Package {LSJM}

LSJM: Estimate Location-Scale Joint Models

Description

Estimation of mixed models including a subject-specific variance that can be time- and covariate-dependent or defined for within- and between-visit variability. In the joint modeling framework, the package handles left truncation, interval censoring, and multistate models, and allows a flexible dependence structure between competing events and the longitudinal marker. Estimation is performed in a frequentist framework using the Marquardt-Levenberg algorithm. Methods are described in Courcoul et al. (2025) doi:10.1002/sim.70244 and in Courcoul et al. (2026) doi:10.1002/bimj.70123.

Author(s)

Maintainer: Léonie Courcoul courcoul.leonie498@gmail.com

Authors:

• Antoine Barbieri antoine.barbieri@u-bordeaux.fr

• Hélène Jacqmin-Gadda helene.jacqmin-gadda@u-bordeaux.fr

Management of longitudinal data

Description

Management of longitudinal data

Usage

data.manag.long(formGroup, formFixed, formRandom, data.long1)

Arguments

Value

A list with the following components :

data_long

a clean dataframe for the longitudinal data

y.new.prog

the vector of responses variable

X

a matrix with the fixed effects

U

a matrix with the random effects

id

a vector with the identification of individuals

offset

a vector with the number of measurements for each individual

I

an integer, the number of individuals

Management of data for residual part

Description

Management of data for residual part

Usage

data.manag.sigma(formGroup, formFixed, formRandom, data.long1)

Arguments

Value

A list with the following components :

X

a matrix with the fixed effects

U

a matrix with the random effects

Management of survival data

Description

Management of survival data

Usage

data.manag.surv(formGroup, formSurv, data.long1)

Arguments

dynpred: compute the dynamic predictions of an event.

Description

This function can be used only with an lsjm object. Individual dynamic predictions can be computed and plotted. They are defined as the predicted probability of having event k between time s and s+t given that the subject i has not experienced any event before time s, and knowing all marker measures collected until time s, denoted by Y_i(s), and the set of estimated parameters. The prediction is defined for subject i by: #'

\pi_i^{0k}(s,t;\widehat{\theta}) = P(s<T_i<s+t, \delta_i = k \mid T_i > s, \mathcal{Y}_i(s), \widehat{\theta}) = \frac{ \int \left[ \int_s^{s+t} \exp\left( -\sum_{c=1}^K \Lambda_{i}^{0c}(u|r_i,\widehat{\theta}) \right) \lambda_{i}^{0k}(u|r_i,\widehat{\theta}) du \right] f(\mathcal{Y}_i(s)|r_i,\widehat{\theta}) f(r_i|\widehat{\theta}) dr_i }{ \int \exp\left( -\sum_{c=1}^K \Lambda_{i}^{0c}(s|r_i,\widehat{\theta}) \right) f(\mathcal{Y}_i(s)|r_i,\widehat{\theta}) f(r_i|\widehat{\theta}) dr_i }

For illness-death and competing risks models, K = 2, whereas for a model with a single event, K = 1. For illness-death and single-event models, only the prediction from state (0) to state (1) can be computed, while for competing risks, transitions (0→1) and (0→2) can both be predicted.

As in the estimation procedure, the integral over the random effects is computed by QMC approximation and the integral over time by the Gauss-Kronrod quadrature.

The 95\ which can be computationally intensive. For L large enough and l = 1,...,L (e.g. L = 1000):

• Generate \widetilde{\theta}^{(l)} \sim \mathcal{N}(\widehat{\theta}, V(\widehat{\theta})), where V(\widehat{\theta}) is the inverse of the Hessian matrix at \widehat{\theta};

• Compute \widetilde{\pi}^{(l)}_i(s,t;\widetilde{\theta}^{(l)}) from the equation above;

• Compute the 95\ 97.5th percentiles of the L-sample of \widetilde{\pi}^{(l)}_i(s,t;\widetilde{\theta}^{(l)}).

Usage

dynpred(object, newdata, s, horizon, event, CI = 95, nb.draws = 1000)

## S3 method for class 'lsjm_classicCR'
dynpred(object, newdata, s, horizon, event, CI = 95, nb.draws = 1000)

## S3 method for class 'lsjm_classicIDM'
dynpred(object, newdata, s, horizon, event = NULL, CI = 95, nb.draws = 1000)

## S3 method for class 'lsjm_classicSingle'
dynpred(object, newdata, s, horizon, event = NULL, CI = 95, nb.draws = 1000)

## S3 method for class 'lsjm_covDepCR'
dynpred(object, newdata, s, horizon, event, CI = 95, nb.draws = 1000)

## S3 method for class 'lsjm_covDepIDM'
dynpred(object, newdata, s, horizon, event = NULL, CI = 95, nb.draws = 1000)

## S3 method for class 'lsjm_covDepSingle'
dynpred(object, newdata, s, horizon, event = NULL, CI = 95, nb.draws = 1000)

## S3 method for class 'lsjm_interintraCR'
dynpred(object, newdata, s, horizon, event, CI = 95, nb.draws = 1000)

## S3 method for class 'lsjm_interintraIDM'
dynpred(object, newdata, s, horizon, event = NULL, CI = 95, nb.draws = 1000)

## S3 method for class 'lsjm_interintraSingle'
dynpred(object, newdata, s, horizon, event = NULL, CI = 95, nb.draws = 1000)

Arguments

Value

A dataframe containing the table of predictions (table.pred).

Examples

set.seed(123)
data <- data.frame(
         ID = rep(1:100, each = 3),
         time = rep(1:3, 100),
         y = rnorm(300),
         event = rep(rbinom(100,1,0.5), each = 3),
         time_event = rep(runif(100), each = 3)
         )


m0 <- lsmm(
   formFixed = y ~ time,
   formRandom = ~ time,
   formGroup = ~ ID,
   formVar = "standard",
   timeVar = "time",
   data.long = data,
   S1 = 5,
   S2 = 5,
   nproc = 1
   )

 fit <- lsjm(
      Objectlsmm = m0,
      survival_type = "Single",
      formSurv_01 = ~ 1,
      sharedtype_01 = "value",
      hazardBase_01 = "Weibull",
      delta1 = ~ event,
      Time_T = ~ time_event,
      S1 = 10,
      S2 = 10,
      nproc = 1
      )

 ind1 <- data[which(data$ID == 1),]
 dynpEvent <- dynpred(fit, ind1,  s = 2, horizon = seq(2.1,3,0.1),
                  event = 1, nb.draws = 100)



library(dplyr)

