PPC censoring

Compare the empirical distribution of censored data y to the distributions of simulated/replicated data yrep from the posterior predictive distribution. See the Plot Descriptions section, below, for details.

Although some of the other bayesplot plots can be used with censored data, ppc_km_overlay() is currently the only plotting function designed specifically for censored data. We encourage you to suggest or contribute additional plots at github.com/stan-dev/bayesplot.

Usage

ppc_km_overlay(
  y,
  yrep,
  ...,
  status_y,
  left_truncation_y = NULL,
  extrapolation_factor = 1.2,
  size = 0.25,
  alpha = 0.7
)

ppc_km_overlay_grouped(
  y,
  yrep,
  group,
  ...,
  status_y,
  left_truncation_y = NULL,
  extrapolation_factor = 1.2,
  size = 0.25,
  alpha = 0.7
)

Arguments

y: A vector of observations. See Details.
yrep: An S by N matrix of draws from the posterior (or prior) predictive distribution, or a posterior::draws object. The number of rows, S, is the size of the posterior (or prior) sample used to generate yrep. The number of columns, N is the number of predicted observations (length(y)). The columns of yrep should be in the same order as the data points in y for the plots to make sense. See the Details and Plot Descriptions sections for additional advice specific to particular plots.
...: Currently only used internally.
status_y: The status indicator for the observations from y. This must be a numeric vector of the same length as y with values in {0, 1} (0 = right censored, 1 = event).
left_truncation_y: Optional parameter that specifies left-truncation (delayed entry) times for the observations from y. This must be a numeric vector of the same length as y. If NULL (default), no left-truncation is assumed.
extrapolation_factor: A numeric value (>=1) that controls how far the plot is extended beyond the largest observed value in y. The default value is 1.2, which corresponds to 20 % extrapolation. Note that all posterior predictive draws may not be shown by default because of the controlled extrapolation. To display all posterior predictive draws, set extrapolation_factor = Inf.
size, alpha: Passed to the appropriate geom to control the appearance of the yrep distributions.
group: A grouping variable of the same length as y. Will be coerced to factor if not already a factor. Each value in group is interpreted as the group level pertaining to the corresponding observation.

Value

A ggplot object that can be further customized using the ggplot2 package.

Plot Descriptions

ppc_km_overlay(): Empirical CCDF estimates of each dataset (row) in yrep are overlaid, with the Kaplan-Meier estimate (Kaplan and Meier, 1958) for y itself on top (and in a darker shade). This is a PPC suitable for right-censored y. Note that the replicated data from yrep is assumed to be uncensored. Left truncation (delayed entry) times for y can be specified using left_truncation_y.
ppc_km_overlay_grouped(): The same as ppc_km_overlay(), but with separate facets by group.

References

Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., and Rubin, D. B. (2013). Bayesian Data Analysis. Chapman & Hall/CRC Press, London, third edition. (Ch. 6)

Kaplan, E. L. and Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association. 53(282), 457–481. doi:10.1080/01621459.1958.10501452.

Examples

# \donttest{
color_scheme_set("brightblue")

# For illustrative purposes, (right-)censor values y > 110:
y <- example_y_data()
status_y <- as.numeric(y <= 110)
y <- pmin(y, 110)

# In reality, the replicated data (yrep) would be obtained from a
# model which takes the censoring of y properly into account. Here,
# for illustrative purposes, we simply use example_yrep_draws():
yrep <- example_yrep_draws()
dim(yrep)
#> [1] 500 434

# Overlay 25 curves
ppc_km_overlay(y, yrep[1:25, ], status_y = status_y)
#> Note: `extrapolation_factor` now defaults to 1.2 (20%).
#> To display all posterior predictive draws, set `extrapolation_factor = Inf`.


# With extrapolation_factor = 1 (no extrapolation)
ppc_km_overlay(y, yrep[1:25, ], status_y = status_y, extrapolation_factor = 1)


# With extrapolation_factor = Inf (show all posterior predictive draws)
ppc_km_overlay(y, yrep[1:25, ], status_y = status_y, extrapolation_factor = Inf)


# With separate facets by group:
group <- example_group_data()
ppc_km_overlay_grouped(y, yrep[1:25, ], group = group, status_y = status_y)
#> Note: `extrapolation_factor` now defaults to 1.2 (20%).
#> To display all posterior predictive draws, set `extrapolation_factor = Inf`.


# With left-truncation (delayed entry) times:
min_vals <- pmin(y, apply(yrep, 2, min))
left_truncation_y <- rep(0, length(y))
condition <- y > mean(y) / 2
left_truncation_y[condition] <- pmin(
  runif(sum(condition), min = 0.6, max = 0.99) * y[condition],
  min_vals[condition] - 0.001
)
ppc_km_overlay(y, yrep[1:25, ], status_y = status_y,
              left_truncation_y = left_truncation_y)
#> Note: `extrapolation_factor` now defaults to 1.2 (20%).
#> To display all posterior predictive draws, set `extrapolation_factor = Inf`.

# }