summary.cfc {CFC}

Summarizing and plotting output of cfc

Description

summary method for class cfc.

Usage

## S3 method for class 'cfc'
summary(object
  , f.reduce = function(x) x
  , pval = 0.05, ...)
## S3 method for class 'summary.cfc'
plot(x, which = c(1, 2), ...)

Arguments

object

An object of class "cfc", usually the result of a call to cfc.

f.reduce

Function to be applied to each sub-array of object$ci (cumulative incidence) and object$s (survival probability).

pval

Desired significance level for confidence intervals produced by summary.cfc. We essentially set the argument probs to c(pval/2, 0.5, 1-pval/2) when calling quantile.

x

An object of class "summary.cfc", usually the result of a call to summary.cfc.

which

Vector of integers, indicating which plot(s) must be produced: 1) cumulative incidence functions, one per cause. For each cause, median and credible bands are plotted vs. time-from-index. 2) (unadjusted) survival functions, one per cause. Similar to (1), median and credible bands are plotted.

...

Further arguments to be passed to f.reduce (for summary.cfc).

Value

Recall that the survival probability and cumulative incidence arrays returned by cfc are three-dimensional, and their first two dimensions indicate 1) time points and 2) causes. f.reduce is expected to produce an array of a fixed length, when applied to each sub-array, ci[i, j, ] and s[i, j, ]. The end-result is two three-dimensional array, where the first two dimensions are identical to its input arrays. This 3D array is then passed to the quantile function to compute median and credible bands. There is a special case where f.reduce returns a scalar, rather than an array, when applied to each sub-array. In this case, quantile calculation is meaningless and we return simply these point estimates. In summary, the return object from summary is a list with elements: 1) ci (cumulative incidence), 2) s (survival), and 3) quantiles, a boolean flag indicating whether the cumulative incidence and survival arrays returned are quantiles or point estimates.

Author(s)

Alireza S. Mahani, Mansour T.A. Sharabiani

References

Mahani A.S. and Sharabiani M.T.A. (2019). Bayesian, and Non-Bayesian, Cause-Specific Competing-Risk Analysis for Parametric and Nonparametric Survival Functions: The R Package CFC. Journal of Statistical Software, 89(9), 1-29. doi:10.18637/jss.v089.i09

See Also

cfc, summary.

Examples

## Not run: 

library("BSGW") # used for Bayesian survival regression

data(bmt)
# splitting data into training and prediction sets
idx.train <- sample(1:nrow(bmt), size = 0.7 * nrow(bmt))
idx.pred <- setdiff(1:nrow(bmt), idx.train)
nobs.train <- length(idx.train)
nobs.pred <- length(idx.pred)

# prepare data and formula for Bayesian cause-specific survival regression
# using R package BSGW
out.prep <- cfc.prepdata(Surv(time, cause) ~ platelet + age + tcell, bmt)
f1 <- out.prep$formula.list[[1]]
f2 <- out.prep$formula.list[[2]]
dat <- out.prep$dat
tmax <- out.prep$tmax

# estimating cause-specific models
# set nsmp to larger number in real-world applications
nsmp <- 10
reg1 <- bsgw(f1, dat[idx.train, ], control = bsgw.control(iter = nsmp)
  , ordweib = T, print.level = 0)
reg2 <- bsgw(f2, dat[idx.train, ], control = bsgw.control(iter = nsmp)
  , ordweib = T, print.level = 0)

# defining survival function for this model
survfunc <- function(t, args, n) {
  nobs <- args$nobs; natt <- args$natt; nsmp <- args$nsmp
  alpha <- args$alpha; beta <- args$beta; X <- args$X
  idx.smp <- floor((n - 1) / nobs) + 1
  idx.obs <- n - (idx.smp - 1) * nobs
  return (exp(- t ^ alpha[idx.smp] * 
                exp(sum(X[idx.obs, ] * beta[idx.smp, ]))));
}

# preparing function and argument lists
X.pred <- as.matrix(cbind(1, bmt[idx.pred, c("platelet", "age", "tcell")]))
arg.1 <- list(nobs = nobs.pred, natt = 4, nsmp = nsmp
  , alpha = exp(reg1$smp$betas), beta = reg1$smp$beta, X = X.pred)
arg.2 <- list(nobs = nobs.pred, natt = 4, nsmp = nsmp
  , alpha = exp(reg2$smp$betas), beta = reg2$smp$beta, X = X.pred)
arg.list <- list(arg.1, arg.2)
f.list <- list(survfunc, survfunc)

# cause-specific competing-risk
# set rel.tol to smaller number in real-world applications
out.cfc <- cfc(f.list, arg.list, nobs.pred * nsmp, tout, rel.tol = 1e-2)

# summarizing (and plotting) the results
# this function calculates the population-average CI and survival, one
# per each MCMC sample; therefore, the quantiles produced by the summary
# method, correspondingly, reflect our confidence in population-average values
my.f.reduce <- function(x, nobs, nsmp) {
  return (colMeans(array(x, dim = c(nobs, nsmp))))
}
my.summ <- summary(out.cfc, f.reduce = my.f.reduce, nobs = nobs.pred, nsmp = nsmp)


## End(Not run)