# Begin by running the examples from the lsjm function (see ?lsjm).
data(threeC)
threeC$age.visit65 <- (threeC$age.visit-65)/10
threeC$SBP <- threeC$SBP/10


# Example: prediction of the risk to be diagnosed with dementia
# (dynpDementia) and to die (dynpDeath) between 85 and 95 years old
# given the blood pressure measurements before 85 years old for
# individual "10003", with a competing risk model
threeC_ex2 <- threeC[,c("ID", "SBP", "age.visit65", "age0_65",
                        "age.final65", "age.last65", "age.first65",
                        "dem", "death", "sex","num.visit")]

threeC_ex2$age65_CR <- NA
threeC_ex2$age65_CR[which(threeC_ex2$dem == 1)] <-
  (threeC_ex2$age.last65[which(threeC_ex2$dem == 1)] +
     threeC_ex2$age.first65[which(threeC_ex2$dem == 1)])/2
threeC_ex2$age65_CR[which(threeC_ex2$dem == 0)] <-
  threeC_ex2$age.final65[which(threeC_ex2$dem == 0)]

threeC_ex2$demCR <- threeC_ex2$dem
threeC_ex2$deathCR <- NA
threeC_ex2$deathCR[which(threeC_ex2$dem == 1)] <- 0
threeC_ex2$deathCR[which(threeC_ex2$dem == 0)] <-
  threeC_ex2$death[which(threeC_ex2$dem == 0)]

threeC_ex2 <- threeC_ex2 %>% group_by(ID) %>% dplyr::filter(age.visit65 <= age65_CR)

threeC_ex2 <- threeC_ex2[,c("ID","SBP","age.visit65","num.visit","age0_65",
                            "demCR","deathCR","age65_CR","sex")]

ind2 <- threeC_ex2[which(threeC_ex2$ID == 3),]

m2 <- lsmm(formFixed = SBP ~ age.visit65,
               formRandom = ~ age.visit65,
               formGroup = ~ ID,
               timeVar = 'age.visit65',
               data.long = threeC_ex2,
               formVar = "inter-intra",
               random_inter = TRUE,
               random_intra = TRUE,
               formGroupVisit = ~num.visit,
               correlated_re = FALSE,
               S1 = 500,
               S2 = 1000,
               nproc = 1)


l2 <- lsjm(Objectlsmm = m2,
           survival_type = 'CR',
           formSurv_01 = ~ sex,
           formSurv_02 = ~ sex,
           sharedtype_01 = c("value", "variability inter"),
           sharedtype_02 = c("value", "variability inter",
                             "variability intra"),
           hazardBase_01 = "Weibull",
           hazardBase_02 = "Weibull",
           delta1 = ~ demCR,
           delta2 = ~ deathCR,
           Time_T0 = ~ age0_65,
           Time_T = ~ age65_CR,
           nproc = 5,
           S1 = 1000,
           S2 = 2000)


dynpDementia <- dynpred(l2, ind2,  s = 2, horizon = seq(2.1,3,0.1),
                  event = 1, nb.draws = 1000)

dynpDeath <- dynpred(l2, ind2,  s = 2, horizon = seq(2.1,3,0.1),
                  event = 2, nb.draws = 1000)

Initialisation of Longitudinal Submodel

Description

Initialisation of Longitudinal Submodel

Usage

initial.long(formFixed, formRandom, idVar, data.long1, ncX, nproc = nproc)

Arguments

Value

A list with the following components :

long_model

the result of the hlme function

priorMean.beta

the estimated parameters for fixed effects in the linear mixed effects model

sigma

the estimated sigma of the model

lsjm : Estimation of a location-scale joint model for longitudinal data with flexible subject-specific variability and complex survival structures

Description

This function fits joint models in which the residual error variance is allowed to be subject-specific and the survival submodel may include either a single event, competing risks, or an illness-death process. Up to nine different model structures can be estimated (see Details). Parameters are estimated by maximum likelihood using a Marquardt-Levenberg algorithm.

Usage

lsjm(
  Objectlsmm,
  survival_type = c("Single", "CR", "IDM"),
  formSurv_01,
  formSurv_02 = NULL,
  formSurv_12 = NULL,
  sharedtype_01,
  sharedtype_02 = NULL,
  sharedtype_12 = NULL,
  hazardBase_01,
  hazardBase_02 = NULL,
  hazardBase_12 = NULL,
  delta1,
  delta2 = NULL,
  Time_T,
  Time_L = NULL,
  Time_R = NULL,
  Time_T0 = NULL,
  formSlopeFixed = NULL,
  formSlopeRandom = NULL,
  index_beta_slope = NULL,
  index_b_slope = NULL,
  nb.knots.splines = c(1, 1, 1),
  nb_pointsGK = 15,
  S1 = 1000,
  S2 = 5000,
  binit = NULL,
  nproc = 1,
  clustertype = "PSOCK",
  maxiter = 500,
  print.info = FALSE,
  file = NULL,
  epsa = 1e-04,
  epsb = 1e-04,
  epsd = 1e-04
)

Arguments

Details

A joint model is composed of two submodels: (1) a linear mixed model or location-scale mixed model(see ?LSJM::lsmm), and (2) a survival model.

Three types of survival processes are supported and are described below.

A. A single event: proportional hazards model

In this case, we consider only a single event. Let T_i = \min(T^*_{i1}, C_i) denote the observed time, where T^*_{i1} is the true event time and C_i the censoring time for subject i. Let \delta_i \in \{0,1\} be the event indicator. The hazard function is given by:

\lambda_i^{01}(t|r_i) = \lambda_0(t) \exp\left( W_i^{01\top}\gamma^{01} + g_y^{01}(b_i, t)^\top \alpha_b^{01} + g_\tau^{01}(\tau_i, t)^\top \alpha_\tau^{01} \right)

where:

• \lambda_0(t) is the baseline hazard function,

• W_i^{01} is a vector of baseline covariates with associated coefficients \gamma^{01},

• \alpha_b^{01} are regression coefficients for the function g_y, representing the association between the event risk and the mean trajectory of Y,

• \alpha_\tau^{01} are regression coefficients for the function g_\tau, representing the association between the event risk and the residual variance.

The association function g_y(b_i,t) can be defined as:

• g_y(b_i,t) = \tilde{y}_i(t) — current value,

• g_y(b_i,t) = \tilde{y}'_i(t) = \frac{\partial \tilde{y}_i(t)}{\partial t} — current slope,

• g_y(b_i,t) = (\tilde{y}_i(t), \tilde{y}'_i(t)) — both value and slope,

• g_y(b_i,t) = b_i — random effects.

