Task view: Survival Analysis

Last updated on 2022-01-10 by Arthur Allignol and Aurelien Latouche

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. The Task View is also on github. Feel free to open an issue or submit a pull request.

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. The kaplan-meier function in spatstat computes the Kaplan-Meier estimator from histogram data. 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. The asbio package permits to compute the Kaplan-Meier estimator following Pollock et al. (1998). The bpcp package provides several functions for computing confidence intervals of the survival distribution (e.g., beta product confidence procedure). The lbiassurv package offers various length-bias corrections to survival curve estimation. The kmc package implements the Kaplan-Meier estimator with constraints. The landest package allows landmark estimation and testing of survival probabilities. The jackknifeKME package computes the original and modified jackknife estimates of Kaplan-Meier estimators. The tranSurv package permits to estimate a survival distribution in the presence of dependent left-truncation and right-censoring. The condSURV package provides methods for estimating the conditional survival function for ordered multivariate failure time data. The gte package implements the generalised Turnbull estimator proposed by Dehghan and Duchesne for estimating the conditional survival function with interval-censored data.
  • Non-Parametric 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 package implements several algorithms permitting to analyse possibly doubly truncated survival data. npsurv computes the NPMLE of a survival function for general interval-censored data.
  • Parametric: The fitdistrplus package permits to fit an univariate distribution by maximum likelihood. Data can be interval censored. The vitality package provides routines for fitting models in the vitality family of mortality models.

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.
  • The bshazard package provides non-parametric smoothing of the hazard through B-splines.


  • 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.
  • 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 Survgini package proposes to test the equality of two survival distributions based on the Gini index.
  • The FHtest package offers several tests based on the Fleming-Harrington class for comparing surival curves with right- and interval-censored data.
  • The LogrankA 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 YPmodel package.
  • The controlTest implements a nonparametric two-sample procedure for comparing the median survival time.
  • The survRM2 package performs two-sample comparison of the restricted mean survival time
  • The emplik2 package permits to compare two samples with censored data using empirical likelihood ratio tests.

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. timecox in package timereg fits Cox models with possibly time-varying effects. A Cox model model can be fitted to data from complex survey design using the svycoxph function in survey. The multipleNCC package fits Cox models using a weighted partial likelihood for nested case-control studies. The MIICD package implements Pan's (2000) multiple imputation approach to Cox models for interval censored data. The ICsurv package fits Cox models for interval-censored data through an EM algorithm. The dynsurv 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 OrdFacReg package implements the Cox model using an active set algorithm for dummy variables of ordered factors. The survivalMPL package fits Cox models using maximum penalised likelihood and provide a non parametric smooth estimate of the baseline hazard function. A Cox model with piecewise constant hazards can be fitted using the pch package. The icenReg package implements several models for interval-censored data, e.g., Cox, proportional odds, and accelerated failure time models. A Cox type Self-Exciting Intensity model can be fitted to right-censored data using the coxsei package. The SurvLong contains methods for estimation of proportional hazards models with intermittently observed longitudinal covariates. The plac package provides routines to fit the Cox model with left-truncated data using augmented information from the marginal of the truncation times.
    The proportionality assumption can be checked using the cox.zph function in survival. The coxphCPE function in clinfun calculates concordance probability estimate for the Cox model. 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 lsmeans package permits to obtain least-squares means (and contrasts thereof) from linear models. In particular, it provides support for the coxph, survreg and coxme functions. 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. The smoothHR package provides hazard ratio curves that allows for nonlinear relationship between predictor and survival. The paf package permits to compute the unadjusted/adjusted attributable fraction function from a Cox proportional hazards model. The PHeval package proposes tools to check the proportional hazards assumption using a standardised score process. The ELYP package implements empirical likelihood analysis for the Cox Model and Yang-Prentice (2005) 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. The flexsurv package 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 regression. The SurvRegCensCov package allows estimation of a Weibull Regression for a right-censored endpoint, one interval-censored covariate, and an arbitrary number of non-censored covariates.
  • 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. The simexaft 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 in RobustAFT. The coarseDataTools package fits AFT models for interval censored data. An alternative weighting scheme for parameter estimation in the AFT model is proposed in the imputeYn package. The AdapEnetClass package implements elastic net regularisation for the AFT model.
  • 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 (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 coxinterval package. The uniah package fits shape-restricted additive hazards models. The addhazard package contains tools to fit additive hazards model to random sampling, two-phase sampling and two-phase sampling with auxiliary information.
  • 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. The bujar package fits the Buckley-James model with high-dimensional covariates (L2 boosting, regression trees and boosted MARS, elastic net).
  • 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 invGauss 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 pseudo package computes the pseudo-observation for modelling the survival function based on the Kaplan-Meier estimator and the restricted mean. The fastpseudo package dose the same for the restricted mean survival time. flexsurv 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 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 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. 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. The surv2sampleComp packages proposes some model-free contrast comparison measures such as difference/ratio of cumulative hazards, quantiles and restricted mean. The rstpm2 package provides link-based survival models that extend the Royston-Parmar models, a family of flexible parametric models. The TransModel package implements a unified estimation procedure for the analysis of censored data using linear transformation models. The ICGOR fits the generalized odds rate hazards model to interval-censored data while GORCure generalized odds rate mixture cure model to interval-censored data. The thregI package permits to fit a threshold regression model for interval-censored data based on the first-hitting-time of a boundary by the sample path of a Wiener diffusion process. The miCoPTCM package fits semiparametric promotion time cure models with possibly mis-measured covariates. The smcure package permits to fit semiparametric proportional hazards and accelerated failure time mixture cure models. The case-base sampling approach for fitting flexible hazard regression models to survival data with single event type or multiple competing causes via logistic and multinomial regression can be found in package casebase.

