#' @title Estimate Survival Time Functions
#' @description This function estimates survival time functions: survival,
#' relative/net survival, and crude/absolute risk functions (CIF).
#'
#' @param adjust can be used as an alternative to passing variables to
#' argument \code{formula} within a call to \code{adjust()}; e.g.
#' \code{adjust = "agegr"}. \link[=flexible_argument]{Flexible input}.
#'
#' @param weights typically a list of weights or a \code{character} string
#' specifying an age group standardization scheme; see
#' the \link[=direct_standardization]{dedicated help page}
#' and examples. NOTE: \code{weights = "internal"} is based on the counts
#' of persons in follow-up at the start of follow-up (typically T = 0)
#'
#' @param surv.type one of \code{'surv.obs'},
#' \code{'surv.cause'}, \code{'surv.rel'},
#' \code{'cif.obs'} or \code{'cif.rel'};
#' defines what kind of survival time function(s) is/are estimated; see Details
#'
#' @param surv.method either \code{'lifetable'} or \code{'hazard'}; determines
#' the method of calculating survival time functions, where the former computes
#' ratios such as \code{p = d/(n - n.cens)}
#' and the latter utilizes subject-times
#' (typically person-years) for hazard estimates such as \code{d/pyrs}
#' which are used to compute survival time function estimates.
#' The former method requires argument \code{n.cens} and the latter
#' argument \code{pyrs} to be supplied.
#'
#' @param relsurv.method either \code{'e2'} or \code{'pp'};
#' defines whether to compute relative survival using the
#' EdererII method or using Pohar-Perme weighting;
#' ignored if \code{surv.type != "surv.rel"}
#'
#' @param subset a logical condition; e.g. \code{subset = sex == 1};
#' subsets the data before computations
#'
#' @param conf.level confidence level used in confidence intervals;
#' e.g. \code{0.95} for 95 percent confidence intervals
#'
#' @param conf.type character string; must be one of \code{"plain"},
#' \code{"log-log"} and \code{"log"};
#' defines the transformation used on the survival time
#' function to yield confidence
#' intervals via the delta method
#'
#' @param verbose logical; if \code{TRUE}, the function is chatty and
#' returns some messages and timings along the process
#'
#' @section Basics:
#'
#' This function computes interval-based estimates of survival time functions,
#' where the intervals are set by the user. For product-limit-based
#' estimation see packages \pkg{survival} and \pkg{relsurv}.
#'
#' if \code{surv.type = 'surv.obs'}, only 'raw' observed survival
#' is estimated over the chosen time intervals. With
#' \code{surv.type = 'surv.rel'}, also relative survival estimates
#' are supplied in addition to observed survival figures.
#'
#' \code{surv.type = 'cif.obs'} requests cumulative incidence functions (CIF)
#' to be estimated.
#' CIFs are estimated for each competing risk based
#' on a survival-interval-specific proportional hazards
#' assumption as described by Chiang (1968).
#' With \code{surv.type = 'cif.rel'}, a CIF is estimated with using
#' excess cases as the ''cause-specific'' cases. Finally, with
#' \code{surv.type = 'surv.cause'}, cause-specific survivals are
#' estimated separately for each separate type of event.
#'
#' In hazard-based estimation (\code{surv.method = "hazard"}) survival
#' time functions are transformations of the estimated corresponding hazard
#' in the intervals. The hazard itself is estimated using counts of events
#' (or excess events) and total subject-time in the interval. Life table
#' \code{surv.method = "lifetable"} estimates are constructed as transformations
#' of probabilities computed using counts of events and counts of subjects
#' at risk.
#'
#'
#' The vignette \href{../doc/survtab_examples.html}{survtab_examples}
#' has some practical examples.
#'
#' @section Relative survival:
#'
#' When \code{surv.type = 'surv.rel'}, the user can choose
#' \code{relsurv.method = 'pp'}, whereupon Pohar-Perme weighting is used.
#' By default \code{relsurv.method = 'e2'}, i.e. the Ederer II method
#' is used to estimate relative survival.
