# Survival Models Part 2 - PSA

#### 2024-01-31

The aim of this vignette is to show how to perform probabilistic sensitivity analyses (PSA) on survival data.

The main function to use is resample_surv() within define_psa().

# From a user-defined parametric distribution

The resample_surv() function uses a random generator with the parameters of the initially defined distribution. All you need to do is specify the n argument to define the number of draws, and you can control variability in this way (the higher n is, the lower the variability). Under the hood, an empirical cumulative function is created with these random draws and a nonlinear model determining Least Squares estimates of the new parameters is then fitted.

surv_dist <- define_surv_dist("gamma", shape = 2, rate = 0.1)
psa <- define_psa(surv_dist ~ resample_surv(n = 500))

You can display the distribution and its confidence interval using the plot() function. This is useful to check the expected variability of your model.

psa2 <- define_psa(surv_dist ~ resample_surv(n = 50))
plot(surv_dist, psa = psa)

plot(surv_dist, psa = psa2)

# From real data

A non-parametric bootstrap (random sampling) of the data.frame is performed. At each iteration of the PSA, a new data.frame is created and the model runs with this new data. To perform a PSA with real data, resample_surv() must not contain any arguments.

fit_cov <- flexsurv::flexsurvreg(survival::Surv(rectime, censrec) ~ group,
data = bc,
dist = "exp")|>
define_surv_fit()

psa <-  define_psa(fit_cov ~ resample_surv())

plot(fit_cov, times = 1:1000, psa = psa, Nrep = 10)
## No covariates provided, returning aggregate survival across all subjects.

It is possible to carry out a PSA with all objects of class surv_object, including complex objects, created using a sequence of operations. Taking the previous vignette as an example:

fitcov_poor   <- set_covariates(fit_cov, group = "Poor")
fitcov_medium <- set_covariates(fit_cov, group = "Medium")
fit_w <- flexsurvreg(
formula = Surv(futime, fustat) ~ 1,
data = ovarian, dist = "weibull"
) |>
define_surv_fit()

fit_cov |>
set_covariates(group = "Good") |>
apply_hr(hr = 2) |>
mix(
fitcov_medium,
weights = c(0.25, 0.75)
) |>
plot(psa = psa, 1:1000, Nrep = 10)