# General Frailty models: shared, joint and nested frailty models with prediction; Evaluation of Failure-Time Surrogate Endpoints Frailtypack fits several classes of frailty models using a penalized likelihood estimation on the hazard function but also a parametric estimation. ## Details The following several classes of frailty models using a penalized likelihood estimation on the hazard function but also a parametric estimation can be fit using this R package: 1) A shared frailty model (with gamma or log-normal frailty distribution) and Cox proportional hazard model. Clustered and recurrent survival times can be studied. 2) Additive frailty models for proportional hazard models with two correlated random effects (intercept random effect with random slope). 3) Nested frailty models for hierarchically clustered data (with 2 levels of clustering) by including two iid gamma random effects. 4) Joint frailty models in the context of the joint modelling for recurrent events with terminal event for clustered data or not. A joint frailty model for two semi-competing risks and clustered data is also proposed. 5) Joint general frailty models in the context of the joint modelling for recurrent events with terminal event data with two independent frailty terms. 6) Joint Nested frailty models in the context of the joint modelling for recurrent events with terminal event, for hierarchically clustered data (with two levels of clustering) by including two iid gamma random effects. 7) Multivariate joint frailty models for two types of recurrent events and a terminal event. 8) Joint models for longitudinal data and a terminal event. 9) Trivariate joint models for longitudinal data, recurrent events and a terminal event. 10) Joint frailty models for the validation of surrogate endpoints in multiple randomized clinical trials with failure-time and/or longitudinal endpoints with the possibility to use a mediation analysis model. 11) Conditional and Marginal two-part joint models for longitudinal semicontinuous data and a terminal event. 12) Joint frailty-copula models for the validation of surrogate endpoints in multiple randomized clinical trials with failure-time endpoints. 13) Generalized shared and joint frailty models for recurrent and terminal events. Proportional hazards (PH), additive hazard (AH), proportional odds (PO) and probit models are available in a fully parametric framework. 14) Competing Joint Frailty Model: A single type of recurrent event and two terminal events. The package includes concordance measures for Cox proportional hazards models and for shared frailty models. Now, you can also consider time-varying covariates effects in Cox, shared and joint frailty models (1-5). Some of the Fortran routines in the package can speed-up computation time by making use of parallelization through OpenMP. Moreover, the package can be used with its shiny application, in a local mode or by following the link below. ||| |:--|:--| |Package:|frailtypack| |Type:|Package| |Version:|3.6.5| |Date:|2024-12-09| |License:|GPL (>= 2.0)| |LazyLoad:|no| ## Examples ```r ## Not run: ###--- Additive model with 1 covariate ---### data(dataAdditive) modAdd <- additivePenal(Surv(t1,t2,event)~ cluster(group)+var1+slope(var1), correlation=TRUE,data=dataAdditive, n.knots=8,kappa=10000,hazard="Splines") ###--- Joint model (recurrent and terminal events) with 2 covariates ---### data(readmission) modJoint.gap <- frailtyPenal(Surv(time,event)~ cluster(id)+sex+dukes+charlson+terminal(death), formula.terminalEvent=~sex+dukes+charlson, data=readmission,n.knots=10,kappa=c(100,100), recurrentAG=FALSE,hazard="Splines") ###--- General Joint model (recurrent and terminal events) with 2 covariates ---### data(readmission) modJoint.general <- frailtyPenal(Surv(time,event) ~ cluster(id) + dukes + charlson + sex + chemo + terminal(death), formula.terminalEvent = ~ dukes + charlson + sex + chemo, data = readmission, jointGeneral = TRUE, n.knots = 8, kappa = c(2.11e+08, 9.53e+11)) ###--- Nested model (or hierarchical model) with 2 covariates ---### data(dataNested) modClu <- frailtyPenal(Surv(t1,t2,event)~ cluster(group)+subcluster(subgroup)+cov1+cov2, data=dataNested,n.knots=8,kappa=50000,hazard="Splines") ###--- Joint Nested Frailty model ---### #-- here is generated cluster (30 clusters) readmissionNested <- transform(readmission,group=id%%30+1) modJointNested_Splines <- frailtyPenal(formula = Surv(t.start, t.stop, event) ~ subcluster(id) + cluster(group) + dukes + terminal(death), formula.terminalEvent = ~dukes, data = readmissionNested, recurrentAG = TRUE, n.knots = 8, kappa = c(9.55e+9, 1.41e+12), initialize = TRUE) modJointNested_Weib <- frailtyPenal(Surv(t.start,t.stop,event)~subcluster(id) +cluster(group)+dukes+ terminal(death),formula.terminalEvent=~dukes, hazard = ('Weibull'), data=readmissionNested,recurrentAG=TRUE, initialize = FALSE) JoiNes-GapSpline <- frailtyPenal(formula = Surv(time, event) ~ subcluster(id) + cluster(group) + dukes + terminal(death), formula.terminalEvent = ~dukes, data = readmissionNested, recurrentAG = FALSE, n.knots = 8, kappa = c(9.55e+9, 1.41e+12), initialize = TRUE, init.Alpha = 1.091, Ksi = "None") ###--- Semiparametric Shared model ---### data(readmission) sha.sp <- frailtyPenal(Surv(t.start,t.stop,event)~ sex+dukes+charlson+cluster(id),data=readmission, n.knots=6,kappa=5000,recurrentAG=TRUE, cross.validation=TRUE,hazard="Splines") ###--- Parametric Shared model ---### data(readmission) sha.p <- frailtyPenal(Surv(t.start,t.stop,event)~ cluster(id)+sex+dukes+charlson, data=readmission,recurrentAG=TRUE, hazard="Piecewise-per",nb.int=6) ###--- Joint model for longitudinal ---### ###--- data and a terminal event ---### data(colorectal) data(colorectalLongi) # Survival data preparation - only terminal events colorectalSurv <- subset(colorectal, new.lesions == 0) model.weib.RE <- longiPenal(Surv(time1, state) ~ age + treatment + who.PS + prev.resection, tumor.size ~ year * treatment + age + who.PS , colorectalSurv, data.Longi = colorectalLongi, random = c("1", "year"), id = "id", link = "Random-effects", left.censoring = -3.33, hazard = "Weibull") ###--- Trivariate joint model for longitudinal ---### ###--- data, recurrent and terminal events ---### data(colorectal) data(colorectalLongi) # (computation takes around 40 minutes) model.spli.RE.cal <-trivPenal(Surv(time0, time1, new.lesions) ~ cluster(id) + age + treatment + who.PS + terminal(state), formula.terminalEvent =~ age + treatment + who.PS + prev.resection, tumor.size ~ year * treatment + age + who.PS, data = colorectal, data.Longi = colorectalLongi, random = c("1", "year"), id = "id", link = "Random-effects", left.censoring = -3.33, recurrentAG = TRUE, n.knots = 6, kappa=c(0.01, 2), method.GH="Pseudo-adaptive", n.nodes=7, init.B = c(-0.07, -0.13, -0.16, -0.17, 0.42, #recurrent events covariates -0.23, -0.1, -0.09, -0.12, 0.8, -0.23, #terminal event covariates 3.02, -0.30, 0.05, -0.63, -0.02, -0.29, 0.11, 0.74)) #biomarker covariates ##---Surrogacy evaluation based on ganerated data with a combination ##of Monte Carlo and classical Gaussian Hermite integration. ## (Computation takes around 5 minutes) # Generation of data to use data.sim <- jointSurrSimul(n.obs=600, n.trial = 30,cens.adm=549.24, alpha = 1.5, theta = 3.5, gamma = 2.5, zeta = 1, sigma.s = 0.7, sigma.t = 0.7, rsqrt = 0.8, betas = -1.25, betat = -1.25, full.data = 0, random.generator = 1, seed = 0, nb.reject.data = 0) # Joint surrogate model estimation joint.surro.sim.MCGH <- jointSurroPenal(data = data.sim, int.method = 2, nb.mc = 300, nb.gh = 20) ## End(Not run) ``` ## References V. Rondeau, Y. Mazroui and J. R. Gonzalez (2012). Frailtypack: An R package for the analysis of correlated survival data with frailty models using penalized likelihood estimation or parametric estimation. **Journal of Statistical Software** 47 , 1-28. Y. Mazroui, S. Mathoulin-Pelissier,P. Soubeyranb and Virginie Rondeau (2012) General joint frailty model for recurrent event data with a dependent terminalevent: Application to follicular lymphoma data. **Statistics in Medecine**, 31 , 11-12, 1162-1176. V. Rondeau and J. R. Gonzalez (2005). Frailtypack: A computer program for the analysis of correlated failure time data using penalized likelihood estimation. **Computer Methods and Programs in Biomedicine** 80 , 2, 154-164. V. Rondeau, S. Michiels, B. Liquet, and J. P. Pignon (2008). Investigating trial and treatment heterogeneity in an individual patient data meta-analysis of survival data by mean of the maximum penalized likelihood approach. **Statistics in Medecine**, 27 , 1894-1910. V. Rondeau, S. Mathoulin-Pellissier, H. Jacqmin-Gadda, V. Brouste, P. Soubeyran (2007). Joint frailty models for recurring events and death using maximum penalized likelihood estimation:application on cancer events. **Biostatistics**, 8 , 4, 708-721. V. Rondeau, D. Commenges, and P. Joly (2003). Maximum penalized likelihood estimation in a gamma-frailty model. **Lifetime Data Analysis** 9 , 139-153. D. Marquardt (1963). An algorithm for least-squares estimation of nonlinear parameters. **SIAM Journal of Applied Mathematics**, 431-441. V. Rondeau, L. Filleul, P. Joly (2006). Nested frailty models using maximum penalized likelihood estimation. **Statistics in Medecine**, 25 , 4036-4052. ## Author(s) Virginie Rondeau, Juan R. Gonzalez, Yassin Mazroui, Audrey Mauguen, Amadou Diakite, Alexandre Laurent, Myriam Lopez, Agnieszka Krol, Casimir L. Sofeu, Denis Rustand, Quentin Le Coent, Lacey Etzkorn and Romain Pierlot

frailtypack-package