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The Bone Marrow Transplant Data

Description

Bone marrow transplant data with 408 rows and 5 columns.

Format

The data has 408 rows and 5 columns.

cause

a numeric vector code. Survival status. 1: dead from treatment related causes, 2: relapse , 0: censored.

time

a numeric vector. Survival time.

platelet

a numeric vector code. Plalelet 1: more than 100 x10^9 per L, 0: less.

tcell

a numeric vector. T-cell depleted BMT 1:yes,0:no.

age

a numeric vector code. Age of patient, scaled andcentered ((age-35)/15).

Source

Simulated data (taken from R package 'timereg')

Cause-specific competing-risk survival analysis

Description

Using adaptive generalized Newton-Cotes for calculating cumulative incidence functions.

Usage

cfc(f.list, args.list, n, tout, Nmax = 100L, rel.tol = 1e-05, ncores = 1)

Arguments

Value

An object of classcfc, which is a list with the following elements:

Author(s)

Mansour T.A. Sharabiani, Alireza S. Mahani

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.

See Also

cfc.survreg

Examples

## Not run: library("survival") # used for constructing survival formulaslibrary("BSGW") # used for Bayesian survival regressiondata("bmt")# splitting data into training and prediction setsidx.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 BSGWout.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$dattmax <- out.prep$tmax# estimating cause-specific models# set nsmp to larger number in real-world applicationsnsmp <- 10reg1 <- 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 modelsurvfunc <- 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 listsX.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 applicationstout <- 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)

Cause-specific competing-risk survival analysis in probability denomination

Description

Constructing cumulative incidence and event-free probability functions from cause-specific survival times give for a fixed set of probabilities.

Usage

cfc.pbasis(t1, t2, probs, unity.tol = 1e-06, diff.tol = 0.01,  diff.tol.policy = c("all", "mean"))

Arguments

Details

For each 'row' oft1, andt2, all elements are processed independently. To combine the survival curves from corresponding elements oft1 andt2, we first form a 'comon denominator' time vector by combining the two time vectors and sorting the results (after removing duplicates). We limit the maximum value in the combined time vector to minimum of the the two maxima from each cause. Next, we use interpolation to find survival probabilities of each cause at all the time points in the combined time vector. Finally, we call the functioncfc.tbasis.

Value

Ift1 andt2 are one-dimensional, a matrix with columns named"time","ci1","ci2" and"efp" is returned. For multi-dimensional arrays, a list is returned with one such matrix for each element of the consolidated dimension representing all but the first dimension oft1 andt2.

Author(s)

Mansour T.A. Sharabiani, Alireza S. Mahani

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

Prentice et al (1978). The analysis of failure times in the presence of competing risks. Biometrics, 541-554.

See Also

cfc.tbasis

Examples

## Not run: # prepare data for cause-specific competing-risk analysisdata(bmt)bmt$status1 <- 1*(bmt$cause==1)bmt$status2 <- 1*(bmt$cause==2)f1 <- Surv(time, status1) ~ platelet + age + tcellf2 <- Surv(time, status2) ~ platelet + age + tcell# perform weibull regression on each cause independentlylibrary(survival)reg1 <- survreg(f1, bmt)reg2 <- survreg(f2, bmt)# predict times for given probabilities# transpose predictions so that first dimension# is time/probability (use first 50 observations for speed)pvec <- seq(from=1.0, to = 0.1, length.out = 100)pred1 <- t(predict(reg1, newdata = bmt[1:50,], p = 1-pvec, type = "quantile"))pred2 <- t(predict(reg2, newdata = bmt[1:50,], p = 1-pvec, type = "quantile"))# cause-specific competing risk analysis - probability modemy.cfc <- cfc.pbasis(pred1, pred2, probs = pvec)# calculating averages across observations (e.g. patients in the study)my.summ <- summary(my.cfc)# plotting average CI and event-free probability curvesplot(my.summ)## End(Not run)

Utility function for CFC data preparation

Description

Preparing a data frame and formulas for cause-specific competing-risk survival analysis. It expands the multi-state status column into a series of binary columns by treating an event for a cause as censoring for all other causes.

Usage

cfc.prepdata(formul, dat)

Arguments

Details

The output data frame will haveK new binary status columns. TheK new status columns will be named"status_1","status_2" through"status_<K>". Each of the output formulas informula.list field will have the correspondingstatus. Column "status_1" will be1 whereverstatus equals1 in original data frame, and0 elsewhere, and similarly for the remainingK-1 newly-added status columns.

