CRAN Task View: Survival Analysis
|Maintainer:||Arthur Allignol and Aurelien Latouche|
|Contact:||arthur.allignol at uni-ulm.de|
Survival analysis, also called event history analysis in social science,
or reliability analysis in engineering, deals with time until occurrence
of an event of interest. However, this failure time may not be observed
within the relevant time period, producing so-called censored observations.
This task view aims at presenting the useful R packages for the analysis
of time to event data.
Please let the
something is inaccurate or missing.
Standard Survival Analysis
Estimation of the Survival Distribution
function from the
computes the Kaplan-Meier estimator for truncated and/or censored data.
(replacement of the Design package)
proposes a modified version of the
package implements a fast algorithm and some features
not included in
Various confidence intervals and confidence bands for the Kaplan-Meier estimator
are implemented in the
the Kaplan-Meier estimator.
package includes a function to compute the Kaplan-Meier
estimator for left-censored data.
provides a weighted
survival curve for each level of categorical variables with
missing data. The
computes the Kaplan-Meier estimator from
histogram data. The
package permits to compute a
weighted Kaplan-Meier estimate. The
plots the survival function using a
variant of the Kaplan-Meier estimator in a hospitalisation risk
presmoothed estimates of the main quantities used for
right-censored data, i.e., survival, hazard and density functions.
package permits to compute the Kaplan-Meier
estimator following Pollock et al. (1998). The
package provides several functions for computing confidence
intervals of the survival distribution (e.g., beta product
confidence procedure). The
implements the modified jackknife estimator of the Kaplan-Meier
package offers various
length-bias corrections to survival curve
estimation. Non-Parametric confidance bands for the Kaplan-Meier
estimator can be computed using the
package implements the Kaplan-Meier estimator
Non-Parametric maximum likelihood estimation (NPMLE):
package provides several ways to compute the NPMLE
of the survival distribution for various censoring and truncation
can also be used to compute the MLE for interval-censored data.
permits to compute the NPMLE of the cumulative distribution
function for left- and right-censored data.
function in package
computes the NPMLE
for interval-censored data.
implements several algorithms permitting to analyse possibly doubly
truncated survival data.
permits to fit an univariate distribution by maximum
likelihood. Data can be interval censored.
package provides routines for fitting
models in the vitality family of mortality models.
to estimate the hazard function through kernel methods for right-censored data.
the instantaneous hazard from the Kaplan-Meier estimator.
to estimate the hazard function using splines.
package aims at estimating the hazard function for interval
package provides non-parametric smoothing
of the hazard through B-splines.
compares survival curves using the Fleming-Harrington G-rho family of test.
implements this class of tests for left-censored
implements a permutation version of the
logrank test and a version of the logrank that adjusts for
implements the shift-algorithm by Streitberg and Roehmel for
computing exact conditional p-values and quantiles, possibly for censored data.
the logrank test reformulated as a linear rank test.
package performs tests using maximally selected
package implements logrank and Wilcoxon type tests
for interval-censored data.
compares 2 hazard ratios.
implements a two stage procedure for comparing
package proposes to test the equality of
two survival distributions based on the Gini index.
package offers several tests based on the
Fleming-Harrington class for comparing surival curves with right-
and interval-censored data.
package provides a logrank test for which
aggregated data can be used as input.
The short term and long term hazard ratio model for two samples
survival data can be found in the
package fits the Cox model.
package propose some extensions to the
function. The package
implements the Firth's penalised maximum likelihood bias reduction
method for the Cox model. An implementation of weighted
estimation in Cox regression can be found in
package proposes a robust implementation
of the Cox model.
fits Cox models
with possibly time-varying effects. The
fits Cox models for covariates with missing data. A Cox model
model can be fitted to data from complex survey design using
package fits Cox
models using a weighted partial likelihood for nested case-control
package implements the
Cox model for interval-censored data using the ICM-algorithm.
package implements Pan's (2000) multiple
imputation approach to Cox models for interval censored data.
package fits Cox models for
interval-censored data through an EM algorithm.
package fits time-varying coefficient
models for interval censored and right censored survival data
using a Bayesian Cox model, a spline based Cox model or a
transformation model. The
the Cox proportional hazards model with shape constrained hazard
package implements the Cox
model using an active set algorithm for dummy variables of ordered
package fits Cox models using
maximum penalised likelihood and provide a non parametric smooth
estimate of the baseline hazard function.
