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 maintainers know if something is inaccurate or missing.

Standard Survival Analysis

Estimation of the Survival Distribution

• Kaplan-Meier: The survfit function from the survival package computes the Kaplan-Meier estimator for truncated and/or censored data. rms (replacement of the Design package) proposes a modified version of the survfit function. The prodlim package implements a fast algorithm and some features not included in survival. Various confidence intervals and confidence bands for the Kaplan-Meier estimator are implemented in the km.ci package. plot.Surv of package eha plots the Kaplan-Meier estimator. The NADA package includes a function to compute the Kaplan-Meier estimator for left-censored data. svykm in survey provides a weighted Kaplan-Meier estimator. nested.km in NestedCohort estimates the survival curve for each level of categorical variables with missing data. The kaplan-meier function in spatstat computes the Kaplan-Meier estimator from histogram data. The MAMSE package permits to compute a weighted Kaplan-Meier estimate. The KM function in package rhosp plots the survival function using a variant of the Kaplan-Meier estimator in a hospitalisation risk context. The survPresmooth package computes presmoothed estimates of the main quantities used for right-censored data, i.e., survival, hazard and density functions.
• Nonparametric maximum likelihood estimation (NPMLE): The Icens package provides several ways to compute the NPMLE of the survival distribution for various censoring and truncation schemes. MLEcens can also be used to compute the MLE for interval-censored data. dblcens permits to compute the NPMLE of the cumulative distribution function for left- and right-censored data. The icfit function in package interval computes the NPMLE for interval-censored data. The DTDA implements several algorithms permitting to analyse possibly doubly truncated survival data.
• MLE: The fitdistrplus package permits to fit an univariate distribution by maximum likelihood. Data can be interval censored.

Hazard Estimation

• The muhaz package permits to estimate the hazard function through kernel methods for right-censored data.
• The epi.insthaz function from epiR computes the instantaneous hazard from the Kaplan-Meier estimator.
• polspline, gss and logspline allow to estimate the hazard function using splines.
• The ICE package aims at estimating the hazard function for interval censored data.

Testing

• The survdiff function in survival compares survival curves using the Fleming-Harrington G-rho family of test. NADA implements this class of tests for left-censored data.
• clinfun implements a permutation version of the logrank test and a version of the logrank that adjusts for covariates.
• The exactRankTests implements the shift-algorithm by Streitberg and Roehmel for computing exact conditional p-values and quantiles, possibly for censored data.
• SurvTest in the coin package implements the logrank test reformulated as a linear rank test.
• surv2sample computes Neyman's smooth, logrank, Kolmogorov-Smirnov, Cramer-von Mises and Anderson-Darling tests to compare 2 survival curves.
• The maxstat package performs tests using maximally selected rank statistics.
• The interval package implements logrank and Wilcoxon type tests for interval-censored data.
• Three generalised logrank tests and a score test for interval-censored data are implemented in the glrt package.
• survcomp compares 2 hazard ratios.
• The TSHRC implements a two stage procedure for comparing hazard functions.
• The cmprskContin package compares continuous mark-specific relative risks in two treatment groups, with a view towards vaccine trials.

Regression Modelling

• Cox model: The coxph function in the survival package fits the Cox model. cph in the rms package and the eha package propose some extensions to the coxph function. The package coxphf 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 coxphw. The coxrobust package proposes a robust implementation of the Cox model. The Cox model can be fitted to interval-censored data using the intcox package. timecox in package timereg fits Cox models with possibly time-varying effects. The mfp package permits to fit Cox models with multiple fractional polynomial. The NestedCohort fits Cox models for covariates with missing data. A Cox model model can be fitted to data from complex survey design using the svycoxph function in survey. The OrdFacReg package implements the Cox model using an active set algorithm for dummy variables of ordered factors.
  