Value

A list with the following elements:

Author(s)

Mansour T.A. Sharabiani, Alireza S. Mahani

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

Examples

data(bmt)prep.out <- cfc.prepdata(Surv(time, cause) ~ platelet + age + tcell, bmt)

Cause-specific competing-risk survival analysis, using parametric survival regression models

Description

Convenient function to build cause-specific, parametric survival models using thesurvival package. This is followed by application ofcfc function to produce cumulative incidence functions.

Usage

cfc.survreg(formula, data, newdata = NULL, dist = "weibull"  , control = survreg.control(), tout, Nmax = 100L  , rel.tol = 1e-05)

Arguments

Value

A list with the following elements:

Author(s)

Mansour T.A. Sharabiani, Alireza S. Mahani

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.prepdata,cfc

Examples

data(bmt)formul <- Surv(time, cause) ~ platelet + age + tcellret <- cfc.survreg(formul, bmt[1:300, ], bmt[-(1:300), ]  , Nmax = 300, rel.tol = 1e-3)

Survival probability function forsurvreg models

Description

Function for predicting survival probability as a function of time forsurvreg regression objects insurvival package. It can be used to mixsurvreg models with other survival models in competing-risk analysis, usingCFC package. This function is used insidecfc.survreg.

Usage

cfc.survreg.survprob(t, args, n)

Arguments

Value

Vector of survival probabilities at time(s)t.

Author(s)

Mansour T.A. Sharabiani, Alireza S. Mahani

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.survreg

Examples

## Not run: library("CFC") # for cfcdata(bmt)library("randomForestSRC") # for rfsrclibrary("survival") # for survregprep <- cfc.prepdata(Surv(time, cause) ~ platelet + age + tcell, bmt)f1 <- prep$formula.list[[1]]f2 <- prep$formula.list[[2]]dat <- prep$dattmax <- prep$tmax# building a parametric Weibull regression model# for cause 1reg1 <- survreg(f1, dat, x = TRUE) # must keep x for prediction# building a random forest survival model for cause 2reg2 <- rfsrc(f2, dat)# implementing a continuous interface for the random forest# survival functionrfsrc.survfunc <- function(t, args, n) {  which.zero <- which(t < .Machine$double.eps)  ret <- approx(args$time.interest, args$survival[n, ], t, rule = 2)$y  ret[which.zero] <- 1.0  return (ret)}# constructing function and argument listf.list <- list(cfc.survreg.survprob, rfsrc.survfunc)arg.list <- list(reg1, reg2)# competing-risk analysistout <- seq(0.0, tmax, length.out = 10)# increase rel.tol for higher accuracycfc.out <- cfc(f.list, arg.list, nrow(bmt), tout, rel.tol = 1e-3)## End(Not run)

Cause-specific competing-risk survival analysis in time denomination

Description

Constructing cumulative incidence and event-free probability functions from cause-specific survival probabilities evaluated at fixed time points.

Usage

cfc.tbasis(p1, p2, unity.tol = 1e-06, diff.tol = 0.01,  diff.tol.policy = c("mean", "all"), check = TRUE)

Arguments

Details

Assuming one-dimensionalp1 andp2 for clarity, the algorithm calculates cumulative incidence function for cuase 1 using a recursive formula:ci1[n+1] = ci1[n] + dci1[n], wheredci1[n] = 0.5*(p2[n] + p2[n+1])*(p1[n] - p1[n+1]). The increment in cumulative incidence function for cause 2 is similarly calculated,dci2[n] = 0.5*(p1[n] + p1[n+1])*(p2[n] - p2[n+1]). These equations guarantee thatdci1[n] + dci2[n] = p1[n]*p2[n] - p1[n+1]*p2[n+1]. Event-free probability is simply calculated asefp[n] = p1[n]*p2[n]. Taken together, this numerical integration ensures thatefp[n+1] - efp[n] + dci1[n] + dci2[n] = 0.

Value

Ifp1 andp2 are one-dimensional arrays (i.e. vectors), a matrix with columns named"ci1","ci2" and"efp" is returned, representing the cummulative incidence functions for cause 1 and cause 2 and the event-free probability, evaluated at same time points asp1 andp2 are provided. Ifp1 andp2 are multi-dimensional arrays, a list is returned with elements"ci1","ci2" and"efp", each one with the same interpretation, and all of the same dimensions asp1 andp2.

Note

The integration algorithm described above does not require knowledge of time step. (Alternatively, using hazard functions for integration would have required specification of time step.) Sincep1 andp2 are integrals (followed by exponentiation) of cause-specific hazard functions, using them directly adds to robustness of numerical integration and avoids error accumulation. The returned cumulative incidence and event-free probabilities correspond to the same time points assumed for input cause-specific probabilities.

