marginal_gof_scr_S_plot {Surrogate}

Goodness-of-fit plot for the marginal survival functions

Description

The marginal_gof_scr_S_plot() and marginal_gof_scr_T_plot() functions plot the estimated marginal survival functions for the surrogate and true endpoints. In these plots, it is assumed that the copula model has been fitted for (T_0, \tilde{S}_0, \tilde{S}_1, T_1)' where

S_k = \min(\tilde{S_k}, T_k)

is the (composite) surrogate of interest. In these plots, the model-based survival functions for (T_0, S_0, S_1, T_1)' are plotted together with the corresponding Kaplan-Meier etimates.

Usage

marginal_gof_scr_S_plot(fitted_model, grid, treated, ...)

marginal_gof_scr_T_plot(fitted_model, 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.

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

True Endpoint

The marginal goodness-of-fit plots for the true endpoint, build by marginal_gof_scr_T_plot(), is simply a comparison of the model-based estimate of P(T_k > t) with the Kaplan-Meier (KM) estimate obtained with survival::survfit(). A pointwise 95% confidence interval for the KM estimate is also plotted.

Surrogate Endpoint

The model-based estimate of P(S_k > s) follows indirectly from the fitted copula model because the copula model has been fitted for \tilde{S}_k instead of S_k. However, the model-based estimate still follows easily from the copula model as follows,

P(S_k > s) = P(\min(\tilde{S}_k, T_k)) = P(\tilde{S}_k > s, T_k > s).

The marginal_gof_scr_T_plot() function plots the model-based estimate for P(\tilde{S}_k > s, T_k > s) together with the KM estimate (see above).

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)