  The cumres function in gof computes goodness-of-fit methods for the Cox proportional hazards model. The proportionality assumption can be checked using the cox.zph function in survival, and also with the proptest package. The CPE package calculates concordance probability estimate for the Cox model, as does the coxphCPE function in clinfun. The coxphQuantile in the latter package draws a quantile curve of the survival distribution as a function of covariates. The multcomp package computes simultaneous tests and confidence intervals for the Cox model and other parametric survival models. The multtest 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 the saws package. The rankhazard package permits to plot visualisation of the relative importance of covariates in a proportional hazards model.
• Parametric Proportional Hazards Model: survreg (from survival) fits a parametric proportional hazards model. The eha and mixPHM packages implement a proportional hazards model with a parametric baseline hazard. The pphsm in rms translates an AFT model to a proportional hazards form. The polspline package includes the hare function that fits a hazard regression model, using splines to model the baseline hazard. Hazards can be, but not necessarily, proportional.
• Accelerated Failure Time (AFT) Models: The survreg function in package survival can fit an accelerated failure time model. A modified version of survreg is implemented in the rms package ( psm function). It permits to use some of the rms functionalities. The eha 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 smoothSurv package. The NADA package proposes the front end of the survreg function for left-censored data. A least-square principled implementation of the AFT model can be found in the lss package. The simexaft package implements the Simulation-Extrapolation algorithm for the AFT model, that can be used when covariates are subject to measurement error.
• Additive Models: Both survival and timereg fit the additive hazards model of Aalen in functions aareg and aalen, respectively. timereg also proposes an implementation of the Cox-Aalen model and the partly parametric additive risk model of McKeague and Sasieni.
• Buckley-James Models: The bj function in rms and BJnoint in emplik compute the Buckley-James model, though the latter does it without an intercept term.
• Other models: Functions like survreg can fit other types of models depending on the chosen distribution, e.g. , a tobit model. The AER package provides the tobit function, which is a wrapper of survreg to fit the tobit model. An implementation of the tobit model for cross-sectional data and panel data can be found in the censReg package. The timereg package provides implementation of the proportional odds model and of the proportional excess hazards model. The pseudo package computes the pseudo-observation for modelling the survival function based on the Kaplan-Meier estimator and the restricted mean. The Icens function in package Epi provides a multiplicative relative risk and an additive excess risk model for interval-censored data. The VGAM package can fit vector generalised linear and additive models for censored data. The gamlss.cens package implements the generalised additive model for location, scale and shape that can be fitted to censored data. The nltm package fits non-linear transformation models for censored data, which include, e.g. , proportional hazards, proportional odds, or cure models. The locfit.censor function in locfit produces local regression estimates. The crq function included in the quantreg package implements a conditional quantile regression model for censored data. The JM package fits shared parameter models for the joint modelling of a longitudinal response and event times. The temporal process regression model is implemented in the tpr package. The TwoWaySurvival package permits to fit an additive model using two time scales. The spef package fits a proportional means model for panel count survival data. Aster models, which combine aspects of generalized linear models and Cox models, are implemented in the aster and aster2 packages. The concreg package implements conditional logistic regression for survival data as an alternative to the Cox model when hazards are non-proportional.

Multistate Models

• General Multistate Models: The coxph function from package survival 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.
  
  The mvna package provides convenient functions for estimating and plotting the cumulative transition hazards in any multistate model, possibly subject to right-censoring and left-truncation. changeLOS permits to estimate and plot the transition probabilities for any multistate model. It also estimates the change of length of hospital stay. The etm 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 changeLOS in the presence of left-truncation. The msSurv package provides nonparametric estimation for multistate models subject to right-censoring (possibly state-dependent) and left-truncation. The mstate 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 msm 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 mspath package, based on msm, can fit non-Markov multistate models by maximum likelihood, using a discrete-time approximation. Nonparametric estimates in illness-death models and other three state models can be obtained with package p3state.msm.
  
  The Epi package implements Lexis objects as a way to represent, manipulate and summarise data from multistate models. The TraMineR package is intended for analysing state or event sequences that describe life courses. Also, the Biograph package provides various functions for exploring life histories.
• Competing risks: surv2sample provides estimation of the cumulative incidence functions for several causes of failure. The package also performs comparison in two samples. The package cmprsk also 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. crrSC extends the cmprsk package to stratified and clustered data. The kmi package 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. Package pseudo computes pseudo observations for modelling competing risks based on the cumulative incidence functions. timereg does flexible regression modelling for competing risks data based on the on the inverse-probability-censoring-weights and direct binomial regression approach. The CompetingRiskFrailty package estimates the cause-specific hazards of a competing risks model using frailties and splines. The Cprob 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 approaches. Packages survival (via survfit) and prodlim can also be used to estimate the cumulative incidence function. The compeir package estimates event-specific incidence rates, rate ratios, event-specific incidence proportions and cumulative incidence functions. RandomSurvivalForest provides summary measures for competing risk such as ensemble CIF.
• Recurrent event data: coxph from the survival package can be used to analyse recurrent event data. The cph function of the rms package fits the Anderson-Gill model for recurrent events, model that can also be fitted with the frailtypack package. The latter also permits to fit joint frailty models for joint modelling of recurrent events and a terminal event. The survrec 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 model. The Peña-Hollander model can be fitted using the gcmrec package. The condGEE package implements the conditional GEE for recurrent event gap times. survivalBIV permits to estimate the bivariate distribution of two gap times.

