Package 'TwoTimeScales'

Description

covariates_plot() produces a plot of the covariates' effects ($\hat\beta$) with confidence intervals, or of the Hazard Ratios ($\exp(\hat\beta)$) with confidence intervals.

Usage

covariates_plot(
  fitted_model,
  confidence_lev = 0.95,
  plot_options = list(),
  ...
)

Arguments

Value

A plot of the covariates' effects. The different covariates are plotted on the x-axis, and on the y-axis the effects on the coefficient- or on the HR-scale are plotted. The main estimate is represented by a point and the CIs are added as vertical bars.

Examples

# Create some fake data - the bare minimum
id <- 1:20
u <- c(
  5.43, 3.25, 8.15, 5.53, 7.28, 6.61, 5.91, 4.94, 4.25, 3.86, 4.05, 6.86,
  4.94, 4.46, 2.14, 7.56, 5.55, 7.60, 6.46, 4.96
)
s <- c(
  0.44, 4.89, 0.92, 1.81, 2.02, 1.55, 3.16, 6.36, 0.66, 2.02, 1.22, 3.96,
  7.07, 2.91, 3.38, 2.36, 1.74, 0.06, 5.76, 3.00
)
ev <- c(1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1)
x1 <- c(0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0)

fakedata <- as.data.frame(cbind(id, u, s, ev, x1))
covs <- subset(fakedata, select = c("x1"))
fakedata2ts <- prepare_data(
  u = fakedata$u,
  s_out = fakedata$s,
  ev = fakedata$ev,
  ds = .5,
  individual = TRUE,
  covs = covs
)
# Fit a fake model - not optimal smoothing
fakemod <- fit2ts(fakedata2ts,
  optim_method = "grid_search",
  lrho = list(
    seq(1, 1.5, .5),
    seq(1, 1.5, .5)
  )
)
# Covariates plot with default options
covariates_plot(fakemod)

# Plot the hazard ratios instead
covariates_plot(fakemod,
  plot_options = list(
    HR = TRUE
  )
)

# Change confidence level
covariates_plot(fakemod,
  confidence_lev = .99
)

Description

Computes the cumulative hazard surface over two time scales from a fitted model. The function is also called internally from plot() if the user wants to plot the cumulative hazard from a fitted model.

Usage

cumhaz2ts(
  fitted_model,
  plot_grid = NULL,
  cause = NULL,
  midpoints = FALSE,
  where_slices = NULL,
  direction = c("u", "s", NULL),
  tmax = NULL
)

Arguments

Value

A list with the following elements: * Haz a list of estimated hazard and associated SEs (obtained from the function get_hazard_2d()); * CumHaz the cumulated hazard estimate over u and s; * cause (if provided) the short name for the cause.

Examples

# Create some fake data - the bare minimum
id <- 1:20
u <- c(5.43, 3.25, 8.15, 5.53, 7.28, 6.61, 5.91, 4.94, 4.25, 3.86, 4.05, 6.86,
       4.94, 4.46, 2.14, 7.56, 5.55, 7.60, 6.46, 4.96)
s <- c(0.44, 4.89, 0.92, 1.81, 2.02, 1.55, 3.16, 6.36, 0.66, 2.02, 1.22, 3.96,
       7.07, 2.91, 3.38, 2.36, 1.74, 0.06, 5.76, 3.00)
ev <- c(1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1)#'

fakedata <- as.data.frame(cbind(id, u, s, ev))
fakedata2ts <- prepare_data(u = fakedata$u,
                            s_out = fakedata$s,
                            ev = fakedata$ev,
                            ds = .5)
# Fit a fake model - not optimal smoothing
fakemod <- fit2ts(fakedata2ts,
                  optim_method = "grid_search",
                  lrho = list(seq(1 ,1.5 ,.5),
                              seq(1 ,1.5 ,.5)))

# Obtain the fake cumulated hazard
fakecumhaz2ts <- cumhaz2ts(fakemod)

Description

Cumulative incidence surface over two time scales

Usage

cuminc2ts(haz = list(), ds, cause = NULL)

Arguments

Value

a list with one cumulative incidence matrix for each cause-specific hazard (named if a vector of short names is passed to cause).