The association function g_\tau(\tau_i, t) is defined according to the longitudinal model type:

• If a standard linear mixed model with homogeneous residual variance is used: g_\tau(\tau_i, t) = 0.

• If a location–scale mixed model with time- or covariate-dependent variance is used: g_\tau(\tau_i, t) = \sigma_i(t).

• If both within- and between-visit variances are modeled: g_\tau(\tau_i, t) = (\sigma_i, \kappa_i)^\top, where \alpha_\tau = (\alpha_\sigma, \alpha_\kappa) correspond to between-visit and within-visit variabilities, respectively.

The baseline hazard function \lambda_0(t) can follow different parametric forms:

• Exponential: \lambda_0(t) = \exp(\alpha_0),

• Weibull: \lambda_0(t) = \zeta^2 t^{\zeta^2 - 1} \exp(\alpha_0),

• Gompertz: \lambda_0(t) = \kappa_1^2 \exp(\kappa_2 t),

• Cubic B-splines with Q knots: \lambda_0(t) = \exp\left( \sum_{q=1}^{Q+4} \eta_q B_q(t, \nu) \right), where B_q(t, \nu) denotes the q-th B-spline basis function with knot vector \nu.

B. Competing events: cause-specific model

When multiple types of events are possible, two competing causes can be modeled. Let T_i = \min(T^*_{i1}, T^*_{i2}, C_i) be the observed time, where T^*_{ik} is the true event time for cause k (with k \in \{1, 2\}), and C_i the censoring time. The event indicator is \delta_i \in \{0, 1, 2\}, where \delta_i = k if cause k occurred and 0 otherwise. The cause-specific hazard is defined as:

\lambda_i^{0k}(t) = \lambda_0^{0k}(t) \exp\left( W_i^{0k\top}\gamma^{0k} + g_y^{0k}(b_i,t)^\top \alpha_b^{0k} + g_\tau^{0k}(\tau_i,t)^\top \alpha_\tau^{0k} \right)

The definitions of \lambda_0^{0k}, W_i^{0k}, g_y^{0k}, and g_\tau^{0k} follow the same principles as in the single-event model. C. Semi-competing events: illness–death model In this setting, transition to state (1) may be interval-censored, whereas transition to state (2) is observed exactly. The observed event data for subject i are given by: D_i = (T_{0i}, L_i, R_i, \delta_i^{(1)}, T_i, \delta_i^{(2)})^\top, where:

• T_{0i} — entry time (in case of delayed entry),

• L_i — time of the last visit where the subject was in state (0),

• R_i — time of the first visit where the subject was observed in state (1),

• T_i — minimum between the transition time to state (2) and the censoring time,

• \delta_i^{(1)} = \mathbb{1}_{R_i < T_i} — indicator of transition to state (1),

• \delta_i^{(2)} — indicator of transition to state (2).

Transition intensities from state k \in \{0,1\} to state l \in \{1,2\} follow a proportional hazards model under the Markov assumption:

\lambda_i^{kl}(t|b_i, \tau_i) = \lambda_0^{kl}(t) \exp\left( W_i^{kl\top}\gamma^{kl} + g_y^{kl}(b_i,t)^\top \alpha_b^{kl} + g_\tau^{kl}(\tau_i,t)^\top \alpha_\tau^{kl} \right)

where the terms are defined analogously to the single-event model.

Value

An object of class lsjm containing:

table.res

Table of parameter estimates and standard errors.

result_step1

A marqLevAlg object with first-step estimation results.

result_step2

A marqLevAlg object with second-step estimation results.

info_conv_step1

Information on first-step convergence (criteria and computation time).

info_conv_step2

Information on second-step convergence (criteria and computation time).

control

List of control parameters used during estimation.

Examples

set.seed(123)

data <- data.frame(
         ID = rep(1:100, each = 3),
         time = rep(1:3, 100),
         y = rnorm(300),
         event = rep(rbinom(100,1,0.5), each = 3),
         time_event = rep(runif(100), each = 3)
         )


m0 <- lsmm(
   formFixed = y ~ time,
   formRandom = ~ time,
   formGroup = ~ ID,
   formVar = "standard",
   timeVar = "time",
   data.long = data,
   S1 = 5,
   S2 = 5,
   nproc = 1
   )

 fit <- lsjm(
      Objectlsmm = m0,
      survival_type = "Single",
      formSurv_01 = ~ 1,
      sharedtype_01 = "value",
      hazardBase_01 = "Weibull",
      delta1 = ~ event,
      Time_T = ~ time_event,
      S1 = 100,
      S2 = 100,
      nproc = 1
      )



library(dplyr)

# First, run the examples from the lsmm function (see ?lsmm).

# Example 1: Illness-death model with time-dependent subject-specific
# variability
data(threeC)
threeC$age.visit65 <- (threeC$age.visit-65)/10
threeC$SBP <- threeC$SBP/10
threeC <- threeC
threeC <- dplyr::group_by(threeC, ID, num.visit)
threeC <- dplyr::mutate(threeC, SBPvisit = mean(SBP))
threeC_ex1 <- threeC[!duplicated(threeC[, c("ID", "num.visit")]),
                                  c("ID", "SBPvisit", "age.visit65", "sex","dem","death",
                                     "age.first65","age.last65","age.final65","age0_65")]

m1 <- lsmm(formFixed = SBPvisit ~ age.visit65,
               formRandom = ~ age.visit65,
               formGroup = ~ ID,
               timeVar = 'age.visit65',
               data.long = threeC_ex1,
               formVar = "cov-dependent",
               formFixedVar = ~ age.visit65+sex,
               formRandomVar = ~ age.visit65,
               correlated_re = FALSE,
               S1 = 500,
               S2 = 1000,
               nproc = 1)


l1 <- lsjm(m1,
           survival_type = 'IDM',
           formSurv_01=~1,
           formSurv_02=~sex,
           formSurv_12=~sex,
           sharedtype_01 = c("value", "variability"),
           sharedtype_02 = c("value", "slope", "variability"),
           sharedtype_12 = c("value", "variability"),
           hazardBase_01 = "Weibull",
           hazardBase_02 = "Weibull",
           hazardBase_12 = "Splines",
           delta1=~dem,
           delta2=~death,
           Time_T =~age.final65,
           Time_L =~age.last65,
           Time_R =~age.first65,
           Time_T0 =~age0_65,
           formSlopeFixed =~1,
           formSlopeRandom =~1,
           index_beta_slope = c(2),
           index_b_slope = c(2),
           nb.knots.splines = c(0,0,1),
           S1 = 1000,
           S2 = 2000,
           nproc = 10)

summary(l1)


