# Cause-specific competing-risk survival analysis Using adaptive generalized Newton-Cotes for calculating cumulative incidence functions. ```r cfc(f.list, args.list, n, tout, Nmax = 100L, rel.tol = 1e-05, ncores = 1) ``` ## Arguments - `f.list`: In `R` mode, this is a list of survival functions, one per cause. Each survival function must have the prototype `f(t, args, n)`, where `t` is a vector of time-from-index values, `args` is a list of all arguments needed by the function, and `n` is the iterator that allows the function to produce a different output for each observation and/or Bayesian sample. The output is a vector of survival probabilities at times `t` for that particular observation/sample combination with iterator value `n`. In `C++` mode, this is a list of lists, one per cause. Each list must contain pointers to three `C++` functions, in order: 1) survival function of type `func` with prototype defined as `typedef arma::vec (*func)(arma::vec x, void* arg, int n)` (using `RcppArmadillo`'s `vec` class) and a similar interpetation as its `R` counterpart, 2) initializer function of type `initfunc`, with prototype defined as `typedef void* (*initfunc)(List arg)`, where `List` is the `Rcpp` wrapper class for `R` lists, and 3) resource de-allocator function of type `freefunc` with this prototype: `typedef void (*freefunc)(void *arg)`. See vignette for `C++` example. - `args.list`: List of arguments (each one a list), one per cause, to be supplied to the survival functions in `f.list`. - `n`: Range of iterator (starting at `1`) for survival functions. This can be the product of number of observations, and number of MCMC samplers in a Bayesian survival function. - `tout`: Vector of time points for which cumulative incidence functions are requested. - `Nmax`: Maximum number of subdivisions in the interval [`0`, `max(tout)`] to be created in the adaptive quadrature algorithm. - `rel.tol`: Threshold for relative integration error, used as stoppage criterion. It is calculated as the maximum relative error at time point `max(tout)` across all causes. Each relative error number is the difference between the Simpson-based and trapezoidal-based numbers, divided by the Simpson-based number. - `ncores`: Number of parallel threads to use. This is currrently only implemented in `C++` mode. ## Returns An object of class `cfc`, which is a list with the following elements: - **ci**: Array of dimensions `(length(tout), length(f.list), n)`, cumulative incidence functions for all causes and all values of the iterator, evaluated at all time points indicated by `tout`. - **s**: Array of same dimensions as `ci`, containing the (unadjusted) survival functions for all causes and all values of the iterator, evaluated at all time points indicated by `tout`. - **is.maxiter**: Binary Array of length `n`, where `1` indicates that subdivision process for quadrature problem applied to survival functions at iteration `n` reached maximum set by `Nmax` before converging, and `0` otherwise. - **n.maxiter**: Number of iterations that did not converge, i.e., `sum(is.maxiter)`. ## References Haller, B., Schmidt, G., & Ulm, K. (2013). Applying competing risks regression models: an overview. Lifetime data analysis, 1-26. 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 Prentice et al (1978). The analysis of failure times in the presence of competing risks. Biometrics, 541-554. ## Author(s) Mansour T.A. Sharabiani, Alireza S. Mahani ## See Also `cfc.survreg` ## Examples ```r ## Not run: library("survival") # used for constructing survival formulas 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 tout <- seq(from = 0.0, to = tmax, length.out = 10) out.cfc <- cfc(f.list, arg.list, nobs.pred * nsmp, tout, rel.tol = 1e-2) ## End(Not run) ```

cfc function