Examples

# Create some fake data - the bare minimum
id <- 1:20
u <- c(5.43, 3.25, 8.15, 5.53, 7.28, 6.61, 5.91, 4.94, 4.25, 3.86, 4.05, 6.86,
       4.94, 4.46, 2.14, 7.56, 5.55, 7.60, 6.46, 4.96)
s <- c(0.44, 4.89, 0.92, 1.81, 2.02, 1.55, 3.16, 6.36, 0.66, 2.02, 1.22, 3.96,
       7.07, 2.91, 3.38, 2.36, 1.74, 0.06, 5.76, 3.00)
ev <- c(1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1)#'

fakedata <- as.data.frame(cbind(id, u, s, ev))
fakedata2ts <- prepare_data(u = fakedata$u,
                            s_out = fakedata$s,
                            ev = fakedata$ev,
                            ds = .5)
# Fit a fake model - not optimal smoothing
fakemod <- fit2ts(fakedata2ts,
                  optim_method = "grid_search",
                  lrho = list(seq(1 ,1.5 ,.5),
                              seq(1 ,1.5 ,.5)))

# Obtain the fake cumulated hazard
fakecumhaz2ts <- cumhaz2ts(fakemod)
# Fake cumulative incidence function 2ts
fakecif2ts <- cuminc2ts(haz = list(fakecumhaz2ts$Haz$hazard),
                        ds = .5)

Description

exposure_events_1d() computes aggregated measures of exposure times and event counts starting from individual records of time at entry, time at exit and event's indicator, over one time scale (s).

Usage

exposures_events_1d(s_in = NULL, s_out, ev, bins)

Arguments

Details

The time scale s is divided into bins of equal size, which are provided as input to the function. Then, the time-at-risk for each individual is split according to these bins, and an event indicator is placed in the bin where the exit time is located. Finally, the individual contributions are summed in each bin to provide a vector of total exposure time and total event counts. See also prepare_data() to conveniently prepare individual data for the analysis with one, or two time scales.

Value

A list with the following elements:

• R A matrix of dimension $n$ by $ns$ containing the exposure times for each individual separately.

• r A vector of exposure times.

• Y A matrix of dimension $n$ by $ns$ containing the event counts for each individual separately

• y A vector of event counts.

If the length of the input vectors do not match, an error message is returned.

Author(s)

Angela Carollo [email protected] and Paul Eilers [email protected]

Examples

# ---- Bin colon cancer data by time since recurrence ----
# First create vector of bins
bins1ts <- make_bins(s_in = reccolon2ts$entrys, s_out = reccolon2ts$timesr, ds = 30)
bindata <- exposures_events_1d(s_in = reccolon2ts$entrys,
s_out = reccolon2ts$timesr, ev = reccolon2ts$status, bins = bins1ts$bins_s)

Description

exposures_events_2d() computes individual or aggregated matrices of exposure times and event counts starting from individual records of time at entry in the process (measured over the first time scale), duration at entry in the process (measured over the second time scale), duration at exit from the process (measured over the second time scale), and event's indicator.

Usage

exposures_events_2d(u, s_in = NULL, s_out, ev, bins_list, individual = FALSE)

Arguments

Details

The fixed-time variable u and the second time scale s are divided into $n_u$ and $n_s$ intervals, respectively. The extremes of these intervals are provided as input to the function. First, the fixed-time at entry is located in one of the $n_u$ bins that cover the whole range of u. Then, the time-at-risk for each individual is split according to the $n_s$ bins that span the whole range of values for s, and an event indicator is placed in the bin where the exit time is located. This is done by calling the function exposure_events_1d(). If individual matrices of exposure and events are required, then the function returns two arrays of dimension $n_u$ by $n_s$ by $n$. If aggregated results are preferred, the individual contributions are summed in each bin to provide a matrix of total exposure times and a matrix of total event counts, both of dimensions $n_u$ by $n_s$. See also prepare_data() to conveniently prepare individual data for the analysis with one, or two time scales.