# Example 2: Competing risks model with between- and within-visit
# subject-specific variabilities

threeC_ex2 <- threeC[,c("ID", "SBP", "age.visit65", "age0_65",
                        "age.final65", "age.last65", "age.first65",
                        "dem", "death", "sex","num.visit")]

threeC_ex2$age65_CR <- NA
threeC_ex2$age65_CR[which(threeC_ex2$dem == 1)] <-
  (threeC_ex2$age.last65[which(threeC_ex2$dem == 1)] +
     threeC_ex2$age.first65[which(threeC_ex2$dem == 1)])/2
threeC_ex2$age65_CR[which(threeC_ex2$dem == 0)] <-
  threeC_ex2$age.final65[which(threeC_ex2$dem == 0)]

threeC_ex2$demCR <- threeC_ex2$dem
threeC_ex2$deathCR <- NA
threeC_ex2$deathCR[which(threeC_ex2$dem == 1)] <- 0
threeC_ex2$deathCR[which(threeC_ex2$dem == 0)] <-
  threeC_ex2$death[which(threeC_ex2$dem == 0)]

threeC_ex2 <- threeC_ex2 %>% group_by(ID) %>% dplyr::filter(age.visit65 <= age65_CR)

threeC_ex2 <- threeC_ex2[,c("ID","SBP","age.visit65","num.visit","age0_65",
                            "demCR","deathCR","age65_CR","sex")]

m2 <- lsmm(formFixed = SBP ~ age.visit65,
               formRandom = ~ age.visit65,
               formGroup = ~ ID,
               timeVar = 'age.visit65',
               data.long = threeC_ex2,
               formVar = "inter-intra",
               random_inter = TRUE,
               random_intra = TRUE,
               formGroupVisit = ~num.visit,
               correlated_re = FALSE,
               S1 = 500,
               S2 = 1000,
               nproc = 1)


l2 <- lsjm(Objectlsmm = m2,
           survival_type = 'CR',
           formSurv_01 = ~ sex,
           formSurv_02 = ~ sex,
           sharedtype_01 = c("value", "variability inter"),
           sharedtype_02 = c("value", "variability inter",
                             "variability intra"),
           hazardBase_01 = "Weibull",
           hazardBase_02 = "Weibull",
           delta1 = ~ demCR,
           delta2 = ~ deathCR,
           Time_T0 = ~ age0_65,
           Time_T = ~ age65_CR,
           nproc = 5,
           S1 = 1000,
           S2 = 2000)

summary(l2)

lsmm : Estimation of a linear mixed model for longitudinal data with flexible subject-specific variability.

Description

This function fits linear mixed effects models for longitudinal data, allowing the residual variance to be subject-specific. Three different model types can be estimated (see Details).Parameters are estimated by maximum likelihood using a Marquardt-Levenberg algorithm.

Usage

lsmm(
  formFixed,
  formRandom,
  formGroup,
  timeVar,
  formVar = "standard",
  formFixedVar = NULL,
  formRandomVar = NULL,
  random_inter = FALSE,
  random_intra = FALSE,
  formGroupVisit = NULL,
  correlated_re = FALSE,
  data.long,
  S1 = 500,
  S2 = 5000,
  nproc = 1,
  clustertype = "PSOCK",
  maxiter = 100,
  print.info = FALSE,
  file = "",
  epsa = 1e-04,
  epsb = 1e-04,
  epsd = 1e-04,
  binit = NULL
)

Arguments

Details

The model is defined as:

Y_{ij} = Y_i(t_{ij}) = \widetilde{Y}_i(t_{ij}) + \epsilon_{ij} = X_{ij}^{\top} \beta + Z_{ij}^{\top} b_i + \epsilon_{ij} , where X_{ij} and Z_{ij} are vectors of explanatory variables for subject i at time t_{ij}, associated with the fixed-effect vector \beta and the subject-specific random-effect vector b_i, respectively.

A. Standard linear mixed model

In this case, b_i \sim \mathcal{N}(0,B), with B an unstructured covariance matrix, and the measurement errors \epsilon_{ij} are independent Gaussian errors with variance \sigma^2_{\epsilon}.

B. Location-scale mixed model with time and/or covariate-dependent variability

In this model, the residual error variance can vary across subjects and over time: we assume the following specification for the residual error:

\epsilon_{ij} \sim \mathcal{N}(0, \sigma_i^2) with \log(\sigma_i(t_{ij})) = O_{ij}^{\top} \mu + M_{ij}^{\top} \tau_i .#' where O_{ij} and M_{ij} are vectors of explanatory variables for subject i at visit j, associated with the fixed-effect vector \mu and the subject-specific random-effect vector \tau_i, respectively.

The random effects are assumed jointly Gaussian:

\quad \left( \begin{array}{c} b_i \\ \tau_i \end{array} \right) \sim N\left( \left( \begin{array}{c} 0 \\ 0 \end{array} \right), \left( \begin{array}{cc} \Sigma_b & \Sigma_{\tau b} \\ \Sigma_{\tau b}' & \Sigma_{\tau} \end{array} \right) \right)

By convention, random effects for the mean (b_i) can be assumed independent from those for the variance (\tau_i) by setting \Sigma_{\tau b} =0.

C. Location-scale mixed model distinguishing within and between visits variabilities

In some studies, multiple measurements of the same marker are collected during each visit. For instance, in clinical research, two or three blood pressure readings are typically recorded per visit, and within-visit variability may carry information.

To account for this, we introduce an LSMM that distinguishes within- and between-visit variabilities.

We introduce an additional level in the data hierarchy, grouping repeated measures by visit.

For each subject i (i=1,...,N), Y_{ijl} represents the l-th measurement (l=1,...,n_{ij}) at visit j (j=1,...,n_i) and time t_{ij}. We then define

\left\{ \begin{array}{ll} Y_{ijl} = \widetilde{Y}_i(t_{ij}) + \epsilon_{ij} + \nu_{ijl} \\ \hspace{5mm} = X_{ij}^{\top} \beta + Z_{ij}^{\top} b_i + \epsilon_{ij} + \nu_{ijl}, \\ \epsilon_{ij} \sim \mathcal{N}(0,\sigma_i^2), \quad \text{with } \log(\sigma_i) = \mu_\sigma + \tau_{\sigma i}, \\ \nu_{ijl} \sim \mathcal{N}(0,\kappa_i^2), \quad \text{with } \log(\kappa_i) = \mu_\kappa + \tau_{\kappa i}, \\ \end{array} \right.

where \mu_\sigma and \mu_\kappa are fixed intercepts for the between-visits and within-visit variances, respectively. The subject-specific random-effect b_i and \tau_i = (\tau_{\sigma i},\tau_{\kappa i})^\top are assumed to be Gaussian as in model (B).