Relative Survival

• The relsurv package proposes several functions to deal with relative survival data. For example, rs.surv computes a relative survival curve. rs.add fits an additive model and rsmul fits the Cox model of Andersen et al. for relative survival, while rstrans fits a Cox model in transformed time.
• The timereg package permits to fit relative survival models like the proportional excess and additive excess models.

Multivariate Survival

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 or use frailty models.

• Joint modelling: Both Icens and MLEcens can estimate bivariate survival data subject to interval censoring.
• Frailties: Frailty terms can be added in coxph and survreg functions in package survival. The coxme function in package kinship fits a mixed-effects Cox model. A more broad version of it is implemented in the coxme package. The two.stage.reg function in the timereg package fits the Clayton-Oakes-Glidden model. The frailtypack 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 the phmm package. The lmec 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 using the frailtyHL package.

Bayesian Models

• survBayes fits through a Bayesian approach a proportional hazards model for right and interval-censored data.
• The bayesSurv package proposes an implementation of a bivariate AFT model.
• The package BMA computes a Bayesian model averaging for Cox proportional hazards models.
• The DPsurvint function in DPpackage fits a Bayesian semiparametric AFT model. LDDPsurvival in the same package fits a Linear Dependent Dirichlet Process Mixture of survival models.
• NMixMCMC in mixAK 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 MCMCtobit in MCMCpack.
• The BayHaz package estimates the hazard function from censored data in a Bayesian framework.
• The weibullregpost function in learnBayes computes the log posterior density for a Weibull proportional-odds regression model.
• The MCMCglmm fits generalised linear mixed models using MCMC to right-, left- and interval censored data.
• The splinesurv package implements a proportional hazards model for possibly clustered survival data using MCMC. Baseline hazard and frailty densities are modelled using B-splines.

High-Dimensional Data

• Recursive partitioning: rpart and mvpart packages implement CART-like trees that can be used with censored outcomes. The party package implements recursive partitioning for survival data. LogicReg can perform logic regression.
• Random forest: Package ipred implements bagging for survival data. The randomSurvivalForest package fits random forest to survival data, while a variant of the random forest is implemented in party.
• Regularised and shrinkage methods: The glmpath package implements a L1 regularised Cox proportional hazards model. An L1 and L2 penalised Cox models are available in penalized. The pamr package computes a nearest shrunken centroid for survival gene expression data. A high dimensional Cox model using univariate shrinkage is available in uniCox. The lpc package implements the lassoed principal components method. The timereg package implements the LASSO estimator for the additive risk model. bujar provides the Buckley-James regression model for high-dimensional data.
• Boosting: Gradient boosting for the Cox model is implemented in the gbm package. The mboost package includes a generic gradient boosting algorithm for the construction of prognostic and diagnostic models for right-censored data. globalboosttest implements permutation-based testing procedure to test the additional predictive value of high-dimensional data. It is based on mboost. CoxBoost provides routines for fitting the Cox proportional hazards model and the Fine and Gray model by likelihood based boosting.
• Other: The superpc package implements the supervised principal components for survival data. Package plsRcox fits Cox models in a high dimensional setting through partial least square regression. The AIM package can construct index models for survival outcomes, that is, construct scores based on a training dataset.

Predictions and Prediction Performance

• The pec package provides utilities to plot prediction error curves for several survival models
• peperr implements prediction error techniques which can be computed in a parallelised way. Useful for high-dimensional data.
• survivalROC 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).
• risksetROC 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 survAUC package.
• The survcomp package provides several functions to assess and compare the performance of survival models.

Miscellaneous

• Inverse probability weights can be estimated using the ipw package. These can be used to fit marginal structural models to estimate causal effects from observational data.
• Package boot proposes the censboot function that implements several types of bootstrap techniques for right-censored data.
• The powerSurvEpi package provides power and sample size calculation for survival analysis (with a focus towards epidemiological studies).
• The PermAlgo package permits to simulate complex survival data, in which event and censoring times could be conditional on an user-specified list of (possibly time-dependent) covariates.
• The survJamda package provides functions for performing meta-analyses of gene expression data and to predict patients' survival and risk assessment.
• ipdmeta provides tools for individual patient data meta-analysis, mixed-level meta-analysis with patient level data and mulivariate survival estimates for aggregate studies.
• The KMsurv package includes the data sets from Klein and Moeschberger (1997). The package SMIR that accompanies Aitkin et al. (2009), SMPracticals that accompanies Davidson (2003) and DAAG that accompanies Maindonald, J.H. and Braun, W.J. (2003, 2007) also contain survival data sets.