Value

A list with the following elements:

• R an array of exposure times: if individual == TRUE, then R is an array of dimension $n_u$ by $n_s$ by $n$, otherwise is an array of dimension $n_u$ by $n_s$

• Yan array of event counts: if individual == TRUE, then Y is an array of dimension $n_u$ by $n_s$ by $n$, otherwise is an array of dimension $n_u$ by $n_s$

Author(s)

Angela Carollo [email protected]

Examples

# ---- Bin colon cancer data by time at randomization and time since recurrence ----
# First create vectors of bins (using function `make_bins()`)
bins <- make_bins(u = reccolon2ts$timer, s_out = reccolon2ts$timesr,
du = 30, ds = 30)
# Now bin data (note: the s_in argument is omitted because data are not left truncated)
bindata2d <- exposures_events_2d(u = reccolon2ts$timer,
s_out = reccolon2ts$timesr, ev = reccolon2ts$status, bins = bins)

Description

exposures_events_Lexis() computes aggregated matrices of exposure times and event counts over two time scales, on the Lexis diagram.

The time scales are t and s. This function uses functions from the package popEpi and from the package Epi, and code shared by Bendix Carstensen on the website bendixcarstensen.com. See also prepare_data() to conveniently prepare individual data for the analysis with one, or two time scales.

Usage

exposures_events_Lexis(t_in = NULL, t_out, s_in = NULL, s_out, ev, bins_list)

Arguments

Value

A list with the following elements:

• R an array of exposure times of dimension $n_t$ by $n_s$

• Y an array of event counts of dimension $n_t$ by $n_s$

Author(s)

Angela Carollo [email protected]

References

Carstensen B, Plummer M, Laara E, Hills M (2022). Epi: A Package for Statistical Analysis in Epidemiology. R package version 2.47.1, https://CRAN.R-project.org/package=Epi.

Miettinen J, Rantanen M, Seppa K (2023). popEpi: Functions for Epidemiological Analysis using Population Data. R package version 0.4.11, https://cran.r-project.org/package=popEpi.

Examples

# ---- Bin colon cancer data by time since randomization and time since recurrence ----
# First create vectors of bins (using function `make_bins()`)
bins <- make_bins(t_out = reccolon2ts$timedc, s_out = reccolon2ts$timesr,
dt = 90, ds = 90)
# Now bin data (note: the t_in and s_in arguments are omitted because data are not left truncated)
bindata2d <- exposures_events_Lexis(t_out = reccolon2ts$timedc,
s_out = reccolon2ts$timesr, ev = reccolon2ts$status, bins = bins)

Description

fit1ts() fits a smooth hazard model with one time scale.

Three methods are implemented for the search of the optimal smoothing parameter (and therefore optimal model): a numerical optimization of the AIC or BIC of the model, a search for the minimum AIC or BIC of the model over a grid of $\log_{10}$ values for the smoothing parameter and the estimation using a sparse mixed model representation of P-splines. Construction of the B-splines basis and of the penalty matrix is incorporated within the function. If a matrix of covariates is provided, the function will estimate a model with covariates.

Usage

fit1ts(
  data1ts = NULL,
  y = NULL,
  r = NULL,
  Z = NULL,
  bins = NULL,
  Bbases_spec = list(),
  Wprior = NULL,
  pord = 2,
  optim_method = c("ucminf", "grid_search", "LMMsolver"),
  optim_criterion = c("aic", "bic"),
  lrho = 0,
  ridge = 0,
  control_algorithm = list(),
  par_gridsearch = list()
)

Arguments

Details

Some functions from the R-package LMMsolver are used here. We refer the interested readers to https://biometris.github.io/LMMsolver/ for more detail on LMMsolver and its usage.

Value

An object of class haz1ts, or of class haz1tsLMM. For objects of class haz1ts this is

• optimal_model A list with:

  • alpha The vector of estimated P-splines coefficients of length $c_s$.

  • SE_alpha The vector of estimated Standard Errors for the alpha coefficients, of length $c_s$.

  • beta The vector of estimated covariate coefficients of length $p$ (if model with covariates).

  • se_beta The vector of estimated Standard Errors for the beta coefficients of length $p$ (if model with covariates).

  • eta or eta0. The vector of values of the (baseline) linear predictor (log-hazard) of length $n_s$.

  • H The hat-matrix.

  • Cov The full variance-covariance matrix.

  • deviance The deviance.

  • ed The effective dimension of the model.

  • aic The value of the AIC.

  • bic The value of the BIC.

  • Bbases a list with the B-spline basis Bs (this is a list for compatibility with functions in 2d).

• optimal_logrho The optimal value of log10(rho_s).

• P_optimal The optimal penalty matrix P.

• AIC (if par_gridsearch$return_aic == TRUE) The vector of AIC values.