Value

An object of class lsmm containing:

table.res

Table of parameter estimates and standard errors.

result_step1

A marqLevAlg object with first-step estimation results.

result_step2

A marqLevAlg object with second-step estimation results.

info_conv_step1

Information on first-step convergence (criteria and computation time).

info_conv_step2

Information on second-step convergence (criteria and computation time).

control

List of control parameters used during estimation.

Examples

data <- data.frame(
         ID = rep(1:5, each = 3),
         time = rep(1:3, 5),
         y = rnorm(15),
         event = rep(rbinom(5,1,0.5), each = 3),
         time_event = rep(runif(5), each = 3)
         )


m0 <- lsmm(
   formFixed = y ~ time,
   formRandom = ~ time,
   formGroup = ~ ID,
   formVar = "standard",
   timeVar = "time",
   data.long = data,
   S1 = 5,
   S2 = 5,
   nproc = 1
   )

 summary(m0)




data(threeC)
threeC$age.visit65 <- (threeC$age.visit-65)/10
threeC$SBP <- threeC$SBP/10
threeC <- dplyr::group_by(threeC, ID, num.visit)
threeC <- dplyr::mutate(threeC, SBPvisit = mean(SBP))
threeC_ex1 <- threeC[!duplicated(threeC[, c("ID", "num.visit")]),
                                 c("ID", "SBPvisit", "age.visit65", "sex")]

#First example : a standard linear mixed model (constant residual variance,
# in time and between subjects, case A in details)

m1 <- lsmm(formFixed = SBPvisit ~ age.visit65+I(age.visit65^2),
               formRandom = ~ age.visit65+I(age.visit65^2),
               formGroup = ~ ID,
               timeVar = 'age.visit65',
               data.long = threeC_ex1,
               formVar = "standard",
               S1 = 500,
               S2 = 1000,
               nproc = 1)

summary(m1)


#Second example : a linear mixed model with subject-specific time-dependent
# and covariate-dependent variability (case B in details)

#We adjust the individual residual variability on age and the sex.

m2 <- lsmm(formFixed = SBPvisit ~ age.visit65,
               formRandom = ~ age.visit65,
               formGroup = ~ ID,
               timeVar = 'age.visit65',
               data.long = threeC_ex1,
               formVar = "cov-dependent",
               formFixedVar = ~ age.visit65+sex,
               formRandomVar = ~ age.visit65,
               correlated_re = FALSE,
               S1 = 500,
               S2 = 1000,
               nproc = 1)

summary(m2)

#Third example : a linear mixed model with subject-specific inter-visits and
# intra-visits variabilities

threeC_ex2 <- threeC[, c("ID", "SBP", "age.visit65", "sex", "num.visit")]

m3 <- lsmm(formFixed = SBP ~ age.visit65,
               formRandom = ~ age.visit65,
               formGroup = ~ ID,
               timeVar = 'age.visit65',
               data.long = threeC_ex2,
               formVar = "inter-intra",
               random_inter = TRUE,
               random_intra = TRUE,
               formGroupVisit = ~num.visit,
               correlated_re = FALSE,
               S1 = 500,
               S2 = 1000,
               nproc = 1)

summary(m3)




#Fourth example : a linear mixed model with subject-specific inter-visits
# variability and constant intra-visit variability

m4 <- lsmm(formFixed = SBP ~ age.visit65+sex,
               formRandom = ~ age.visit65,
               formGroup = ~ ID,
               timeVar = 'age.visit65',
               data.long = threeC_ex2,
               formVar = "inter-intra",
               random_inter = TRUE,
               random_intra = FALSE,
               formGroupVisit = ~num.visit,
               correlated_re = FALSE,
               S1 = 500,
               S2 = 1000,
               nproc = 1)

summary(m4)

plot: Plot methods for lsjm or lsmm objects

Description

This function produces different plots (longitudinal and survival goodness-of-fit, individual trajectory) of a fitted object of class lsmm or lsjm.

Usage

## S3 method for class 'lsjm_classicCR'
plot(
  x,
  which = "long.fit",
  Objectpredict,
  break.times = NULL,
  ID.ind = NULL,
  xlim = NULL,
  ylim = NULL,
  ...
)

## S3 method for class 'lsjm_classicIDM'
plot(
  x,
  which = "long.fit",
  Objectpredict,
  break.times = NULL,
  ID.ind = NULL,
  ObjectSmoothHazard = NULL,
  xlim = NULL,
  ylim = NULL,
  ...
)

## S3 method for class 'lsjm_classicSingle'
plot(
  x,
  which = "long.fit",
  Objectpredict,
  break.times = NULL,
  ID.ind = NULL,
  xlim = NULL,
  ylim = NULL,
  ...
)

## S3 method for class 'lsjm_covDepCR'
plot(
  x,
  which = "long.fit",
  Objectpredict,
  break.times = NULL,
  ID.ind = NULL,
  xlim = NULL,
  ylim = NULL,
  ...
)

## S3 method for class 'lsjm_covDepIDM'
plot(
  x,
  which = "long.fit",
  Objectpredict,
  break.times = NULL,
  ID.ind = NULL,
  ObjectSmoothHazard = NULL,
  xlim = NULL,
  ylim = NULL,
  ...
)

## S3 method for class 'lsjm_covDepSingle'
plot(
  x,
  which = "long.fit",
  Objectpredict,
  break.times = NULL,
  ID.ind = NULL,
  xlim = NULL,
  ylim = NULL,
  ...
)

## S3 method for class 'lsjm_interintraCR'
plot(
  x,
  which = "long.fit",
  Objectpredict,
  break.times = NULL,
  ID.ind = NULL,
  xlim = NULL,
  ylim = NULL,
  ...
)

## S3 method for class 'lsjm_interintraIDM'
plot(
  x,
  which = "long.fit",
  Objectpredict,
  break.times = NULL,
  ID.ind = NULL,
  ObjectSmoothHazard = NULL,
  xlim = NULL,
  ylim = NULL,
  ...
)

## S3 method for class 'lsjm_interintraSingle'
plot(
  x,
  which = "long.fit",
  Objectpredict,
  break.times = NULL,
  ID.ind = NULL,
  xlim = NULL,
  ylim = NULL,
  ...
)

## S3 method for class 'lsmm_classic'
plot(
  x,
  which = "long.fit",
  Objectpredict,
  break.times = NULL,
  ID.ind = NULL,
  ylim = NULL,
  xlim = NULL,
  ...
)

## S3 method for class 'lsmm_covDep'
plot(
  x,
  which = "long.fit",
  Objectpredict,
  break.times = NULL,
  ID.ind = NULL,
  ylim = NULL,
  xlim = NULL,
  ...
)

## S3 method for class 'lsmm_interintra'
plot(
  x,
  which = "long.fit",
  Objectpredict,
  break.times = NULL,
  ID.ind = NULL,
  ylim = NULL,
  xlim = NULL,
  ...
)

Arguments

Details

With which="long.fit", this function allows to assess the fit of the longitudinal submodel comparing the mean of marker predictions collected in some windows of times (defined by break.times or using percentiles) to the mean of the observed measurements and its 95\

With which="traj.ind", represents the individual trajectory with its prediction interval.

