mean_S_before_T_plot_scr {Surrogate}

Goodness of fit plot for the fitted copula

Description

The mean_S_before_T_plot_scr() and prob_dying_without_progression_plot() functions build plots to assess the goodness-of-fit of the copula model fitted by fit_model_SurvSurv(). Specifically, these two functions focus on the appropriateness of the copula. Note that to assess the appropriateness of the marginal functions, two other functions are available: marginal_gof_scr_S_plot() and marginal_gof_scr_T_plot().

Usage

mean_S_before_T_plot_scr(fitted_model, plot_method = NULL, grid, treated, ...)

prob_dying_without_progression_plot(
  fitted_model,
  plot_method = NULL,
  grid,
  treated,
  ...
)

Arguments

fitted_model

Returned value from fit_model_SurvSurv(). This object essentially contains the estimated identifiable part of the joint distribution for the potential outcomes.

plot_method

Defaults to NULL. Should not be modified.

grid

Grid of time-points at which the model-based estimated regression functions, survival functions, or probabilities are evaluated.

treated

(numeric) Treatment group. Should be 0 or 1.

...

Additional arguments to pass to plot().

Value

NULL

Progression Before Death

If a patient progresses before death, this means that S_k < T_k. For these patients, we can look at the expected progression time given that the patient has died at T_k = t:

E(S_k | T_k = t, S_k < T_k).

The mean_S_before_T_plot_scr() function plots the model-based estimate of this regression function together with a non-parametric estimate.

This regression function can also be estimated non-parametrically by regressing S_k onto T_k in the subset of uncensored patients. This non-parametric estimate is obtained via mgcv::gam(y~s(x)) with additionally family = stats::quasi(link = "log", variance = "mu") because this tends to describe survival data better. The 95% confidence intervals are added for this non-parametric estimate; although, they should be interpreted with caution because the Poisson mean-variance relation may be wrong.

Death Before Progression

If a patient dies before progressing, this means that S_k = T_k. This probability can be modeled as a function of time, i.e.,

\pi_k(t) = P(S_k = t \, | \, T_k = t).

The prob_dying_without_progression_plot() function plots the model-based estimate of this regression function together with a non-parametric estimate.

This regression function can also be estimated non-parametrically by regressing the censoring indicator for S_k, \delta_{S_k}, onto T_k in the subset of patients with uncensored T_k.

Examples

# Load Ovarian data
data("Ovarian")
# Recode the Ovarian data in the semi-competing risks format.
data_scr = data.frame(
  ttp = Ovarian$Pfs,
  os = Ovarian$Surv,
  treat = Ovarian$Treat,
  ttp_ind = ifelse(
    Ovarian$Pfs == Ovarian$Surv &
      Ovarian$SurvInd == 1,
    0,
    Ovarian$PfsInd
  ),
  os_ind = Ovarian$SurvInd
)
# Fit copula model.
fitted_model = fit_model_SurvSurv(data = data_scr,
                                  copula_family = "clayton",
                                  n_knots = 1)
# Define grid for GoF plots.
grid = seq(from = 1e-3,
           to = 2.5,
           length.out = 30)
# Assess marginal goodness-of-fit in the control group.
marginal_gof_scr_S_plot(fitted_model, grid = grid, treated = 0)
marginal_gof_scr_T_plot(fitted_model, grid = grid, treated = 0)
# Assess goodness-of-fit of the association structure, i.e., the copula.
prob_dying_without_progression_plot(fitted_model, grid = grid, treated = 0)
mean_S_before_T_plot_scr(fitted_model, grid = grid, treated = 0)