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. 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. The msSurv package provides non-parametric 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 msmtools package provides utilities to facilitate the modelling of longitudinal data under a multistate framework using the msm package.The SemiMarkov package 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 p3state.msm. The TPmsm package permits to estimate transition probabilities of an illness-death model or three-state progressive model. The gamboostMSM package extends the mboost package to estimation in the mulstistate model framework, while the penMSM package proposes L1 penalised estimation. The coxinterval 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 SmoothHazard 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 intensities. The TP.idm package implement the estimator of Una-Alvarez and Meira-Machado (2015) for non-Markov illness-death models.
    The Epi package implements Lexis objects as a way to represent, manipulate and summarise data from multistate models. The LexisPlotR package, based on ggplot2, permits to draw Lexis diagrams. The TraMineR package is intended for analysing state or event sequences that describe life courses. asbio computes the expected numbers of individuals in specified age classes or life stages given survivorship probabilities from a transition matrix.
  • Competing risks: The package cmprsk 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. The crrstep package implements stepwise covariate selection for the Fine and Gray model. 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. riskRegression implements risk regression for competing risks data, along with other extensions of existing packages useful for survival analysis and competing risks data. 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 NPMLEcmprsk package implements the semi-parametric mixture model for competing risks data. The MIICD package implements Pan's (2000) multiple imputation approach to the Fine and Gray model for interval censored data. The CFC package permits to perform Bayesian, and non-Bayesian, cause-specific competing risks analysis for parametric and non-parametric survival functions. The gcerisk package provides some methods for competing risks data. Estimation, testing and regression modeling of subdistribution functions in the competing risks setting using quantile regressions can be had in cmprskQR. The intccr package permits to fit the Fine and Gray model as well other models that belong to the class of semiparametric generalized odds rate transformation models to interval-censored competing risks data.
  • 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 condGEE package implements the conditional GEE for recurrent event gap times. The reda package provides function to fit gamma frailty model with either a piecewise constant or a spline as the baseline rate function for recurrent event data, as well as some miscellaneous functions for recurrent event data. Several regression models for recurrent event data are implemented in the reReg package. The spef package includes functions for fitting semiparametric regression models for panel count survival data.

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.
  • The mexhaz package allows fitting an hazard regression model using different shapes for the baseline hazard. The model can be used in the relative survival setting (excess mortality hazard) as well as in the overall survival setting (overall mortality hazard).
  • The flexrsurv package implements the models of Remontet et al. (2007) and Mahboubi et al. (2011).
  • The survexp.fr package computes relative survival, absolute excess risk and standardized mortality ratio based on French death rates.
  • The MRsurv package permits to fit multiplicative regression models for relative survival.

Random Effect Models

  • Frailties: Frailty terms can be added in coxph and survreg functions in package survival. A mixed-effects Cox model is implemented in the coxme package. The two.stage function in the timereg package fits the Clayton-Oakes-Glidden model. The parfm package fits fully parametric frailty models via maximisation of the marginal likelihood. 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. 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. The tlmec package implements a linear mixed effects model for censored data with Student-t or normal distributions. The frailtySurv package simulates and fits semiparametric shared frailty models under a wide range of frailty distributions. The parfm package implements parametric frailty models by maximum marginal likelihood. The PenCoxFrail package provides a regularisation approach for Cox frailty models through penalisation. The mexhaz enables modelling of the excess hazard regression model with time-dependent and/or non-linear effect(s) and a random effect defined at the cluster level. The frailtyEM package contains functions for fitting shared frailty models with a semi-parametric baseline hazard with the Expectation-Maximization algorithm. Supported data formats include clustered failures with left truncation and recurrent events in gap-time or Andersen-Gill format
  • Joint modelling of time-to-event and longitudinal data: The joineR package allows the analysis of repeated measurements and time-to-event data via joint random effects models. The joint.Cox package performs Cox regression and dynamic prediction under the joint frailty-copula model between tumour progression and death for meta-analysis. JointModel fits semiparametric regression model for longitudinal responses and a semiparametric transformation model for time-to-event data. The joineRML package fits the joint model proposed by Henderson and colleagues (2000) doi:10.1093/biostatistics/1.4.465, but extended to the case of multiple continuous longitudinal measures. The rstanarm package fits joint models for one or more longitudinal outcomes (continuous, binary or count data) and a time-to-event, estimated under a Bayesian framework.