For a lsjm object only, with which="survival.fit", the function allows to assess the fit of the survival submodel. For each transition, the predicted cumulative hazard function at each event time is computed given the predicted random effects. Then the mean of the predicted cumulative hazard functions are compared with there Nelson-Aalen estimator in the case of a single event or with competing risks. For an illness-death model, the predicted cumulative hazard function for each transition is compared to an illness-death model estimated by penalized likelihood accounting for interval censoring with the SmoothHazard package

Value

A list containing one or more plots:

long.fit

A plot comparing the mean marker predictions with the mean observed measurements and their 95 confidence intervals.

graph.traj.ind

One or more plots representing individual trajectories together with their prediction intervals.

survB

A plot comparing the predicted cumulative hazard function with either the Nelson–Aalen estimator or an Illness–Death model.

Examples

set.seed(123)

data <- data.frame(
         ID = rep(1:5, each = 3),
         time = rep(1:3, 5),
         y = rnorm(15),
         event = rep(rbinom(5,1,0.5), each = 3),
         time_event = rep(runif(5), each = 3)
         )


m0 <- lsmm(
   formFixed = y ~ time,
   formRandom = ~ time,
   formGroup = ~ ID,
   formVar = "standard",
   timeVar = "time",
   data.long = data,
   S1 = 5,
   S2 = 5,
   nproc = 1
   )

pred.m0 <- predict(m0, which = c("RE","Y"), data.long = data)

plot(m0,
     which = "long.fit",
     Objectpredict = pred.m0,
     break.times = c(0,1,2,3))

plot(m0,
     which = "traj.ind",
     Objectpredict = pred.m0,
     ID.ind = c(1,2))








library(dplyr)
data(threeC)
threeC$age.visit65 <- (threeC$age.visit-65)/10
threeC$SBP <- threeC$SBP/10
threeC <- threeC %>% group_by(ID, num.visit) %>% mutate(SBPvisit = mean(SBP))
threeC$age65_CR <- NA
threeC$age65_CR[which(threeC$dem == 1)] <- (threeC$age.last65[which(threeC$dem == 1)]
                                       +threeC$age.first65[which(threeC$dem == 1)])/2
threeC$age65_CR[which(threeC$dem == 0)] <- threeC$age.final65[which(threeC$dem == 0)]
threeC$demCR <- threeC$dem
threeC$deathCR <- NA
threeC$deathCR[which(threeC$dem == 1)] <- 0
threeC$deathCR[which(threeC$dem == 0)]<-threeC$death[which(threeC$dem == 0)]
threeC <- threeC %>% group_by(ID) %>% filter(age.visit65 <= age65_CR)


threeC_ex1 <- threeC[!duplicated(threeC[, c("ID", "num.visit")]), c("ID",
     "SBPvisit", "age.visit65", "sex","age0_65", "demCR","deathCR",
      "age65_CR")]


# Estimation of a lsmm with time-dependent variability model:
m2 <- lsmm(formFixed = SBPvisit ~ age.visit65,
               formRandom = ~ age.visit65,
               formGroup = ~ ID,
               timeVar = 'age.visit65',
               data.long = threeC_ex1,
               formVar = "cov-dependent",
               formFixedVar = ~ age.visit65+sex,
               formRandomVar = ~ age.visit65,
               correlated_re = FALSE,
               S1 = 500,
               S2 = 1000,
               nproc = 1)

# Predictions:
pred.m2 <- predict(m2, which = c("RE", "Y"))

#Plot:
plot(m2, which = "long.fit", Objectpredict = pred.m2,
                           break.times = (seq(65,95,by = 2.5)-65)/10)
plot(m2, which = "traj.ind", Objectpredict = pred.m2,
                                            ID.ind = c(3,120))

# Estimation of a lsjm with time-dependent variability model and
# competing events:
l2 <- lsjm(Objectlsmm = m2,
           survival_type = 'CR',
           formSurv_01 = ~ sex,
           formSurv_02 = ~ sex,
           sharedtype_01 = c("value", "variability"),
           sharedtype_02 = c("value", "variability"),
           hazardBase_01 = "Weibull",
           hazardBase_02 = "Weibull",
           delta1 = ~ demCR,
           delta2 = ~ deathCR,
           Time_T0 = ~ age0_65,
           Time_T = ~ age65_CR,
           nproc = 5,
           S1 = 1000,
           S2 = 2000)

# Predictions:
pred.l2 <- predict(l2, which = c("RE", "Y", "Cum"))

# Plot:
plot(l2, which = "long.fit", Objectpredict = pred.l2,
                         break.times = (seq(65,95,by = 2.5)-65)/10)
plot(l2, which = "traj.ind", Objectpredict = pred.l2,
                          ID.ind = c(3,120))
plot(l2, which = "survival.fit", Objectpredict = pred.l2)

predict: Prediction of some quantities for each subjects

Description

This function computes different predicted quantities. For a lsmm object, it is possible to compute, for each subject, their random effects, their value of the marker and the residual variability (for each measurement time)). For a lsjm object we could also compute cumulative hazard function for each risk transition.