• BIC (if par_gridsearch$return_bic == TRUE) The vector of BIC values.

Objects of class haz1tsLMM have a slight different structure. They are a list with:

• optimal_model an object of class LMMsolve

• AIC_BIC a list with, among other things, the AIC and BIC values and the ED of the model

• n_events the number of events

• ns the number of bins over the s-axis

• cs the number of B-splines over the s-axis

• covariates an indicator for PH model

References

Boer, Martin P. 2023. “Tensor Product P-Splines Using a Sparse Mixed Model Formulation.” Statistical Modelling 23 (5-6): 465–79. https://doi.org/10.1177/1471082X231178591.#'

Examples

## preparing data - no covariates
dt1ts <- prepare_data(
  data = reccolon2ts,
  s_in = "entrys",
  s_out = "timesr",
  events = "status",
  ds = 180
)

## fitting the model with fit1ts() - default options, that is ucminf optimization

mod1 <- fit1ts(dt1ts)

## fitting with LMMsolver
mod2 <- fit1ts(dt1ts,
  optim_method = "LMMsolver"
)

## preparing the data - covariates

dt1ts_cov <- prepare_data(
  data = reccolon2ts,
  s_in = "entrys",
  s_out = "timesr",
  events = "status",
  ds = 180,
  individual = TRUE,
  covs = c("rx", "node4", "sex")
)

## fitting the model with fit1ts() - grid search over only two log_10(rho_s) values

mod3 <- fit1ts(dt1ts_cov,
  optim_method = "grid_search",
  lrho = c(1, 1.5)
)

Description

fit2ts() fits a smooth hazard model with two time scales.

Three methods are implemented for the search of the optimal smoothing parameters (and therefore optimal model): a numerical optimization of the AIC or BIC of the model, a search for the minimum AIC or BIC of the model over a grid of $\log_{10}$ values for the smoothing parameters, and a solution that uses a sparse mixed model representation of the P-spline model to estimate the smoothing parameters. Construction of the B-splines bases and of the penalty matrix is incorporated within the function. If a matrix of covariates is provided, the function will estimate a model with covariates.

Usage

fit2ts(
  data2ts = NULL,
  Y = NULL,
  R = NULL,
  Z = NULL,
  bins = NULL,
  Bbases_spec = list(),
  pord = 2,
  optim_method = c("ucminf", "grid_search", "LMMsolver"),
  optim_criterion = c("aic", "bic"),
  lrho = c(0, 0),
  Wprior = NULL,
  ridge = 0,
  control_algorithm = list(),
  par_gridsearch = list()
)

Arguments

Details

Some functions from the R-package LMMsolver are used here. We refer the interested readers to https://biometris.github.io/LMMsolver/ for more details on LMMsolver and its usage.

     For the numerical optimization using `ucminf` a tolerance parameter is
     specified internally: `control = list(xtol = 1e-5)`. The default in
     `ucminf` is `xtol = 1e-12`. As ucminf is used here to find the minimum
     AIC or BIC, often this level of precision is not needed.
     Nevertheless, this value can be adjusted in `control_algorithm`.

Value

An object of class haz2ts, or of class haz2tsLMM. For objects of class haz2ts this is

• optimal_model A list with :

  • Alpha The matrix of estimated P-splines coefficients of dimension $c_u$ by $c_s$.

  • Cov_alpha The variance-covariance matrix of the Alpha coefficients, of dimension $c_uc_s$ by $c_uc_s$.

  • beta The vector of length $p$ of estimated covariates coefficients (if model with covariates).

  • Cov_beta The variance-covariance matrix of the beta coefficients, of dimension $p$ by $p$ (if model with covariates).

  • SE_beta The vector of length $p$ of estimated Standard Errors for the beta coefficients (if model with covariates)..

  • Eta or Eta0 The matrix of values of the (baseline) linear predictor (log-hazard) of dimension $n_u$ by $n_s$.

  • H The hat-matrix.

  • deviance The deviance.

  • ed The effective dimension of the model.

  • aic The value of the AIC.

  • bic The value of the BIC.

  • Bbases a list with the B-spline bases Bu and Bs

• optimal_logrho A vector with the optimal values of $\log_{10}(\rho_u)$ and $\log_{10}(\rho_u)$.