computes goodness-of-fit methods for the Cox proportional hazards
model. The proportionality assumption can be checked using
package calculates concordance probability
estimate for the Cox model, as does the
the latter package draws a quantile curve of the survival
distribution as a function of covariates. The
package computes simultaneous tests and confidence intervals for
the Cox model and other parametric survival
package permits to obtain
least-squares means (and contrasts thereof) from linear models. In
particular, it provides support for
package on Bioconductor proposes a resampling based multiple
hypothesis testing that can be applied to the Cox model. Testing
coefficients of Cox regression models using a Wald test with a
sandwich estimator of variance can be done using
permits to plot visualisation of the relative importance of
covariates in a proportional hazards
package provides hazard ratio
curves that allows for nonlinear relationship between predictor
and survival. The
package permits to compute the
unadjusted/adjusted attributable fraction function from a Cox
proportional hazards model. The
tools to check the proportional hazards assumption using a standardised
Parametric Proportional Hazards Model:
survival) fits a parametric
proportional hazards model. The
packages implement a proportional hazards
model with a parametric baseline hazard. The
translates an AFT model to a proportional
hazards form. The
function that fits a hazard regression
model, using splines to model the baseline hazard. Hazards can be,
but not necessarily, proportional. The
implements the model of Royston and Parmar (2002). The model uses
natural cubic splines for the baseline survival function, and
proportional hazards, proportional odds or probit functions for
package fits a Weibull
regression model for right-censored data in which one covariate
might be censored.
Accelerated Failure Time (AFT) Models:
function in package
can fit an accelerated failure time model.
A modified version of
is implemented in the
function). It permits to
use some of the
package also proposes an implementation of the
AFT model (function
aftreg). An AFT model with an
error distribution assumed to be a mixture of G-splines is
implemented in the
package proposes the front end of
function for left-censored data. A
least-square principled implementation of the AFT model can be
found in the
package implements the Simulation-Extrapolation algorithm for the
AFT model, that can be used when covariates are subject to
measurement error. A robust version of the accelerated failure
time model can be found
fits AFT models for interval censored data. The
package implements both rank-based estimates and least square
estimates (via generalised estimating equations) to the AFT model.
An alternative weighting scheme for parameter estimation in the
AFT model is proposed in the
package implements elastic
net regularisation for the AFT model.
fit the additive hazards model of Aalen in
also proposes an implementation
of the Cox-Aalen model (that can also be used to perform the Lin, Wei and
Ying (1994) goodness-of-fit for Cox regression models) and the
partly parametric additive risk model of McKeague and Sasieni. A
version of the Cox-Aalen model for interval censored data is
available in the
Buckley-James model, though the latter does it without
an intercept term. The
package fits the Buckley-James
model with high-dimensional covariates (L2 boosting, regression
trees and boosted MARS, elastic net).
can fit other types of models depending on the chosen
, a tobit model. The
package provides the
function, which is a
to fit the tobit model. An
implementation of the tobit model for cross-sectional data and
panel data can be found in the
package provides implementation of the
proportional odds model and of the proportional excess hazards
package fits the inverse Gaussian
distribution to survival data. The model is based on describing
time to event as the barrier hitting time of a Wiener process,
where drift towards the barrier has been randomized with a
Gaussian distribution. The
package computes the
pseudo-observation for modelling the survival function based on
the Kaplan-Meier estimator and the restricted mean.
fits parametric time-to-event models, in which
any parametric distribution can be used to model the survival
probability, and where one of the parameters is a linear function
of covariates. The
provides a multiplicative relative risk and
an additive excess risk model for interval-censored data.
package can fit vector generalised linear and
additive models for censored data. The
package implements the generalised additive model for location,
scale and shape that can be fitted to censored data.
produces local regression estimates. The
function included in the
package implements a
conditional quantile regression model for censored data.
package fits shared parameter models for the
joint modelling of a longitudinal response and event times. The
temporal process regression model is implemented in
package. Aster models, which combine aspects
of generalized linear models and Cox models, are implemented in
package implements conditional logistic
regression for survival data as an alternative to the Cox model
when hazards are non-proportional.