Usage

## S3 method for class 'lsjm_classicCR'
predict(object, which = "RE", Objectranef = NULL, data.long = NULL, ...)

## S3 method for class 'lsjm_classicIDM'
predict(object, which = "RE", Objectranef = NULL, data.long = NULL, ...)

## S3 method for class 'lsjm_classicSingle'
predict(object, which = "RE", Objectranef = NULL, data.long = NULL, ...)

## S3 method for class 'lsjm_covDepCR'
predict(object, which = "RE", Objectranef = NULL, data.long = NULL, ...)

## S3 method for class 'lsjm_covDepIDM'
predict(object, which = "RE", Objectranef = NULL, data.long = NULL, ...)

## S3 method for class 'lsjm_covDepSingle'
predict(object, which = "RE", Objectranef = NULL, data.long = NULL, ...)

## S3 method for class 'lsjm_interintraCR'
predict(object, which = "RE", Objectranef = NULL, data.long = NULL, ...)

## S3 method for class 'lsjm_interintraIDM'
predict(object, which = "RE", Objectranef = NULL, data.long = NULL, ...)

## S3 method for class 'lsjm_interintraSingle'
predict(object, which = "RE", Objectranef = NULL, data.long = NULL, ...)

## S3 method for class 'lsmm_classic'
predict(object, which = "RE", Objectranef = NULL, data.long = NULL, ...)

## S3 method for class 'lsmm_covDep'
predict(object, which = "RE", Objectranef = NULL, data.long = NULL, ...)

## S3 method for class 'lsmm_interintra'
predict(object, which = "RE", Objectranef = NULL, data.long = NULL, ...)

Arguments

Value

A table for each type of prediction (RE/Y/Cum)

predictRE

A table with predicted random effects for each subjects.

predictY

A table with predicted marker and residual variability for each subjects and at each measurement time.

predictCum_01

A table for predicted cumulative hazard function for transition 0-1.

predictCum_02

A table for predicted cumulative hazard function for transition 0-2.

predictCum_12

A table for predicted cumulative hazard function for transition 1-2.

grid.time.Cum

A vector of times for which the cumulative hazard functions are computed.

Examples

data <- data.frame(
         ID = rep(1:5, each = 3),
         time = rep(1:3, 5),
         y = rnorm(15),
         event = rep(rbinom(5,1,0.5), each = 3),
         time_event = rep(runif(5), each = 3)
         )


m0 <- lsmm(
   formFixed = y ~ time,
   formRandom = ~ time,
   formGroup = ~ ID,
   formVar = "standard",
   timeVar = "time",
   data.long = data,
   S1 = 5,
   S2 = 5,
   nproc = 1
   )

pred.m0 <- predict(m0, which = c("RE","Y"), data.long = data)



library(dplyr)

data(threeC)
threeC$age.visit65 <- (threeC$age.visit-65)/10
threeC$SBP <- threeC$SBP/10
threeC <- threeC
threeC <- dplyr::group_by(threeC, ID, num.visit)
threeC <- dplyr::mutate(threeC, SBPvisit = mean(SBP))
threeC_ex1 <- threeC[!duplicated(threeC[, c("ID", "num.visit")]),
                                  c("ID", "SBPvisit", "age.visit65", "sex","dem","death",
                                    "age.first65","age.last65","age.final65","age0_65")]

m1 <- lsmm(formFixed = SBPvisit ~ age.visit65,
               formRandom = ~ age.visit65,
               formGroup = ~ ID,
               timeVar = 'age.visit65',
               data.long = threeC_ex1,
               formVar = "cov-dependent",
               formFixedVar = ~ age.visit65+sex,
               formRandomVar = ~ age.visit65,
               correlated_re = FALSE,
               S1 = 500,
               S2 = 1000,
               nproc = 1)

l1 <- lsjm(m1,
           survival_type = 'IDM',
           formSurv_01=~1,
           formSurv_02=~sex,
           formSurv_12=~sex,
           sharedtype_01 = c("value", "variability"),
           sharedtype_02 = c("value", "slope", "variability"),
           sharedtype_12 = c("value", "variability"),
           hazardBase_01 = "Weibull",
           hazardBase_02 = "Weibull",
           hazardBase_12 = "Splines",
           delta1=~dem,
           delta2=~death,
           Time_T =~age.final65,
           Time_L =~age.last65,
           Time_R =~age.first65,
           Time_T0 =~age0_65,
           formSlopeFixed =~1,
           formSlopeRandom =~1,
           index_beta_slope = c(2),
           index_b_slope = c(2),
           nb.knots.splines = c(0,0,1),
           S1 = 1000,
           S2 = 2000,
           nproc = 10)

pred.m1 <- predict(m1, which = c("RE","Y"), data.long = threeC_ex1)

pred.l1 <- predict(l1, which = c("RE","Y","Cum"), data.long = threeC_ex1)

ranef: the predicted random effects for all subjects

Description

ranef: the predicted random effects for all subjects

Usage

## S3 method for class 'lsjm_classicCR'
ranef(object, ...)

## S3 method for class 'lsjm_classicIDM'
ranef(object, ...)

## S3 method for class 'lsjm_classicSingle'
ranef(object, ...)

## S3 method for class 'lsjm_covDepCR'
ranef(object, ...)

## S3 method for class 'lsjm_covDepIDM'
ranef(object, ...)

## S3 method for class 'lsjm_covDepSingle'
ranef(object, ...)

## S3 method for class 'lsjm_interintraCR'
ranef(object, ...)

## S3 method for class 'lsjm_interintraIDM'
ranef(object, ...)

## S3 method for class 'lsjm_interintraSingle'
ranef(object, ...)

## S3 method for class 'lsmm_classic'
ranef(object, ...)

## S3 method for class 'lsmm_covDep'
ranef(object, ...)

## S3 method for class 'lsmm_interintra'
ranef(object, ...)

Arguments

Value

A table with predicted random effects for each subjects.

Examples

data <- data.frame(
         ID = rep(1:5, each = 3),
         time = rep(1:3, 5),
         y = rnorm(15),
         event = rep(rbinom(5,1,0.5), each = 3),
         time_event = rep(runif(5), each = 3)
         )


m0 <- lsmm(
   formFixed = y ~ time,
   formRandom = ~ time,
   formGroup = ~ ID,
   formVar = "standard",
   timeVar = "time",
   data.long = data,
   S1 = 5,
   S2 = 5,
   nproc = 1
   )

ranef.m0 <- ranef(m0)



library(dplyr)

data(threeC)
threeC$age.visit65 <- (threeC$age.visit-65)/10
threeC$SBP <- threeC$SBP/10
threeC <- threeC
threeC <- dplyr::group_by(threeC, ID, num.visit)
threeC <- dplyr::mutate(threeC, SBPvisit = mean(SBP))
threeC_ex1 <- threeC[!duplicated(threeC[, c("ID", "num.visit")]),
                                  c("ID", "SBPvisit", "age.visit65", "sex","dem","death",
                                    "age.first65", "age.last65","age.final65","age0_65")]

