ≤t

i

∏

ni n −d

i i

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DataCamp Survival Analysis in R

Survival function estimation: Kaplan-Meier estimate

(t) = (2) = = = 1 (3) = = = 1 (4) = = = = 0.5 (5) = ⋅ = = 0.25 (6) = ⋅ = = 0.25 S ^

i: t ≤t

i

∏ ni n − d

i i

S ^ 5 5 − 0 5 5 S ^ 4 4 − 0 4 4 S ^ 4 4 − 2 4 2 2 1 S ^ 2 1 2 2 − 1 4 1 S ^ 4 1 1 1 − 0 4 1

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DataCamp Survival Analysis in R

Survival function estimation: Kaplan-Meier estimate

km <- survfit(Surv(time, event) ~ 1) ggsurvplot(km, conf.int = FALSE, risk.table = "nrisk_cumevents", legend = "none")

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DataCamp Survival Analysis in R

Let's practice!

SURVIVAL ANALYSIS IN R

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DataCamp Survival Analysis in R

Understanding and visualizing Kaplan-Meier curves

SURVIVAL ANALYSIS IN R

Heidi Seibold

Statistician at LMU Munich

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DataCamp Survival Analysis in R

The ggsurvplot function

library(survminer) ggsurvplot(fit) ggsurvplot( fit, palette = NULL, linetype = 1, surv.median.line = "none", risk.table = FALSE, cumevents = FALSE, cumcensor = FALSE, tables.height = 0.25, ... )

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DataCamp Survival Analysis in R

The ggsurvplot function

ggsurvplot( fit = km, palette = "blue", linetype = 1, surv.median.line = "hv", risk.table = TRUE, cumevents = TRUE, cumcensor = TRUE, tables.height = 0.1 )

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DataCamp Survival Analysis in R

The survfit function

If object is a formula: Kaplan-Meier estimation Other options for object (see upcoming chapters):

coxph survreg

survfit(object)

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DataCamp Survival Analysis in R

Let's practice!

SURVIVAL ANALYSIS IN R

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DataCamp Survival Analysis in R

The Weibull model for estimating smooth survival curves

SURVIVAL ANALYSIS IN R

Heidi Seibold

Statistician at LMU Munich

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DataCamp Survival Analysis in R

Why use a Weibull model?

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DataCamp Survival Analysis in R

Computing a Weibull model in R

Weibull model:

wb <- survreg(Surv(time, event) ~ 1, data)

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DataCamp Survival Analysis in R

Computing a Weibull model in R

Weibull model: Kaplan-Meier estimate:

wb <- survreg(Surv(time, event) ~ 1, data) km <- survfit(Surv(time, event) ~ 1, data)

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DataCamp Survival Analysis in R

Computing measures from a Weibull model

90 Percent of patients survive beyond time point:

p = 1 - 0.9 because the distribution function is 1 - the survival function.

wb <- survreg(Surv(time, cens) ~ 1, data = GBSG2) predict(wb, type = "quantile", p = 1 - 0.9, newdata = data.frame(1)) 1 384.9947

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DataCamp Survival Analysis in R

Computing the survival curve from a Weibull model

Survival curve:

wb <- survreg(Surv(time, cens) ~ 1, data = GBSG2) surv <- seq(.99, .01, by = -.01) t <- predict(wb, type = "quantile", p = 1 - surv, newdata = data.frame(1)) head(data.frame(time = t, surv = surv)) #> time surv #> 1 60.6560 0.99 #> 2 105.0392 0.98 #> 3 145.0723 0.97 #> 4 182.6430 0.96 #> 5 218.5715 0.95 #> 6 253.3125 0.94

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DataCamp Survival Analysis in R

Let's practice!

SURVIVAL ANALYSIS IN R

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DataCamp Survival Analysis in R

Visualizing the results of a Weibull model

SURVIVAL ANALYSIS IN R

Heidi Seibold

Statistician at LMU Munich

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DataCamp Survival Analysis in R

Visualizing a Weibull model

Visualization tools often focus on step functions. So the following code does NOT work:

wb <- survreg(Surv(time, cens) ~ 1) ggsurvplot(wb)

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DataCamp Survival Analysis in R

Visualizing a Weibull model

Survival curve: Plot:

wb <- survreg(Surv(time, cens) ~ 1) surv <- seq(.99, .01, by = -.01) t <- predict(wb, type = "quantile", p = 1 - surv, newdata = data.frame(1)) surv_wb <- data.frame(time = t, surv = surv, upper = NA, lower = NA, std.err = NA) ggsurvplot_df(fit = surv_wb, surv.geom = geom_line)

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DataCamp Survival Analysis in R

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DataCamp Survival Analysis in R

Let's practice!

SURVIVAL ANALYSIS IN R