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

  • Joint modelling: Both Icens and MLEcens can estimate bivariate survival data subject to interval censoring.
  • The mets package implements various statistical models for multivariate event history data, e.g., multivariate cumulative incidence models, bivariate random effects probit models, Clayton-Oakes model.
  • The MST package constructs trees for multivariate survival data using marginal and frailty models.
  • The SurvCorr package permits to estimate correlation coefficients with associated confidence limits for bivariate, partially censored survival times.

Bayesian Models

  • The bayesSurv package proposes an implementation of a bivariate AFT model.
  • The package BMA computes a Bayesian model averaging for Cox proportional hazards 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 BaSTA 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.
  • The JMbayes package performs joint modelling of longitudinal and time-to-event data under a bayesian approach.
  • The rstanarm package fits a joint model for one or more longitudinal outcomes (continuous, binary or count data) and a time-to-event under a Bayesian framework.
  • Bayesian parametric and semi-parametric estimation for semi-competing risks data is available via the SemiCompRisks package.
  • The psbcGroup package implements penalized semi-parametric Bayesian Cox models with elastic net, fused lasso and group lasso priors.
  • The PReMiuM package implements Bayesian clustering using a Dirichlet process mixture model to censored responses.
  • The spBayesSurv 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.
  • The IDPSurvival package implements non-parametric survival analysis techniques using a prior near-ignorant Dirichlet Process.
  • The ICBayes packages permits to fit Bayesian semiparametric regression survival models (proportional hazards model, proportional odds model, and probit model) to interval-censored time-to-event data
  • The BayesPiecewiseICAR package fits a piecewise exponential hazard to survival data using a Hierarchical Bayesian model.

Machine learning

  • Recursive partitioning: rpart implements CART-like trees that can be used with censored outcomes. The party package implements recursive partitioning for survival data. LogicReg can perform logic regression. kaps implements K-adaptive partitioning and recursive partitioning algorithms for censored survival data. The DStree package implements trees and bagged trees for discrete-times survival data. The LTRCtrees package provides recursive partition algorithms designed for fitting survival tree with left-truncated and right censored data. The package also includes an implementation of recursive partitioning (conditional inference trees) for interval-censored data. bnnSurvival implements a bootstrap aggregated version of the k-nearest neighbors survival probability prediction method.
  • Random forest: Package ipred implements bagging for survival data. The randomForestSRC package fits random forest to survival data, while a variant of the random forest is implemented in party. A faster implementation can be found in package ranger. An alternative algorithm for random forests is implemented in icRSF.
  • Regularised and shrinkage methods: The glmnet package provides procedures for fitting the entire lasso or elastic-net regularization path for Cox models. 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. The lpc package implements the lassoed principal components method. The ahaz package implements the LASSO and elastic net estimator for the additive risk model. The fastcox package implements the Lasso and elastic-net penalized Cox's regression using the cockail algorithm. The SGL package permits to fit Cox models with a combination of lasso and group lasso regularisation. The hdnom package implements 9 types of penalised Cox regression methods and provides methods for model validation, calibration, comparison, and nomogram visualisation. A penalised version of the Fine and Gray model can be found in crrp. The Cyclops package implements cyclic coordinate descent for the Cox proportional hazards model.
  • 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.
  • Other: The superpc package implements the supervised principal components for survival data. The compound.Cox package fits Cox proportional hazards model using the compound covariate method. plsRcox provides partial least squares regression and various techniques for fitting Cox models in high dimensionnal settings. The mlr3proba package, part of the mlr3 ecosystem implements survival models, including classical models (Cox, AFT) and machine learning models(random forests, SVMs).

Predictions and Prediction Performance

  • The pec package provides utilities to plot prediction error curves for several survival models. The riskRegression package now includes most of the functionality of the pec package.
  • peperr implements prediction error techniques which can be computed in a parallelised way. Useful for high-dimensional data.
  • The timeROC package permits to estimate time-dependent ROC curves and time-dependent AUC with censored data, possibly with competing risks.
  • 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).
  • tdROCcan be used to compute time-dependent ROC curve from censored survival data using nonparametric weight adjustments.
  • 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.
  • C-statistics for risk prediction models with censored survival data can be computed via the survC1 package.
  • The survIDINRI package implements the integrated discrimination improvement index and the category-less net reclassification index for comparing competing risks prediction models.
  • The compareC package permits to compare C indices with right-censored survival outcomes
  • The APtools package provide tools to estimate the average positive predictive values and the AUC for risk scores or marker.

Power Analysis

  • The NPHMC permits to calculate sample size based on proportional hazards mixture cure models.
  • The powerSurvEpi package provides power and sample size calculation for survival analysis (with a focus towards epidemiological studies).
  • Power analysis and sample size calculation for SNP association studies with time-to-event outcomes can be done using the survSNP package.