m1 <- lsmm(formFixed = SBPvisit ~ age.visit65,
               formRandom = ~ age.visit65,
               formGroup = ~ ID,
               timeVar = 'age.visit65',
               data.long = threeC_ex1,
               formVar = "cov-dependent",
               formFixedVar = ~ age.visit65+sex,
               formRandomVar = ~ age.visit65,
               correlated_re = FALSE,
               S1 = 500,
               S2 = 1000,
               nproc = 1)

l1 <- lsjm(m1,
           survival_type = 'IDM',
           formSurv_01=~1,
           formSurv_02=~sex,
           formSurv_12=~sex,
           sharedtype_01 = c("value", "variability"),
           sharedtype_02 = c("value", "slope", "variability"),
           sharedtype_12 = c("value", "variability"),
           hazardBase_01 = "Weibull",
           hazardBase_02 = "Weibull",
           hazardBase_12 = "Splines",
           delta1=~dem,
           delta2=~death,
           Time_T =~age.final65,
           Time_L =~age.last65,
           Time_R =~age.first65,
           Time_T0 =~age0_65,
           formSlopeFixed =~1,
           formSlopeRandom =~1,
           index_beta_slope = c(2),
           index_b_slope = c(2),
           nb.knots.splines = c(0,0,1),
           S1 = 1000,
           S2 = 2000,
           nproc = 10)

r1 <- ranef(m1)
r1.1 <- ranef(l1)

The population-average probability of being free of any events at a given time $t$ and covariates

Description

The population-average probability of being free of any events at a given time $t$ and covariates

Usage

## S3 method for class 'lsjm_classicCR'
survmarg(object, individual, time)

## S3 method for class 'lsjm_classicIDM'
survmarg(object, individual, time)

## S3 method for class 'lsjm_classicSingle'
survmarg(object, individual, time)

## S3 method for class 'lsjm_covDepCR'
survmarg(object, individual, time)

## S3 method for class 'lsjm_covDepIDM'
survmarg(object, individual, time)

## S3 method for class 'lsjm_covDepSingle'
survmarg(object, individual, time)

## S3 method for class 'lsjm_interintraCR'
survmarg(object, individual, time)

## S3 method for class 'lsjm_interintraIDM'
survmarg(object, individual, time)

## S3 method for class 'lsjm_interintraSingle'
survmarg(object, individual, time)

Arguments

Value

A numeric, the population-average probability of being free of any events at a given time $t$ and chosen covariates

Examples

set.seed(123)

data <- data.frame(
         ID = rep(1:100, each = 3),
         time = rep(1:3, 100),
         y = rnorm(300),
         event = rep(rbinom(100,1,0.5), each = 3),
         time_event = rep(runif(100), each = 3)
         )


m0 <- lsmm(
   formFixed = y ~ time,
   formRandom = ~ time,
   formGroup = ~ ID,
   formVar = "standard",
   timeVar = "time",
   data.long = data,
   S1 = 5,
   S2 = 5,
   nproc = 1
   )

 fit <- lsjm(
      Objectlsmm = m0,
      survival_type = "Single",
      formSurv_01 = ~ 1,
      sharedtype_01 = "value",
      hazardBase_01 = "Weibull",
      delta1 = ~ event,
      Time_T = ~ time_event,
      S1 = 100,
      S2 = 100,
      nproc = 1
      )

individual <- data[1, ]
survmarg(fit, individual, time = 2)




# Begining by estimating the examples from \code{lsmm} and \code{lsjm}, we then compute
# the average-probability of being alive and without dementia at age 85 for a Women

data(threeC)
threeC$age.visit65 <- (threeC$age.visit-65)/10
threeC$SBP <- threeC$SBP/10
threeC <- threeC
threeC <- dplyr::group_by(threeC, ID, num.visit)
threeC <- dplyr::mutate(threeC, SBPvisit = mean(SBP))
threeC_ex1 <- threeC[!duplicated(threeC[, c("ID", "num.visit")]),
                                  c("ID", "SBPvisit", "age.visit65", "sex","dem","death",
                                    "age.first65","age.last65","age.final65","age0_65")]

m1 <- lsmm(formFixed = SBPvisit ~ age.visit65,
               formRandom = ~ age.visit65,
               formGroup = ~ ID,
               timeVar = 'age.visit65',
               data.long = threeC_ex1,
               formVar = "cov-dependent",
               formFixedVar = ~ age.visit65+sex,
               formRandomVar = ~ age.visit65,
               correlated_re = FALSE,
               S1 = 500,
               S2 = 1000,
               nproc = 1)

l1 <- lsjm(m1,
           survival_type = 'IDM',
           formSurv_01=~1,
           formSurv_02=~sex,
           formSurv_12=~sex,
           sharedtype_01 = c("value", "variability"),
           sharedtype_02 = c("value", "slope", "variability"),
           sharedtype_12 = c("value", "variability"),
           hazardBase_01 = "Weibull",
           hazardBase_02 = "Weibull",
           hazardBase_12 = "Splines",
           delta1=~dem,
           delta2=~death,
           Time_T =~age.final65,
           Time_L =~age.last65,
           Time_R =~age.first65,
           Time_T0 =~age0_65,
           formSlopeFixed =~1,
           formSlopeRandom =~1,
           index_beta_slope = c(2),
           index_b_slope = c(2),
           nb.knots.splines = c(0,0,1),
           S1 = 1000,
           S2 = 2000,
           nproc = 10)

individual <- threeC_ex1[1, c("Sex")]
survmarg(l1, individual, time = 2)

ThreeC dataset

Description

A random subsample of 500 subjects from the French Three-Cities cohort, aimed at assessing the relation between vascular factors and dementia in the elderly, for the example of the LSJM package.

Usage

data(threeC)

Format

A data frame with 5248 rows and 13 variables:

ID

id of each subject

Apoe4

indicator of the apoe4 gene

Edu

Educational level (0 = less than 10 years, 1 = more than 10 years)

SBP

systolic blood pressure in mmHg

age.visit

age at measurement of SBP

age.final

age at death or censoring (last news)

age0

age at entry in the cohort

age.last

age of last visit without dementia

age.first

age at visit diagnosis for dementia

sex

sex of the subject

dem

indicator of dementia

death

indicator of death

num.visit

visit identifier

age.visit65

(age.visit-65)/10

age.final65

(age.final-65)/10

age.last65

(age.last-65)/10

age.first65

(age.first-65)/10

age0_65

(age0-65)/10

Details

The sample includes participants without dementia at baseline and aged 65 years old or older. Repeated measures of systolic blood pressure were collected over a maximum period of 20 years. At each visit, systolic blood pressure was measured two or three times.