extension of the
package, fits latent variable models
for censored outcomes via a probit link
package implements Markov
beta and gamma processes for modelling the hazard ratio for
discrete failure time data. The
packages proposes some model-free contrast comparison measures
such as difference/ratio of cumulative hazards, quantiles and
General Multistate Models:
function from package
can be fitted for any
transition of a multistate model. It can also be used for
comparing two transition hazards, using correspondence between
multistate models and time-dependent covariates. Besides, all the
regression methods presented above can be used for multistate
models as long as they allow for left-truncation.
package provides convenient functions for
estimating and plotting the cumulative transition hazards in any
multistate model, possibly subject to right-censoring and
permits to estimate and
plot the transition probabilities for any multistate model. It
also estimates the change of length of hospital stay. The
package estimates and plots transition
probabilities for any multistate models. It can also estimate the
variance of the Aalen-Johansen estimator, and handles
left-truncated data. It also implements the technique for
estimating the length of hospital stay included in
in the presence of left-truncation. The
package provides non-parametric estimation for
multistate models subject to right-censoring (possibly
state-dependent) and left-truncation. The
package permits to estimate hazards and probabilities, possibly
depending on covariates, and to obtain prediction probabilities in
the context of competing risks and multistate models. The
package contains functions for fitting general
continuous-time Markov and hidden Markov multistate models to
longitudinal data. Transition rates and output processes can be
modelled in terms of covariates. The
can be used to fit semi-Markov multistate models in continuous
time. The distribution of the waiting times can be chosen between
the exponential, the Weibull and exponentiated Weibull
distributions. Non-parametric estimates in illness-death models
and other three state models can be obtained with package
package permits to
estimate transition probabilities of an illness-death model or
three-state progressive model. The
package to estimation in the
mulstistate model framework, while the
proposes L1 penalised estimation. The
package permits to fit Cox models to the progressive illness-death
model observed under right-censored survival times and interval-
or right-censored progression times. The
package fits proportional hazards models for the illness-death model
with possibly interval-censored data for transition toward the
transient state. Left-truncated and right-censored data are also
allowed. The model is either parametric (Weibull) or
semi-parametric with M-splines approximation of the baseline
Lexis objects as a way to represent, manipulate and summarise data
from multistate models. The
intended for analysing state or event sequences that describe life
package permits to describe and
analyse life histories following a multistate perspective on the
expected numbers of individuals in specified age classes or life
stages given survivorship probabilities from a transition matrix.
estimates the cumulative incidence functions, but they can be
compared in more than two samples. The package also implements
the Fine and Gray model for regressing the subdistribution hazard
of a competing risk.
stratified and clustered data. The
performs a Kaplan-Meier multiple imputation to recover missing
potential censoring information from competing risks events,
permitting to use standard right-censored methods to analyse
cumulative incidence functions. The
implements stepwise covariate selection for the Fine and Gray
computes pseudo observations for
modelling competing risks based on the cumulative incidence
does flexible regression modelling for
competing risks data based on the on the
inverse-probability-censoring-weights and direct binomial
implements risk regression for competing
risks data, along with other extensions of existing packages
useful for survival analysis and competing risks data.
package estimates the conditional probability
of a competing event, aka., the conditional cumulative
incidence. It also implements a proportional-odds model using
either the temporal process regression or the pseudo-value
can also be used
to estimate the cumulative incidence function.
package estimates event-specific incidence
rates, rate ratios, event-specific incidence proportions and
cumulative incidence functions.
provides summary measures for
competing risk such as ensemble CIF. The
package implements the semi-parametric mixture model for competing
risks data. The
package implements a
proportional subdistribution hazards model with adjustment for
covariate-dependent censoring. The
implements Pan's (2000) multiple imputation approach to the Fine
and Gray model for interval censored data.
Recurrent event data:
package can be used to analyse recurrent event
function of the
fits the Anderson-Gill model for recurrent events, model that can
also be fitted with the
package. The latter
also permits to fit joint frailty models for joint modelling of
recurrent events and a terminal event. The
package proposes implementations of several models for recurrent
events data, such as the Peña-Strawderman-Hollander,
Wang-Chang estimators, and MLE estimation under a Gamma Frailty
implements the conditional GEE for recurrent event gap times.
implements weighted logrank type tests for recurrent events.
package proposes several functions to deal
with relative survival data. For example,
computes a relative
fits an additive model and
fits the Cox model of Andersen et al. for relative survival, while
fits a Cox model in transformed time.
package permits to fit relative survival models like
the proportional excess and additive excess models.
package implements methods for
population-based survival analysis, like the proportional hazard
relative survival model and the join point relative survival model.
package computes relative survival,
absolute excess risk and standardized mortality ratio based on
French death rates.
package permits to fit multiplicative
regression models for relative survival.
package implements time-dependent ROC curves
and extensions to relative survival.