  • The genSurv package permits to generate data wih one binary time-dependent covariate and data stemming from a progressive illness-death model.
  • The PermAlgo 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) covariates.
  • The prodlim package proposes some functions for simulating complex event history data.
  • The gems 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.
  • The simMSM package provides functions for simulating complex multistate models data with possibly nonlinear baseline hazards and nonlinear covariate effects.
  • The simPH package implements tools for simulating and plotting quantities of interest estimated from proportional hazards models.
  • The survsim package permits to simulate simple and complex survival data such as recurrent event data and competing risks.
  • The simsurv package enables the user to simulate survival times from standard parametric survival distributions (exponential, Weibull, Gompertz), 2-component mixture distributions, or a user-defined hazard or log hazard function. Time dependent effects (i.e. non-proportional hazards) can be included by interacting covariates with linear time or some transformation of time.
  • The MicSim 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.
  • The SimHaz package permits to simulate data with a dichotomous time-dependent exposure.
  • The SimSCRPiecewise package can be used to simulate univariate and semi-competing risks data given covariates and piecewise exponential baseline hazards.
  • The SimSurvNMarker package provides functions to simulate from joint survival and potentially multivariate marker models. User-defined basis expansions in time can be passed which effect the log hazard, the markers, and the association between the two.


This section tries to list some specialised plot functions that might be useful in the context of event history analysis.

  • The rms package proposes functions for plotting survival curves with the at risk table aligned to the x axis. prodlim extends this to the competing risks model.
  • The plot.Hist function in prodlim permits to draw the states and transitions that characterize a multistate model.
  • The Epi package provides many plot functions for representing multistate data, in particular Lexis diagrams.
  • The FamEvent generates time-to-event outcomes for families that habour genetic mutation under different sampling designs and estimates the penetrance functions for family data with ascertainment correction.


  • The survminer package contains the function ggsurvplot for drawing survival curves with the 'number at risk' table. Other functions are also available for visual examinations of cox model assumptions.
  • The InformativeCensoring package multiple imputation methods for dealing with informative censoring.
  • The discSurv provides data transformations, estimation utilities, predictive evaluation measures and simulation functions for discrete time survival analysis.
  • dynpred is the companion package to "Dynamic Prediction in Clinical Survival Analysis".
  • Package boot proposes the censboot function that implements several types of bootstrap techniques for right-censored data.
  • The currentSurvival package estimates the current cumulative incidence and the current leukaemia free survival function.
  • The survJamda package provides functions for performing meta-analyses of gene expression data and to predict patients' survival and risk assessment.
  • The KMsurv package includes the data sets from Klein and Moeschberger (1997). The package SMPracticals that accompanies Davidson (2003) and DAAG that accompanies Maindonald, J.H. and Braun, W.J. (2003, 2007) also contain survival data sets.
  • The SvyNom package permits to construct, validate and calibrate nomograms stemming from complex right-censored survey data.
  • The logconcens package compute the MLE of a density (log-concave) possibly for interval censored data.
  • The TBSSurvival package fits parametric Transform-both-sides models used in reliability analysis
  • The coarseDataTools package implements an EM algorithm to estimate the relative case fatality ratio between two groups.
  • The GSSE package proposes a fully efficient sieve maximum likelihood method to estimate genotype-specific distribution of time-to-event outcomes under a nonparametric model
  • power and sample size calculation based on the difference in restricted mean survival times can be performed using the SSRMST package.
  • The survMisc provides miscellaneous routines to help in the analysis of right-censored survival data.
  • Accompanying data sets to the book Applied Survival Analysis Using R can be found in package asaur.


AdapEnetClass — 1.2

A Class of Adaptive Elastic Net Methods for Censored Data

addhazard — 1.1.0

Fit Additive Hazards Models for Survival Analysis

AER — 1.2-9

Applied Econometrics with R

ahaz — 1.14

Regularization for semiparametric additive hazards regression

APtools — 6.8.8

Average Positive Predictive Values (AP) for Binary Outcomes and Censored Event Times

asaur — 0.50

Data Sets for "Applied Survival Analysis Using R""

asbio — 1.7

A Collection of Statistical Tools for Biologists

aster2 — 0.3

Aster Models

aster — 1.1-2

Aster Models

BaSTA — 1.9.4

Age-Specific Survival Analysis from Incomplete Capture-Recapture/Recovery Data

BayesPiecewiseICAR — 0.2.1

Hierarchical Bayesian Model for a Hazard Function

bayesSurv — 3.3

Bayesian Survival Regression with Flexible Error and Random Effects Distributions