• P_optimal The optimal penalty matrix P.

• AIC (if par_gridsearch$return_aic == TRUE) The matrix of AIC values.

• BIC (if par_gridsearch$return_bic == TRUE) The matrix of BIC values.

Objects of class haz2tsLMM have a slight different structure. They are a list with:

• optimal_model an object of class LMMsolve

• AIC_BIC a list with, among other things, the AIC and BIC values and the ED of the model

• n_events the number of events

• nu the number of bins over the u-axis

• ns the number of bins over the s-axis

• cu the number of B-splines over the u-axis

• cs the number of B-splines over the s-axis

• covariates an indicator for PH model

References

Boer, Martin P. 2023. “Tensor Product P-Splines Using a Sparse Mixed Model Formulation.” Statistical Modelling 23 (5-6): 465–79. doi:10.1177/1471082X231178591. Carollo, A., Eilers, P., Putter, H. and Gampe, J. (2025), "Smooth Hazards With Multiple Time Scales." Statistics in Medicine, 44: e10297. doi:10.1002/sim.10297

Examples

# Create some fake data - the bare minimum
id <- 1:20
u <- c(
  5.43, 3.25, 8.15, 5.53, 7.28, 6.61, 5.91, 4.94, 4.25, 3.86, 4.05, 6.86,
  4.94, 4.46, 2.14, 7.56, 5.55, 7.60, 6.46, 4.96
)
s <- c(
  0.44, 4.89, 0.92, 1.81, 2.02, 1.55, 3.16, 6.36, 0.66, 2.02, 1.22, 3.96,
  7.07, 2.91, 3.38, 2.36, 1.74, 0.06, 5.76, 3.00
)
ev <- c(1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1) #'

fakedata <- as.data.frame(cbind(id, u, s, ev))
fakedata2ts <- prepare_data(
  data = fakedata,
  u = "u",
  s_out = "s",
  ev = "ev",
  ds = .5
)
# Fit a fake model - not optimal smoothing
fit2ts(fakedata2ts,
  optim_method = "grid_search",
  lrho = list(seq(1, 1.5, .5), seq(1, 1.5, .5))
)
# For more examples please check the vignettes! Running more complicated examples
# here would imply longer running times...

Description

Fits a log-additive model over two time scales. If covariates are included in the model, fitpgam() will fit a proportional hazards model, where the baseline hazard is a surface over the two time scales, where the effect of the time scales is additive on the log-scale. The model is described in Carollo et al. (2025).

Usage

fitpgam(
  data2ts = NULL,
  Y = NULL,
  R = NULL,
  Z = NULL,
  bins = NULL,
  Bbases_spec = list(),
  pord = 2,
  ridge = 1e-06,
  lrho = c(0, 0),
  optim_method = c("ucminf", "grid_search"),
  optim_criterion = c("aic", "bic"),
  control_algorithm = list(),
  par_gridsearch = list()
)

Arguments

Details

The name P-GAM follows from the way this class of models is named in Eilers and Marx (2021) Practical Smoothing. The Joys of P-splines. In Carollo et al. (2025) this model is referred to as log-additive.

@references Carollo, A., Putter, H., Eilers, P. H. C., & Gampe, J. (2025). Analysis of Time-to-Event Data With Two Time Scales. An Application to Transitions out of Cohabitation. Sociological Methods & Research, 0(0). doi:10.1177/00491241251374193

Value

An object of class haz2tsPGAM, that is a list with the following elements:

• optimal_model A list with :

  • alpha The vector of estimated P-splines coefficients of length $c_u + c_s$.

  • SE_alpha The vector of estimated standard errors of the alpha coefficients, of dimension $c_u + c_s$.

  • beta (if covariates) The vector of length $p$ of estimated covariates coefficients.

  • se_beta The vector of length $p$ of estimated Standard Errors for the beta coefficients.

  • eta0 (if covariates) The vector of values of the baseline linear predictor (log-hazard).

  • eta (if covariates) The vector of values of the baseline linear predictor (log-hazard) of length $n_u * n_s$.

  • H The hat-matrix.

  • deviance The deviance.

  • ed The (total) effective dimension of the model.

  • aic The value of the AIC.

  • bic The value of the BIC.

  • Bbases a list with the B-spline bases Bu and Bs

• optimal_logrho A vector with the optimal values of $\log_{10}(\rho_u)$ and $\log_{10}(\rho_s)$.