#'
#' @section Adjusted estimates:
#'
#' Adjusted estimates in this context mean computing estimates separately
#' by the levels of adjusting variables and returning weighted averages
#' of the estimates. For example, computing estimates separately by
#' age groups and returning a weighted average estimate (age-adjusted estimate).
#'
#' Adjusting requires specification of both the adjusting variables and
#' the weights for all the levels of the adjusting variables. The former can be
#' accomplished by using \code{adjust()} with the argument \code{formula},
#' or by supplying variables directly to argument \code{adjust}. E.g. the
#' following are all equivalent:
#'
#' \code{formula = fot ~ sex + adjust(agegr) + adjust(area)}
#'
#' \code{formula = fot ~ sex + adjust(agegr, area)}
#'
#' \code{formula = fot ~ sex, adjust = c("agegr", "area")}
#'
#' \code{formula = fot ~ sex, adjust = list(agegr, area)}
#'
#' The adjusting variables must match with the variable names in the
#' argument \code{weights};
#' see the \link[=direct_standardization]{dedicated help page}.
#' Typically weights are supplied as a \code{list} or
#' a \code{data.frame}. The former can be done by e.g.
#'
#' \code{weights = list(agegr = VEC1, area = VEC2)},
#'
#' where \code{VEC1} and \code{VEC2} are vectors of weights (which do not
#' have to add up to one). See
#' \href{../doc/survtab_examples.html}{survtab_examples}
#' for an example of using a \code{data.frame} to pass weights.
#'
#'
#' @section Period analysis and other data selection schemes:
#'
#' To calculate e.g. period analysis (delayed entry) estimates,
#' limit the data when/before supplying to this function.See
#' \href{../doc/survtab_examples.html}{survtab_examples}.
#'
#' @return
#' Returns a table of life time function values and other
#' information with survival intervals as rows.
#' Returns some of the following estimates of survival time functions:
#'
#' \itemize{
#' \item \code{surv.obs} - observed (raw, overall) survival
#' \item \code{surv.obs.K} - observed cause-specific survival for cause K
#' \item \code{CIF_k} - cumulative incidence function for cause \code{k}
#' \item \code{CIF.rel} - cumulative incidence function using excess cases
#' \item \code{r.e2} - relative survival, EdererII
#' \item \code{r.pp} - relative survival, Pohar-Perme weighted
#' }
#' The suffix \code{.as} implies adjusted estimates, and \code{.lo} and
#' \code{.hi} imply lower and upper confidence limits, respectively.
#' The prefix \code{SE.} stands for standard error.
#'
#'
#' @seealso
#' \code{\link{splitMulti}}, \code{\link{lexpand}},
#' \code{\link{ICSS}}, \code{\link{sire}}
#' \href{../doc/survtab_examples.html}{The survtab_examples vignette}
#'
#' @references
#'
#' Perme, Maja Pohar, Janez Stare, and Jacques Esteve.
#' "On estimation in relative survival." Biometrics 68.1 (2012): 113-120.
#' \doi{10.1111/j.1541-0420.2011.01640.x}
#'
#' Hakulinen, Timo, Karri Seppa, and Paul C. Lambert.
#' "Choosing the relative survival method for cancer survival estimation."
#' European Journal of Cancer 47.14 (2011): 2202-2210.
#' \doi{10.1016/j.ejca.2011.03.011}
#'
#' Seppa, Karri, Timo Hakulinen, and Arun Pokhrel.
#' "Choosing the net survival method for cancer survival estimation."
#' European Journal of Cancer (2013).
#' \doi{10.1016/j.ejca.2013.09.019}
#'
#' CHIANG, Chin Long. Introduction to stochastic processes in biostatistics.
#' 1968. ISBN-14: 978-0471155003
#'
#' Seppa K., Dyba T. and Hakulinen T.: Cancer Survival,
#' Reference Module in Biomedical Sciences. Elsevier. 08-Jan-2015.
#' \doi{10.1016/B978-0-12-801238-3.02745-8}
#'
#' @family main functions
#' @family survtab functions
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