BayHaz — 0.1-3

R Functions for Bayesian Hazard Rate Estimation

BMA — 3.18.15

Bayesian Model Averaging

bnnSurvival — 0.1.5

Bagged k-Nearest Neighbors Survival Prediction

boot — 1.3-28

Bootstrap Functions (Originally by Angelo Canty for S)

bpcp — 1.4

Beta Product Confidence Procedure for Right Censored Data

bshazard — 1.1

Nonparametric Smoothing of the Hazard Function

bujar — 0.2-9

Buckley-James Regression for Survival Data with High-Dimensional Covariates

casebase — 0.10.1

Fitting Flexible Smooth-in-Time Hazards and Risk Functions via Logistic and Multinomial Regression

censReg — 0.5-32

Censored Regression (Tobit) Models

CFC — 1.1.2

Cause-Specific Framework for Competing-Risk Analysis

clinfun — 1.0.15

Clinical Trial Design and Data Analysis Functions

cmprsk — 2.2-11

Subdistribution Analysis of Competing Risks

cmprskQR — 0.9.2

Analysis of Competing Risks Using Quantile Regressions

coarseDataTools — 0.6-6

Analysis of Coarsely Observed Data

coin — 1.4-2

Conditional Inference Procedures in a Permutation Test Framework

compareC — 1.3.1

Compare Two Correlated C Indices with Right-censored Survival Outcome

compound.Cox — 3.20

Univariate Feature Selection and Compound Covariate for Predicting Survival

concreg — 0.7

Concordance Regression

condGEE — 0.1-4

Parameter estimation in conditional GEE for recurrent event gap times

condSURV — 2.0.1

Estimation of the Conditional Survival Function for Ordered Multivariate Failure Time Data

controlTest — 1.1.0

Quantile Comparison for Two-Sample Right-Censored Survival Data

coxinterval — 1.2

Cox-Type Models for Interval-Censored Data

coxme — 2.2-16

Mixed Effects Cox Models

coxphf — 1.13.1

Cox Regression with Firth's Penalized Likelihood

coxphw — 4.0.2

Weighted Estimation in Cox Regression

coxrobust — 1.0

Robust Estimation in Cox Model

coxsei — 0.3

Fitting a CoxSEI Model

Cprob — 1.4.1

The Conditional Probability Function of a Competing Event

crrp — 1.0

Penalized Variable Selection in Competing Risks Regression

crrSC — 1.1

Competing risks regression for Stratified and Clustered data

crrstep — 2015-2.1

Stepwise Covariate Selection for the Fine & Gray Competing Risks Regression Model

currentSurvival — 1.0

Estimation of CCI and CLFS Functions

Cyclops — 3.1.2

Cyclic Coordinate Descent for Logistic, Poisson and Survival Analysis

DAAG — 1.24

Data Analysis and Graphics Data and Functions

dblcens — 1.1.7

Compute the NPMLE of distribution from doubly censored data

discSurv — 1.4.1

Discrete Time Survival Analysis

DStree — 1.0

Recursive Partitioning for Discrete-Time Survival Trees

DTDA — 3.0.1

Doubly Truncated Data Analysis

dynpred — 0.1.2

Companion Package to "Dynamic Prediction in Clinical Survival Analysis"

dynsurv — 0.4-2

Dynamic Models for Survival Data

eha — 2.9.0

Event History Analysis

ELYP — 0.7-5

Empirical Likelihood Analysis for the Cox Model and Yang-Prentice (2005) Model

emplik2 — 1.32

Empirical Likelihood Ratio Test for Two Samples with Censored Data

emplik — 1.1-1

Empirical Likelihood Ratio for Censored/Truncated Data

Epi — 2.44

Statistical Analysis in Epidemiology

epiR — 2.0.41

Tools for the Analysis of Epidemiological Data

etm — 1.1.1

Empirical Transition Matrix

exactRankTests — 0.8-34

Exact Distributions for Rank and Permutation Tests

FamEvent — 2.1

Family Age-at-Onset Data Simulation and Penetrance Estimation

fastcox — 1.1.3

Lasso and Elastic-Net Penalized Cox's Regression in High Dimensions Models using the Cocktail Algorithm

fastpseudo — 0.1

Fast Pseudo Observations

FHtest — 1.5

Tests for Right and Interval-Censored Survival Data Based on the Fleming-Harrington Class

fitdistrplus — 1.1-6

Help to Fit of a Parametric Distribution to Non-Censored or Censored Data

flexrsurv — 1.4.5

Flexible Relative Survival Analysis

flexsurv — 2.1

Flexible Parametric Survival and Multi-State Models

frailtyEM — 1.0.1

Fitting Frailty Models with the EM Algorithm

frailtyHL — 2.3

Frailty Models via Hierarchical Likelihood

frailtypack — 3.5.0

Shared, Joint (Generalized) Frailty Models; Surrogate Endpoints

frailtySurv — 1.3.7

General Semiparametric Shared Frailty Model

gamboostMSM — 1.1.87

Estimating multistate models using gamboost()

