CRAN Task View: Survival Analysis

Maintainer:	Arthur Allignol and Aurélien Latouche
Contact:	arthur.allignol at fdm.uni-freiburg.de
Version:	2008-06-04

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.

This is a preliminary task view, and we have likely missed some important information. Please email the task view maintener with any feedback.

Standard Survival Analysis

Basic Methods: The recommended package survival provides the necessary tools for estimating the distribution (survival probability) of time to the event and cumulative hazards for various censoring and truncation schemes. muhaz allows estimation of the hazard function. Packages eha and Design provide additional tools for dealing with time to event data, like facilities to obtain risk sets or number of events. surv2sample yields tests for comparing two survival distributions. TSHRC provides a two-stage procedure for comparing hazard rates. That is useful when hazard functions cross. Package emplik can performs empirical likelihood for means, quantiles and hazards from possibly censored and/or truncated data. Package dblcens computes the NPMLE estimator of CDF for doubly censored data, along with the CDF of the two censoring distributions. Package coin provides conditional inference (aka permutation tests) for a general indepence hypothesis for arbitrary scales including censored variables. Notably the surv_test function for testing the equality of survival distributions in two or more independent groups.
Cox Model: survival permits to fit the well-known Cox proportional hazards model for right-, left-, interval-censored and counting process data. It can also be used with time-dependent covariates. Goodness-of-fit tests are also implemented. The cph function of the Design package fits the Cox model for interval time-dependent covariates and time-dependent strata. CPE can use either a coxph or cph object to evaluate the discriminatory power and the predictive accuracy of the model. The coxphf function from coxphf package performs a Cox regression with Firth's penalized likelihood. This method has been shown to provide a solution in case of monotone likelihood. coxrobust fits efficiently and robustly Cox models, but in its basic form, that is without time-dependent covariates. intcox fits a Cox model for interval censored data by the iterative convex minorant algorithm. The NestedCohort package permits to display the Kaplan-Meier estimates of the survival probability and to fit a Cox proportional hazards model for nested cohorts. survival and proptest provides methods to test for the proportional hazards assumption. The path following algorithms for GLMs and Cox proportional hazards models have been implemented in the glmpath package. This strategy provided much smoother feature selection mechanism than the forward stepwise process.
Other Regression Models: The survival package proposes as a complement of the Cox model the survreg function, which fits linear models for the mean of survival or its logarithm with various parametric error distributions. Package eha implements maximum likelihood estimation of proportional hazards models. It reduces to a Cox model when there are no ties in the data. This package also proposes the Weibull regression model. As for the Design package, it contains an implementation of the Buckley-James regression model. The emplik package also has a function to compute the Buckley-James model, but without intercept term. rankreg computes rank regression estimator for the accelerated failure time model and tests the coefficients against a given value. emplik performs the same test through empirical likelihood estimation. A conditional quantile regression model for censored data can be fitted using crq from the quantreg package. (An older implementation of one of the fitting algorithms is available also available in package crq.) lss implements a recent inference procedure based on the least-squares principle for the accelerated failure time model. The generalized additive models for location, scale and shape (GAMLSS) can also be fitted for censored data, and are implemented in the gamlss.cens package. The mixPHM fits multiple mixtures of various parametric hazard models using an EM algorithm. smoothSurv allows the fit of a regression model with possible left-, right- and interval-censoring and the error distribution expressed as a mixture of G-splines. The pseudo package computes pseudo observations for regressing survival function based on the restricted mean and the Kaplan-Meier estimator. The tpr package fits regression models for temporal process responses with time-varying coefficients

The timereg package, not available on CRAN (see links below), contains implementations of various models to deal with time-varying effects, like the Aalen additive risk model, the semi-parametric additive risk model by McKeague and Sasieni, the Cox-Aalen model by Scheike and Zhang, the proportional excess hazards model by Martinussen and Scheike, the Cox model with partly time-varying effects by Martinussen, Scheike and Skovgaard, the two-stage estimation method for the Clayton-Oakes-Glidden model and the semiparametric proportional odds model. Can also do flexible regression modelling for competing risks data based on the IPCW direct binomial regression approach (Scheike, Zhang, Gerds, 2008).

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 correspondance 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 probabilties for any multistate model. It also estimates the change of length of hospital stay. 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.
Recurrent Events: coxph from the survival can be used to analyze recurrent event data. The cph function of the Design package fits the Anderson-Gill model for recurrent events, model which can also be fitted with the frailtypack package. The survrec package proposes implementations of several models for recurrent events data, such as the Pena-Strawderman-Hollander, Wang-Chang estimators, and MLE estimation under a Gamma Frailty model. The Pena-Hollander model can be fitted using the gcmrec package.
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 hazards. Package pseudo computes pseudo observations for modelling competing risks based on the cumulative incidence functions.

Relative Survival

relsurv implements various regression models used in relative survival, such as the additive model for relative survival with a binomial or a Poisson error, or the Andersen at al. multiplicative regression model, which is an extension of the Cox model for relative survival. It can also fit the Cox proportional hazards model in transformed times. The package also includes display facilities and miscellaneous others.

Multivariate Survival

We mean by multivariate survival 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 Package Icens provides various implemention of methods to find the NPMLE for censored and truncated multivariate survival data. Note that some of these techniques can be used for standard survival. The package MLEcens permits to compute the nonparametric maximum likelihood estimator for bivariate distributions when the failure times cannot be directly observed.
Frailties: The CompetingRiskFrailty package fits a Cox model for each cause-specific hazards of competing risks data with random effects and possible smooth varying coefficients. frailypack fits a shared gamma frailty model using a penalized likelihood on the hazard function for left-truncated and censored data, with a maximum of two strata. Joint models for survival data can be fitted using the JM package. It can fit a Weibull accelerated failure time model, an additive log cumulative hazard model or a time-dependent proportional hazards model. kinship implements a mixed-effects Cox model.

Bayesian Models

bayesSurv package proposes an implementation of several accelerated failure time models with random effects. Parameter estimation is made using MCMC methods. The package DPpackage includes a generic function to fit a mixture of Dirichlet process in an accelerated failure time model for interval censored data. A proportional hazards model using a Bayesian approach is implemented in package survBayes. Right- and interval-censored data and a lognormal or gamma frailty term can be fitted.

Boosting techniques

The mboost package includes a random forest and a generic gradient boosting algorithm for the construction of prognostic and diagnostic models for right-censored data. CoxBoost provides routines for fitting Cox proportional hazards models by likelihood based boosting. An extension of Random Forest techniques to right-censored data can be found in randomSurvivalForest.

Other

KMsurv includes the data sets and functions which illustrates Klein and Moeschberger (1997), Survival Analysis, Techniques for Censored and Truncated Data , Springer-Verlag. The package boot contains the function bootcens, which performs various resampling plans for censored data. survivalROC computes time-dependent ROC curve from censored data using Kaplan-Meier or nearest neighbor estimation method. The TwoWaySurv package fits an additive hazard model for data where, besides the follow-time, a non-periodic calendar time is also taken into account. The package party provides various recursive partitioning algorithms that are also applicable to censored responses (conditional inference trees/forests, model-based recursive partitioning).