Survival function with two time scales

Computes the survival matrix, that contains the probability of not experiencing an event (of any cause) by time s and fixed entry time u. The survival function can be obtained from one fitted model with only one event type, or combining information from several cause-specific hazard in a competing risks model. In the first case, a fitted object of class 'haz2ts' or 'haz2tsLMM' can be passed directly as argument to the function. In the competing risks framework, the user should provide a list of cause-specific cumulative hazard matrices. The function is also called internally from plot() if the user wants to plot the cumulative hazard from a fitted model.

Usage

surv2ts(
  cumhaz = NULL,
  fitted_model = NULL,
  plot_grid = NULL,
  cause = NULL,
  midpoints = FALSE,
  where_slices = NULL,
  direction = c("u", "s", NULL),
  tmax = NULL
)

Arguments

cumhaz

(optional) a list with all the cause-specific cumulated hazard matrices (minimum one element needs to be supplied). If more than one cause-specific cumulated hazard is provided, then they should all be matrices of the same dimension.

fitted_model

(optional) The output of the function fit2ts. This is an object of class 'haz2ts' or 'haz2tsLMM'.

plot_grid

(optional) A list containing the parameters to build a new finer grid of intervals over u and s for plotting. This must be of the form:

• plot_grid = list(c(umin, umax, du), c(smin, smax, ds)) where umin, umax and smin, smax are the minimum and maximum values desired for the grid-points over u and s respectively, and du, ds are distances between points over u and s respectively. Specifying a new denser grid is used to evaluate the B-spline bases used for estimation on such grid and plot the estimated surfaces with a greater level of details. If not specified, the plotting is done using the same B-splines bases as for the estimation. The function will check if the parameters for the grid provided by the user are compatible with those originally used to construct the B-splines for estimating the model. If not, the grid will be adjusted accordingly and a warning will be returned.

cause

a character string with a short name for the cause (optional).

midpoints

A Boolean. Default is FALSE. If TRUE, the estimated quantities are evaluated at the midpoints of the rectangles (or parallelograms) of the grids, rather than at each grid-point.

where_slices

A vector of values for the cutting points of the desired slices of the surface. This option is included mostly for the plotting function. When using plot.haz2ts(), the user selects which_plot = "survival" and surv_slices = TRUE, then where_slices indicates the location of the cutting points over the u time.

direction

If cross-sectional one-dimensional curves are plotted, this indicates whether the cutting points are located on the u time, or on the s time. For plots of the survival function, only cutting points over the u time are meaningful.

tmax

The maximum value of t that should be plotted.

Value

a matrix containing the values of the survival function over s and u.

Examples

# Create some fake data - the bare minimum
id <- 1:20
u <- c(5.43, 3.25, 8.15, 5.53, 7.28, 6.61, 5.91, 4.94, 4.25, 3.86, 4.05, 6.86,
       4.94, 4.46, 2.14, 7.56, 5.55, 7.60, 6.46, 4.96)
s <- c(0.44, 4.89, 0.92, 1.81, 2.02, 1.55, 3.16, 6.36, 0.66, 2.02, 1.22, 3.96,
       7.07, 2.91, 3.38, 2.36, 1.74, 0.06, 5.76, 3.00)
ev <- c(1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1)


fakedata <- as.data.frame(cbind(id, u, s, ev))
fakedata2ts <- prepare_data(u = fakedata$u,
                            s_out = fakedata$s,
                            ev = fakedata$ev,
                            ds = .5)
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
# Fit a fake model - not optimal smoothing
fakemod <- fit2ts(fakedata2ts,
                  optim_method = "grid_search",
                  lrho = list(seq(1 , 1.5, .5),
                              seq(1 , 1.5, .5)))

# Obtain the fake cumulated hazard
fakecumhaz2ts <- cumhaz2ts(fakemod)
# Fake survival curve
fakesurv2ts <- surv2ts(fitted_model = fakemod)