gamlss.cens — 5.0-1

Fitting an Interval Response Variable Using `gamlss.family' Distributions

gbm — 2.1.8

Generalized Boosted Regression Models

gcerisk — 19.05.24

Generalized Competing Event Model

gems — 1.1.1

Generalized Multistate Simulation Model

genSurv — 1.0.4

Generating Multi-State Survival Data

glmnet — 4.1-3

Lasso and Elastic-Net Regularized Generalized Linear Models

glmpath — 0.98

L1 Regularization Path for Generalized Linear Models and Cox Proportional Hazards Model

glrt — 2.0

Generalized Logrank Tests for Interval-censored Failure Time Data

GORCure — 2.0

Fit Generalized Odds Rate Mixture Cure Model with Interval Censored Data

gss — 2.2-3

General Smoothing Splines

GSSE — 0.1

Genotype-Specific Survival Estimation

gte — 1.2-2

Generalized Turnbull's Estimator

hdnom — 6.0.0

Benchmarking and Visualization Toolkit for Penalized Cox Models

ICBayes — 1.2

Bayesian Semiparametric Models for Interval-Censored Data

ICE — 0.69

Iterated Conditional Expectation

icenReg — 2.0.15

Regression Models for Interval Censored Data

ICGOR — 2.0

Fit Generalized Odds Rate Hazards Model with Interval Censored Data

icRSF — 1.2

A Modified Random Survival Forest Algorithm

ICsurv — 1.0

A package for semiparametric regression analysis of interval-censored data

IDPSurvival — 1.2

Imprecise Dirichlet Process for Survival Analysis

InformativeCensoring — 0.3.5

Multiple Imputation for Informative Censoring

imputeYn — 1.3

Imputing the Last Largest Censored Observation(s) Under Weighted Least Squares

intccr — 3.0.3

Semiparametric Competing Risks Regression under Interval Censoring

interval — 1.1-0.8

Weighted Logrank Tests and NPMLE for Interval Censored Data

invGauss — 1.1

Threshold regression that fits the (randomized drift) inverse Gaussian distribution to survival data.

ipred — 0.9-12

Improved Predictors

jackknifeKME — 1.2

Jackknife Estimates of Kaplan-Meier Estimators or Integrals

JM — 1.4-8

Joint Modeling of Longitudinal and Survival Data

JMbayes — 0.8-85

Joint Modeling of Longitudinal and Time-to-Event Data under a Bayesian Approach

joineR — 1.2.6

Joint Modelling of Repeated Measurements and Time-to-Event Data

joineRML — 0.4.5

Joint Modelling of Multivariate Longitudinal Data and Time-to-Event Outcomes

joint.Cox — 3.15

Joint Frailty-Copula Models for Tumour Progression and Death in Meta-Analysis

JointModel — 1.0

Semiparametric Joint Models for Longitudinal and Counting Processes

kaps — 1.0.2

K-Adaptive Partitioning for Survival data

km.ci — 0.5-2

Confidence intervals for the Kaplan-Meier estimator

kmc — 0.2-4

Kaplan-Meier Estimator with Constraints for Right Censored Data -- a Recursive Computational Algorithm

kmi — 0.5.5

Kaplan-Meier Multiple Imputation for the Analysis of Cumulative Incidence Functions in the Competing Risks Setting

KMsurv — 0.1-5

Data sets from Klein and Moeschberger (1997), Survival Analysis

landest — 1.1

Landmark Estimation of Survival and Treatment Effect

lbiassurv — 1.1

Length-biased correction to survival curve estimation.

LearnBayes — 2.15.1

Functions for Learning Bayesian Inference

LexisPlotR — 0.4.0

Plot Lexis Diagrams for Demographic Purposes

lmec — 1.0

Linear Mixed-Effects Models with Censored Responses

locfit — 1.5-9.4

Local Regression, Likelihood and Density Estimation

logconcens — 0.17-0

Maximum Likelihood Estimation of a log-Concave Density Based on Censored Data

LogicReg — 1.6.4

Logic Regression

LogrankA — 1.0

Logrank Test for Aggregated Survival Data

logspline — 2.1.16

Routines for Logspline Density Estimation

lpc —

Lassoed Principal Components for Testing Significance of Features

lsmeans — 2.30-0

Least-Squares Means

LTRCtrees — 1.1.1

Survival Trees to Fit Left-Truncated and Right-Censored and Interval-Censored Survival Data

maxstat — 0.7-25

Maximally Selected Rank Statistics

mboost — 2.9-5

Model-Based Boosting

MCMCglmm — 2.32

MCMC Generalised Linear Mixed Models

MCMCpack — 1.6-0

Markov Chain Monte Carlo (MCMC) Package

mets — 1.2.9

Analysis of Multivariate Event Times

mexhaz — 2.2

Mixed Effect Excess Hazard Models

miCoPTCM — 1.1

Promotion Time Cure Model with Mis-Measured Covariates

MicSim — 1.0.15

Performing Continuous-Time Microsimulation

MIICD — 2.4

Multiple Imputation for Interval Censored Data

mixAK — 5.3

Multivariate Normal Mixture Models and Mixtures of Generalized Linear Mixed Models Including Model Based Clustering

mixPHM — 0.7-2

Mixtures of Proportional Hazard Models

MLEcens — 0.1-4

Computation of the MLE for bivariate (interval) censored data

mlr3proba — 0.4.2

Probabilistic Supervised Learning for 'mlr3'

