# ci.Crisk: Compute cumulative risk and/or expected sojourn time from... In Epi: Statistical Analysis in Epidemiology

## Description

Consider a list of parametric models for rates of competing events, such as different causes of death, A, B, C, say. From estimates of the cause-specific rates we can then by simple numerical integration compute the cumulative risk of being in each state ('Surv' (=no event) and A, B and C) at different times, as well as the stacked cumulative rates such as A, A+C, A+C+Surv. Finally, we can compute the expected (truncated) sojourn times in each state up to each time point.

This function does this for simulated samples from the parameter vectors of supplied model objects, and computes the mentioend quantities with simulation-based confidence intervals. Some call this a prametric bootstrap.

The times and other covariates determining the cause-specific rates must be supplied in a data frame which will be used for predicting rates for all transitions.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```ci.Crisk(mods, nd, int = mean(diff(nd[, 1])), nB = 1000, perm = length(mods):0 + 1, alpha = 0.05, sim.res = 'none') sim2ci.Crisk(probs, alpha = 0.05) sim2ci.Srisk(probs, perm = 1:dim(probs), alpha = 0.05) sim2ci.Stime(probs, int = attr(probs, "int"), alpha = 0.05) ```

## Arguments

 `mods` A named list of `glm`/`gam` model objects representing the cause-specific rates. If the list is not named the function will crash. The names will be used as names for the states (competing risks), while the state without any event will be called "`Surv`". `nd` A data frame of prediction points and covariates. Must represent midpoints of equidistant intervals. `int` Numeric, the length of the intervals. Defaults to the differences in the first column of `nd`. `nB` Scalar. The number of simulations, that is samples from the (posterior) distribution of the model parameters. `perm` Numerical vector of length `lengh(mods)+1` indicating the order in which states are to be stacked. The `'Surv'` state is taken to be the first, the remaining in the reverse order supplied in the `mods` argument. The default is therefore to stack with the survival as the first, which may not be what you normally want. `alpha` numeric. 1 minus the confidence level used in calculating the c.i.s `sim.res` Character. What simulation samples should be returned. If `'none'` (the default) the function returns a list of 3 arrays (see under 'value'). If `'rates'` it returns an array of dimension `nrow(nd)` x `length(mod)` x `nB` of bootstrap samples of the rates. If `'crisk'` it returns an array of dimension `(nrow(nd)+1)` x `length(mod)` x `nB` of bootstrap samples of the culmulative rates. Only the first letter matters, regardless of whether it is in upper lower case. `probs` Three-way array of simulated cumulative risks classified by 1) time points, 2) causes (incl. surv) and 3) Samples. A structure as returned by `ci.Crisk` with `sim.res='crisk'`.

## Value

A named list of three-way arrays with results from simulation (parametric bootstrap) from the distribution of the parameters in the models in `mods`:

• `Crisk` Cumulative risks for the `length(mods)` events and the survival

• `Srisk` Stacked versions of the cumulative risks

• `Stime` Sojourn times in each states

All three arrays have (almost) the same dimensions:

• `time`: end points of intervals starting with "`0`". Length `nrow(nd)+1`, except for `Stime` where it is only `nrow(nd)`, "`0`" not included.

• State. `Crisk` and `Stime` has values `Surv` plus the names of the list `mods` (first argument). `Srisk` has length `length(mod)`, with each level representing a cumultive sum of cumulatieve risks, in order indicated by the `perm` argument.

• `ci.50%`, `ci.2.5%`, `ci.97.5%` representing quantiles of the quantities derived from the bootstrap samples. If `alpha` is different from 0.05, names are of course different.

## Author(s)

Bendix Carstensen, http://bendixcarstensen.com

`mat2pol` `simLexis` `plotCIF` `ci.surv`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56``` ```library(Epi) data(DMlate) # A Lexis object for survival Ldm <- Lexis(entry = list( per = dodm, age = dodm-dobth, tfd = 0 ), exit = list( per = dox ), exit.status = factor( !is.na(dodth), labels = c("DM","Dead") ), data = DMlate[sample(1:nrow(DMlate),1000),] ) summary(Ldm, timeScales = TRUE) # Cut at OAD and Ins times Mdm <- mcutLexis( Ldm, wh = c('dooad','doins'), new.states = c('OAD','Ins'), precursor = 'Alive', seq.states = FALSE, ties = TRUE ) summary( Mdm\$lex.dur ) # restrict to DM state Sdm <- splitLexis(factorize(subset(Mdm, lex.Cst == "DM")), time.scale = "tfd", breaks = seq(0,20,1/12)) summary(Sdm) summary(Relevel(Sdm, c(1, 4, 2, 3))) boxes(Relevel(Sdm, c(1, 4, 2, 3)), boxpos = list(x = c(15, 85, 80, 15), y = c(85, 85, 20, 15)), scale.R = 100) # glm models for the cause-specific rates system.time( mD <- glm.Lexis(Sdm, ~ Ns(tfd, knots=0:6*2), to = 'Dead') ) system.time( mO <- glm.Lexis(Sdm, ~ Ns(tfd, knots=0:6*2), to = 'OAD' ) ) system.time( mI <- glm.Lexis(Sdm, ~ Ns(tfd, knots=0:6*2), to = 'Ins' ) ) # intervals for calculation of predicted rates int <- 1/100 nd <- data.frame( tfd = seq(int,10,int)-int/2 ) # not the same as the split, # and totally unrelated to it # cumulaive risks with confidence intervals # (too few timepoints, too few simluations) system.time( res <- ci.Crisk(list(OAD = mO, Ins = mI, Dead = mD), nd = data.frame(tfd = (1:100-0.5)/10), nB = 100, perm = 4:1)) str(res) ```