library(dplyr) #> Warning: replacing previous import 'lifecycle::last_warnings' by #> 'rlang::last_warnings' when loading 'pillar' #> #> Attaching package: 'dplyr' #> The following objects are masked from 'package:stats': #> #> filter, lag #> The following objects are masked from 'package:base': #> #> intersect, setdiff, setequal, union library(ggplot2) library(survival) library(survParamSim) set.seed(12345)
The goal of survParamSim is to perform survival simulation with parametric survival model generated from ‘survreg’ function in ‘survival’ package. In each simulation, coefficients are resampled from variance-covariance matrix of parameter estimates, in order to capture uncertainty in model parameters.
Before running a parametric survival simulation, you need to fit a model to your data using
survreg() function of
In this vignette, we will be using
colon dataset available in
survival package, where the treatment effect of adjuvant Levamisole+5-FU for colon cancer over placebo is evaluated.
First, we load the data and do some data wrangling.
# ref for dataset https://vincentarelbundock.github.io/Rdatasets/doc/survival/colon.html <- colon2 as_tibble(colon) %>% # recurrence only and not including Lev alone arm filter(rx != "Lev", == 1) %>% etype # Same definition as Lin et al, 1994 mutate(rx = factor(rx, levels = c("Obs", "Lev+5FU")), depth = as.numeric(extent <= 2))
Shown below are Kaplan-Meier curves for visually checking the data.
The second plot is looking at how many censoring we have over time.
Looks like we have a fairly uniform censoring between 1800 to 3000 days - this is attributable to a steady clinical study enrollment.
<- survfit(Surv(time, status) ~ rx, data = colon2) survfit.colon ::ggsurvplot(survfit.colon)survminer
<- survfit(Surv(time, 1-status) ~ rx, data = colon2) survfit.colon.censor ::ggsurvplot(survfit.colon.censor)survminer
Next we fit a lognormal parametric model for the data.
Here we are using
depth as additional covariates in addition to treatment (
You can see that all of the factor has strong association with the outcome.
<- survreg(Surv(time, status) ~ rx + node4 + depth, fit.colon data = colon2, dist = "lognormal") summary(fit.colon) #> #> Call: #> survreg(formula = Surv(time, status) ~ rx + node4 + depth, data = colon2, #> dist = "lognormal") #> Value Std. Error z p #> (Intercept) 7.5103 0.1343 55.92 < 2e-16 #> rxLev+5FU 0.7606 0.1677 4.54 5.7e-06 #> node4 -1.3474 0.1816 -7.42 1.2e-13 #> depth 1.1243 0.2661 4.22 2.4e-05 #> Log(scale) 0.6040 0.0461 13.10 < 2e-16 #> #> Scale= 1.83 #> #> Log Normal distribution #> Loglik(model)= -2561.7 Loglik(intercept only)= -2607.6 #> Chisq= 91.8 on 3 degrees of freedom, p= 9e-20 #> Number of Newton-Raphson Iterations: 4 #> n= 619
surv_param_sim() is the main function of the package that takes
survreg object as described above.
It also require you to supply
newdata, which is required even if it is not new - i.e. the same data was used for both
What it does is: 1. Re-sample all the coefficients in the parametric survival model from variance-covariance matrix for
n.rep times. 2. Perform survival time for all subjects in
newdata with the corresponding covariates, using one of the resampled coefficients. Also generate censoring time according to
censor.dur (if not NULL), and replace the simulated survival time above if censoring time is earlier. 4. Repeat the steps 2. for
<- sim surv_param_sim(object = fit.colon, newdata = colon2, # Simulate censoring according to the plot above censor.dur = c(1800, 3000), # Simulate only 100 times to make the example go fast n.rep = 100)
After the simulation is performed, you can either extract raw simulation results or further calculate Kaplan-Meier estimates or hazard ratio of treatment effect, as you see when you type
sim in the console.
sim#> ---- Simulated survival data with the following model ---- #> survreg(formula = Surv(time, status) ~ rx + node4 + depth, data = colon2, #> dist = "lognormal") #> #> * Use `extract_sim()` function to extract individual simulated survivals #> * Use `calc_km_pi()` function to get survival curves and median survival time #> * Use `calc_hr_pi()` function to get hazard ratio #> #> * Settings: #> #simulations: 100 #> #subjects: 619 (without NA in model variables)
To calculate survival curves for each simulated dataset,
calc_km_pi() can be used on the simulated object above.