MRsurv — 0.2

A multiplicative-regression model for relative survival.

msm — 1.6.9

Multi-State Markov and Hidden Markov Models in Continuous Time

msmtools — 2.0.1

Building Augmented Data to Run Multi-State Models with 'msm' Package

msSurv — 1.2-2

Nonparametric Estimation for Multistate Models

MST — 2.2

Multivariate Survival Trees

mstate — 0.3.2

Data Preparation, Estimation and Prediction in Multi-State Models

muhaz —

Hazard Function Estimation in Survival Analysis

multcomp — 1.4-18

Simultaneous Inference in General Parametric Models

multipleNCC — 1.2-2

Weighted Cox-Regression for Nested Case-Control Data

mvna — 2.0.1

Nelson-Aalen Estimator of the Cumulative Hazard in Multistate Models

NADA — 1.6-1.1

Nondetects and Data Analysis for Environmental Data

NPHMC — 2.2

Sample Size Calculation for the Proportional Hazards Mixture Cure Model

NPMLEcmprsk — 3.0

Type-Specific Failure Rate and Hazard Rate on Competing Risks Data

npsurv — 0.5-0

Nonparametric Survival Analysis

OrdFacReg — 1.0.6

Least Squares, Logistic, and Cox-Regression with Ordered Predictors

p3state.msm — 1.3

Analyzing survival data

paf — 1.0

Attributable Fraction Function for Censored Survival Data

pamr — 1.56.1

Pam: Prediction Analysis for Microarrays

parfm — 2.7.6

Parametric Frailty Models

party — 1.3-9

A Laboratory for Recursive Partytioning

pch — 2.0

Piecewise Constant Hazard Models for Censored and Truncated Data

pec — 2021.10.11

Prediction Error Curves for Risk Prediction Models in Survival Analysis

penalized — 0.9-51

L1 (Lasso and Fused Lasso) and L2 (Ridge) Penalized Estimation in GLMs and in the Cox Model

PenCoxFrail — 1.0.1

Regularization in Cox Frailty Models

penMSM — 0.99

Estimating Regularized Multi-state Models Using L1 Penalties

peperr — 1.3

Parallelised Estimation of Prediction Error

PermAlgo — 1.1

Permutational Algorithm to Simulate Survival Data

PHeval — 0.5.4

Evaluation of the Proportional Hazards Assumption with a Standardized Score Process

plac — 0.1.1

A Pairwise Likelihood Augmented Cox Estimator for Left-Truncated Data

plsRcox — 1.7.6

Partial Least Squares Regression for Cox Models and Related Techniques

polspline — 1.1.19

Polynomial Spline Routines

powerSurvEpi — 0.1.3

Power and Sample Size Calculation for Survival Analysis of Epidemiological Studies

PReMiuM — 3.2.7

Dirichlet Process Bayesian Clustering, Profile Regression

prodlim — 2019.11.13

Product-Limit Estimation for Censored Event History Analysis

psbcGroup — 1.5

Penalized Parametric and Semiparametric Bayesian Survival Models with Shrinkage and Grouping Priors

pseudo — 1.4.3

Computes Pseudo-Observations for Modeling

quantreg — 5.86

Quantile Regression

randomForestSRC — 3.0.0

Fast Unified Random Forests for Survival, Regression, and Classification (RF-SRC)

ranger — 0.13.1

A Fast Implementation of Random Forests

rankhazard — 1.1.0

Rank-Hazard Plots

reda — 0.5.3

Recurrent Event Data Analysis

relsurv — 2.2-6

Relative Survival

reReg — 1.4.2

Recurrent Event Regression

rhosp — 1.10

Side Effect Risks in Hospital : Simulation and Estimation

riskRegression — 2021.10.10

Risk Regression Models and Prediction Scores for Survival Analysis with Competing Risks

risksetROC — 1.0.4

Riskset ROC curve estimation from censored survival data

rms — 6.2-0

Regression Modeling Strategies

RobustAFT — 1.4-5

Truncated Maximum Likelihood Fit and Robust Accelerated Failure Time Regression for Gaussian and Log-Weibull Case

rpart — 4.1-15

Recursive Partitioning and Regression Trees

rstanarm — 2.21.1

Bayesian Applied Regression Modeling via Stan

rstpm2 — 1.5.2

Smooth Survival Models, Including Generalized Survival Models

saws — 0.9-6.2

Small-Sample Adjustments for Wald Tests Using Sandwich Estimators

SemiCompRisks — 3.4

Hierarchical Models for Parametric and Semi-Parametric Analyses of Semi-Competing Risks Data

