# Survival Models Part 2 - PSA

#### 2025-06-16

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)
      ) |>
      add_hazards(
        fit_w
      ) |>
      join(
        fitcov_poor,
        at = 500
      ) |>
    plot(psa = psa, 1:1000, Nrep = 10)