Random Effect Models
Frailty terms can be added
survival. A mixed-effects Cox model is
implemented in the
function in the
package fits the Clayton-Oakes-Glidden model.
package fits fully parametric frailty models
via maximisation of the marginal likelihood.
package fits proportional hazards
models with a shared Gamma frailty to right-censored and/or
left-truncated data using a penalised likelihood on the hazard
function. The package also fits additive and nested frailty models
that can be used for, e.g., meta-analysis and for hierarchically
clustered data (with 2 levels of clustering), respectively. A
proportional hazards model with mixed effects can be fitted using
package fits a
linear mixed-effects model for left-censored data. The Cox model
using h-likelihood estimation for the frailty terms can be fitted
package implements a linear mixed effects model for censored data
with Student-t or normal distributions.
Joint modelling of time-to-event and longitudinal
package allows the analysis
of repeated measurements and time-to-event data via joint random effects
Multivariate survival refers to the analysis of unit, e.g., the
survival of twins or a family. To analyse such data, we can estimate
the joint distribution of the survival times
can estimate bivariate
survival data subject to interval censoring.
package implements various statistical models
for multivariate event history data, e.g., multivariate cumulative
incidence models, bivariate random effects probit models,
package constructs trees for multivariate
survival data using marginal and frailty models.
package proposes an implementation of a bivariate
computes a Bayesian model averaging for
Cox proportional hazards models.
fits a Bayesian
semi-parametric AFT model.
in the same package
fits a Linear Dependent Dirichlet Process Mixture of survival models.
performs an MCMC estimation
of normal mixtures for censored data.
A MCMC for Gaussian linear regression with left-, right- or interval-censored
data can be fitted using the
package estimates the hazard function from censored
data in a Bayesian framework.
the log posterior density for a Weibull proportional-odds regression model.
fits generalised linear mixed models using MCMC
to right-, left- and interval censored data.
package aims at drawing inference on
age-specific mortality from capture-recapture/recovery data when
some or all records have missing information on times of birth
and death. Covariates can also be included in the model.
package performs joint modelling of
longitudinal and time-to-event data under a bayesian approach.
Bayesian parametric and semi-parametric estimation for
semi-competing risks data is available via the
package implements penalized
semi-parametric Bayesian Cox models with elastic net, fused lasso and
group lasso priors.
package fits a Bayesian parametric
proportional hazards model for which events have been geo-located.
package implements Bayesian clustering
using a Dirichlet process mixture model to censored responses.
package provides Bayesian model fitting
for several survival models including spatial copula, linear
dependent Dirichlet process mixture model, anova Dirichlet process
mixture model, proportional hazards model and marginal spatial
proportional hazards model.
package implements non-parametric
survival analysis techniques using a prior near-ignorant Dirichlet
packages implement CART-like trees that can be used with
package implements recursive partitioning for survival
can perform logic regression.
implements K-adaptive partitioning and recursive
partitioning algorithms for censored survival data.
package implements trees and bagged trees for
discrete-times survival data.
bagging for survival data. The
package fits random forest to survival data, while a variant of
the random forest is implemented in
implementation is proposed in the
Regularised and shrinkage methods:
package implements a L1 regularised Cox
proportional hazards model. An L1 and L2 penalised Cox models are
computes a nearest shrunken centroid for survival gene expression
data. A high dimensional Cox model using univariate shrinkage is
implements the lassoed principal components method.
package implements the LASSO and elastic net
estimator for the additive risk model. The
package implements the Lasso and elastic-net penalized Cox's
regression using the cockail algorithm. The
package permits to fit Cox models with a combination of lasso and
group lasso regularisation.
fits Cox models
with penalized ridge-type (ridge, dynamic and weighted dynamic)
partial likelihood. The
accelerated failure time models using regularised weighted least
squares (e.g., weighted elastic net, adaptive elastic net).