SemiMarkov — 1.4.6

Multi-States Semi-Markov Models

SGL — 1.3

Fit a GLM (or Cox Model) with a Combination of Lasso and Group Lasso Regularization

simexaft —


SimHaz — 0.1

Simulated Survival and Hazard Analysis for Time-Dependent Exposure

simMSM — 1.1.41

Simulation of Event Histories for Multi-State Models

simPH — 1.3.13

Simulate and Plot Estimates from Cox Proportional Hazards Models

SimSCRPiecewise — 0.1.1

'Simulates Univariate and Semi-Competing Risks Data Given Covariates and Piecewise Exponential Baseline Hazards'

simsurv — 1.0.0

Simulate Survival Data

SimSurvNMarker — 0.1.1

Simulate Survival Time and Markers

smcure — 2.0

Fit Semiparametric Mixture Cure Models

SmoothHazard — 1.4.1

Estimation of Smooth Hazard Models for Interval-Censored Data with Applications to Survival and Illness-Death Models

smoothHR — 1.0.3

Smooth Hazard Ratio Curves Taking a Reference Value

smoothSurv — 2.3

Survival Regression with Smoothed Error Distribution

SMPracticals — 1.4-3

Practicals for Use with Davison (2003) Statistical Models

spatstat — 2.3-0

Spatial Point Pattern Analysis, Model-Fitting, Simulation, Tests

spBayesSurv — 1.1.5

Bayesian Modeling and Analysis of Spatially Correlated Survival Data

spef — 1.0.9

Semiparametric Estimating Functions

SSRMST — 0.1.1

Sample Size Calculation using Restricted Mean Survival Time

superpc — 1.12

Supervised Principal Components

surv2sampleComp — 1.0-5

Inference for Model-Free Between-Group Parameters for Censored Survival Data

survAUC — 1.0-5

Estimators of prediction accuracy for time-to-event data.

survC1 — 1.0-3

C-Statistics for Risk Prediction Models with Censored Survival Data

SurvCorr — 1.0

Correlation of Bivariate Survival Times

survexp.fr — 1.0

Relative survival, AER and SMR based on French death rates

survey — 4.1-1

Analysis of Complex Survey Samples

Survgini — 1.0

The Gini concentration test for survival data

survIDINRI — 1.1-1

IDI and NRI for comparing competing risk prediction models with censored survival data

survival — 3.2-13

Survival Analysis

survivalMPL — 0.2-1

Penalised Maximum Likelihood for Survival Analysis Models

survivalROC — 1.0.3

Time-dependent ROC curve estimation from censored survival data

survJamda — 1.1.4

Survival Prediction by Joint Analysis of Microarray Gene Expression Data

SurvLong — 1.1

Analysis of Proportional Hazards Model with Sparse Longitudinal Covariates

survminer — 0.4.9

Drawing Survival Curves using 'ggplot2'

survMisc — 0.5.5

Miscellaneous Functions for Survival Data

survPresmooth — 1.1-11

Presmoothed Estimation in Survival Analysis

SurvRegCensCov — 1.5

Weibull Regression for a Right-Censored Endpoint with Interval-Censored Covariate

survRM2 — 1.0-3

Comparing Restricted Mean Survival Time

survsim — 1.1.8

Simulation of Simple and Complex Survival Data

survSNP — 0.25

Power Calculations for SNP Studies with Censored Outcomes

SvyNom — 1.1

Nomograms for Right-Censored Outcomes from Survey Designs

TBSSurvival — 1.3

Survival Analysis using a Transform-Both-Sides Model

tdROC — 1.0

Nonparametric Estimation of Time-Dependent ROC Curve from Right Censored Survival Data

thregI — 1.0.4

Threshold Regression for Interval-Censored Data with a Cure Rate Option

timereg — 2.0.1

Flexible Regression Models for Survival Data

timeROC — 0.4

Time-Dependent ROC Curve and AUC for Censored Survival Data

tlmec — 0.0-2

Linear Student-t Mixed-Effects Models with Censored Data

TP.idm — 1.5

Estimation of Transition Probabilities for the Illness-Death Model

TPmsm — 1.2.5

Estimation of Transition Probabilities in Multistate Models

tpr — 0.3-2

Temporal Process Regression

TraMineR — 2.2-3

Trajectory Miner: a Toolbox for Exploring and Rendering Sequences

TransModel — 2.1

Fit Linear Transformation Models for Right Censored Data

tranSurv — 1.2.2

Transformation Model Based Estimation of Survival and Regression Under Dependent Truncation and Independent Censoring

TSHRC — 0.1-6

Two Stage Hazard Rate Comparison

uniah — 1.0

Unimodal Additive Hazards Model

VGAM — 1.1-5

Vector Generalized Linear and Additive Models

vitality — 1.3

Fitting Routines for the Vitality Family of Mortality Models

YPmodel — 1.4

The Short-Term and Long-Term Hazard Ratio Model for Survival Data

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