Author(s)

Mansour T.A. Sharabiani, Alireza S. Mahani

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

Prentice et al (1978). The analysis of failure times in the presence of competing risks. Biometrics, 541-554.

See Also

cfc.pbasis

Examples

## Not run: # prepare data for cause-specific competing-risk analysisdata(bmt)bmt$status1 <- 1*(bmt$cause==1)bmt$status2 <- 1*(bmt$cause==2)f1 <- Surv(time, status1) ~ platelet + age + tcellf2 <- Surv(time, status2) ~ platelet + age + tcell# sample-based bayesian weibull regressionlibrary(BSGW)reg1 <- bsgw(f1, bmt, ordweib = TRUE, control = bsgw.control(iter = 500, burnin = 100, nskip = 50))reg2 <- bsgw(f2, bmt, ordweib = TRUE, control = bsgw.control(iter = 500, burnin = 100, nskip = 50))# prediction on a uniform grid of 100 time points# (use first 50 observations for speed)pred1 <- predict(reg1, newdata = bmt[1:50,], tvec = 100)pred2 <- predict(reg2, newdata = bmt[1:50,], tvec = 100)# permuting dimensions of survival objects to conform with cfcS1 <- aperm(pred1$smp$S, c(2,1,3))S2 <- aperm(pred2$smp$S, c(2,1,3))# cause-specific competing risk analysis - time modemy.cfc <- cfc.tbasis(S1, S2)# calculating averages across observations (e.g. patients in the study)my.summ <- summary(my.cfc, MARGIN = c(1,2))# plotting mean CI and event-free functions# as well as their sampled-based confidence intervalsplot(my.summ, t = pred1$tvec)## End(Not run)

Summarizing and plotting output ofcfc

Description

summary method for classcfc.

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

Value

Recall that the survival probability and cumulative incidence arrays returned bycfc 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, ] ands[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 thequantile function to compute median and credible bands. There is a special case wheref.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 fromsummary 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 regressiondata(bmt)# splitting data into training and prediction setsidx.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 BSGWout.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$dattmax <- out.prep$tmax# estimating cause-specific models# set nsmp to larger number in real-world applicationsnsmp <- 10reg1 <- 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 modelsurvfunc <- 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 listsX.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 applicationsout.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 valuesmy.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)

Summarizing probability-denominated CFC objects

Description

summary method for classcfc.pbasis.

Usage

## S3 method for class 'cfc.pbasis'summary(object, ...)## S3 method for class 'summary.cfc.pbasis'plot(x, ...)

Arguments

Value

The functionsummary.cfc.pbasis calculates the average of cumulative incidence and event-free probability functions at each time point across all elements of the object list. If the object is a matrix, it is returned without change.

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

The model fitting function iscfc.pbasis. Seesummary andplot for descriptions of the generic methods. Seecfc.tbasis for time-denominated CFC, as well as usage examples.

Summarizing and plotting output ofcfc.survreg

Description

summary and method for classcfc.survreg.

Usage

## S3 method for class 'cfc.survreg'summary(object, obs.idx = "all", ...)## S3 method for class 'summary.cfc.survreg'plot(x, which = c(1, 2), ...)

Arguments

Value

summary.cfc.surveeg produces a matrix of dimensionslength(object$tout) (number of time points) byobject$K (number of causes). See description ofwhich aregument forplot.summary.cfc.survreg.

Author(s)

Mansour T.A. Sharabiani, Alireza S. Mahani

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

The model fitting function iscfc.survreg. Seesummary andplot for descriptions of the generic methods. For more flexible ways of cause-specific competing-risk analysis, seecfc.

Summarizing time-denominated CFC objects

Description

summary method for classcfc.tbasis.

Usage

## S3 method for class 'cfc.tbasis'summary(object,  MARGIN = if (class(object)[2] == "matrix") NULL else 1,  ...)## S3 method for class 'summary.cfc.tbasis'plot(x, t = 1, ci = 0.95, ...)

Arguments

Value

The functionsummary.cfc.tbasis calculates the average of cumulative incidence and event-free probability functions as directed byMARGIN. For example, if the elementci1 of the object list is three-dimensional, then usingMARGIN=c(1,2) causes the last dimension to be averaged out.

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

The model fitting function iscfc.tbasis. Seesummary andplot for descriptions of the generic methods. Seecfc.pbasis for probability-denominated CFC, as well as usage examples.