<- calc_km_pi(sim, trt = "rx") km.pi #> Warning in calc_km_pi(sim, trt = "rx"): 70 of 200 simulations (#rep * #trt #> * #group) did not reach median survival time and these are not included for #> prediction interval calculation. You may want to delay the `censor.dur` in #> simulation. km.pi#> ---- Simulated and observed (if calculated) survival curves ---- #> * Use `extract_medsurv_pi()` to extract prediction intervals of median survival times #> * Use `extract_km_pi()` to extract prediction intervals of K-M curves #> * Use `plot_km_pi()` to draw survival curves #> #> * Settings: #> trt: rx #> group: NA #> pi.range: 0.95 #> calc.obs: TRUE
Similar to the raw simulated object, you can have a few options for further processing - one of them is plotting prediction intervals with
plot_km_pi(km.pi) + theme(legend.position = "bottom") + labs(y = "Recurrence free rate") + expand_limits(y = 0)
Or providing median survival summary table with
extract_medsurv_pi(km.pi) #> # A tibble: 8 × 5 #> rx n description median quantile #> <fct> <dbl> <chr> <dbl> <dbl> #> 1 Obs 315 pi_low 1108. 0.0250 #> 2 Obs 315 pi_med 1538. 0.5 #> 3 Obs 315 pi_high 2113. 0.975 #> 4 Obs 315 obs 1236 NA #> 5 Lev+5FU 304 pi_low 2126. 0.0250 #> 6 Lev+5FU 304 pi_med 2697. 0.5 #> 7 Lev+5FU 304 pi_high 2927. 0.975 #> 8 Lev+5FU 304 obs NA NA
Plot can also be made for subgroups.
You can see that prediction interval is wide for (depth: 1 & nodes4: 1) group, mainly due to small number of subjects
<- calc_km_pi(sim, trt = "rx", group = c("node4", "depth")) km.pi #> Warning in calc_km_pi(sim, trt = "rx", group = c("node4", "depth")): 339 of 800 #> simulations (#rep * #trt * #group) did not reach median survival time and these #> are not included for prediction interval calculation. You may want to delay the #> `censor.dur` in simulation. plot_km_pi(km.pi) + theme(legend.position = "bottom") + labs(y = "Recurrence free rate") + expand_limits(y = 0)
To calculate prediction intervals of HRs,
calc_hr_pi() can be used on the simulated object above. Here I only generated subgroups based on “depth”, since the very small N in (depth: 1 & nodes4: 1) can cause issue with calculating HRs.
<- calc_hr_pi(sim, trt = "rx", group = c("depth")) hr.pi hr.pi#> ---- Simulated and observed (if calculated) hazard ratio ---- #> * Use `extract_hr_pi()` to extract prediction intervals and observed HR #> * Use `extract_hr()` to extract individual simulated HRs #> * Use `plot_hr_pi()` to draw histogram of predicted HR #> #> * Settings: #> trt: rx #> ('Lev+5FU' as test trt, 'Obs' as control) #> group: depth #> pi.range: 0.95 #> calc.obs: TRUE plot_hr_pi(hr.pi)
You can also extract prediction intervals and observed HR with
extract_hr_pi(hr.pi) #> # A tibble: 8 × 5 #> depth rx description HR quantile #> <dbl> <fct> <chr> <dbl> <dbl> #> 1 0 Lev+5FU pi_low 0.464 0.0250 #> 2 0 Lev+5FU pi_med 0.624 0.5 #> 3 0 Lev+5FU pi_high 0.794 0.975 #> 4 0 Lev+5FU obs 0.590 NA #> 5 1 Lev+5FU pi_low 0.233 0.0250 #> 6 1 Lev+5FU pi_med 0.597 0.5 #> 7 1 Lev+5FU pi_high 1.13 0.975 #> 8 1 Lev+5FU obs 0.607 NA