Gradient boosting for the Cox model is implemented in the
package includes a generic gradient boosting algorithm
for the construction of prognostic and diagnostic models for right-censored data.
implements permutation-based testing procedure to test
the additional predictive value of high-dimensional data. It is based on
provides routines for fitting the Cox proportional hazards model
and the Fine and Gray model by likelihood based boosting.
the supervised principal components for survival data.
package can construct index models for survival
outcomes, that is, construct scores based on a training dataset.
package fits Cox proportional hazards
model using the compound covariate method.
provides partial least squares regression and various techniques
for fitting Cox models in high dimensionnal
package implements feature selection
algorithms based on subsampling and averaging linear models
obtained from the Lasso algorithm for predicting survival risk.
Predictions and Prediction Performance
package provides utilities to plot prediction error
curves for several survival models
implements prediction error techniques which can
be computed in a parallelised way. Useful for high-dimensional
package permits to estimate time-dependent
ROC curves and time-dependent AUC with censored data, possibly
with competing risks.
computes time-dependent ROC curves and time-dependent AUC from
censored data using Kaplan-Meier or Akritas's nearest neighbour estimation method
(Cumulative sensitivity and dynamic specificity).
implements time-dependent ROC curves,
AUC and integrated AUC of Heagerty and Zheng (Biometrics, 2005).
Various time-dependent true/false positive rates and
Cumulative/Dynamic AUC are implemented in the
package provides several functions to
assess and compare the performance of survival models.
C-statistics for risk prediction models with censored survival
data can be computed via the
package implements the integrated
discrimination improvement index and the category-less net
reclassification index for comparing competing risks prediction
package provides functions for
estimating the AUC, TPR(c), FPR(c), PPV(c), and NPV(c) for
package proposes power calculation for weighted
Log-Rank tests in cure rate models.
permits to calculate sample size based on
proportional hazards mixture cure models.
package provides power and sample size
calculation for survival analysis (with a focus towards
Power analysis and sample size calculation for SNP association
studies with time-to-event outcomes can be done using
package permits to generate data wih one
binary time-dependent covariate and data stemming from a
progressive illness-death model.
package permits the user to simulate
complex survival data, in which event and censoring times could be
conditional on an user-specified list of (possibly time-dependent)
package permits to simulate
complex survival cohort data (e.g., multiple events, recurrent
package proposes some functions for
simulating complex event history data.
package also permits to simulate and analyse
multistate models. The package allows for a general specification
of the transition hazard functions, for non-Markov models and
for dependencies on the history.
package provides functions for simulating
complex multistate models data with possibly nonlinear baseline
hazards and nonlinear covariate effects.
package implements tools for simulating and
plotting quantities of interest estimated from proportional
package permits to simulate simple and
complex survival data such as recurrent event data and competing
package provides routines for performing
continuous-time microsimulation for population projection. The
basis for the microsimulation are a multistate model, Markov or
non-Markov, for which the transition intensities are specified, as
well as an initial cohort.
This section tries to list some specialised plot functions that might be
useful in the context of event history analysis.
packages both propose
functions for plotting survival curves with the at risk table aligned to
the x axis.
extends this to the competing risks
to draw the states and transitions that characterize a multistate
package provides many plot functions for
representing multistate data, in particular Lexis diagrams.
package provide multistate-type graphics
for competing risks, in which the thickness of the transition
arrows from the initial event to each competing event describes
the particular amount of every incidence rate.
implements several types of bootstrap techniques for right-censored data.
package estimates the current
cumulative incidence and the current leukaemia free survival function.
provides tools for individual patient data meta-analysis, mixed-level meta-analysis with patient
level data and mulivariate survival estimates for aggregate studies.
package includes the data sets from Klein
and Moeschberger (1997). Some supplementary data sets and
functions can be found in the
that accompanies Aitkin et al. (2009),
that accompanies Davidson (2003)
that accompanies Maindonald, J.H. and Braun,
W.J. (2003, 2007) also contain survival data sets.
package permits to construct, validate and
calibrate nomograms stemming from complex right-censored survey
package compute the MLE of a density
(log-concave) possibly for interval censored data.
package fits parametric
Transform-both-sides models used in reliability analysis
package implements algorithms to detect outliers
based on quantile regression for censored data.
package proposes miscellaneous functions
that extends the
package, e.g., additional
logrank type tests, goodness of fit plots.
package implements an EM algorithm
to estimate the relative case fatality ratio between two groups.