• P_optimal The optimal penalty matrix P.

• EDu The effective dimensions along the u axis.

• EDs The effective dimensions along the s axis.

• AIC (if par_gridsearch$return_aic == TRUE) The matrix of AIC values.

• BIC (if par_gridsearch$return_bic == TRUE) The matrix of BIC values.

Examples

# Create some fake data - the bare minimum
id <- 1:20
u <- c(
  5.43, 3.25, 8.15, 5.53, 7.28, 6.61, 5.91, 4.94, 4.25, 3.86, 4.05, 6.86,
  4.94, 4.46, 2.14, 7.56, 5.55, 7.60, 6.46, 4.96
)
s <- c(
  0.44, 4.89, 0.92, 1.81, 2.02, 1.55, 3.16, 6.36, 0.66, 2.02, 1.22, 3.96,
  7.07, 2.91, 3.38, 2.36, 1.74, 0.06, 5.76, 3.00
)
ev <- c(1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1) #'

fakedata <- as.data.frame(cbind(id, u, s, ev))
fakedata2ts <- prepare_data(
  data = fakedata,
  u = "u",
  s_out = "s",
  ev = "ev",
  ds = .5
)
# Fit a fake model - not optimal smoothing
fitpgam(fakedata2ts,
  optim_method = "grid_search",
  lrho = list(seq(1, 1.5, .5), seq(1, 1.5, .5))
)

Description

fitvcm() fits a varying coefficient model over two time scales with P-splines. The model is described in Carollo et al. (2025).

Usage

fitvcm(
  data2ts = NULL,
  Y = NULL,
  R = NULL,
  Z = NULL,
  bins = NULL,
  Bbases_spec = list(),
  pord = 2,
  kappa = 1e-10,
  lsmpar = c(0, 0),
  control_algorithm = list()
)

Arguments

Value

An object of class haz2tsVCM, that is a list with the following elements:

• optimal_model A list with :

  • Alpha The matrix of estimated P-splines coefficients of dimension $c_s$ by 2.

  • Cov_alpha The variance-covariance matrix of the Alpha coefficients, of dimension $c_uc_s$ by $c_uc_s$.

  • Eta The matrix of values of the baseline linear predictor (log-hazard) of dimension $n_u$ by $n_s$.

  • H The hat-matrix.

  • deviance The deviance.

  • ed The effective dimension of the model.

  • aic The value of the AIC.

  • bic The value of the BIC.

  • Bbases a list with the B-spline bases Bu and Bs

• optimal_logsmpar A vector with the optimal values of $\log_{10}(\theta)$ and $\log_{10}(\phi)$.

• P_optimal The optimal penalty matrix P.

• AIC (if par_gridsearch$return_aic == TRUE) The matrix of AIC values.

• BIC (if par_gridsearch$return_bic == TRUE) The matrix of BIC values.

@references Carollo, A., Putter, H., Eilers, P. H. C., & Gampe, J. (2025). Analysis of Time-to-Event Data With Two Time Scales. An Application to Transitions out of Cohabitation. Sociological Methods & Research, 0(0). doi:10.1177/00491241251374193

Examples

# Create some fake data - the bare minimum
id <- 1:20
u <- c(
  5.43, 3.25, 8.15, 5.53, 7.28, 6.61, 5.91, 4.94, 4.25, 3.86, 4.05, 6.86,
  4.94, 4.46, 2.14, 7.56, 5.55, 7.60, 6.46, 4.96
)
s <- c(
  0.44, 4.89, 0.92, 1.81, 2.02, 1.55, 3.16, 6.36, 0.66, 2.02, 1.22, 3.96,
  7.07, 2.91, 3.38, 2.36, 1.74, 0.06, 5.76, 3.00
)
ev <- c(1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1) #'

fakedata <- as.data.frame(cbind(id, u, s, ev))
fakedata2ts <- prepare_data(
  data = fakedata,
  u = "u",
  s_out = "s",
  ev = "ev",
  ds = .5
)
# Fit a fake model - not optimal smoothing
fitvcm(fakedata2ts)

Description

get_hazard_1d() takes as input the results of a model estimated by fit1ts() and it returns the estimated values of the smooth log-hazard and the smooth hazard together with their standard errors.

If the model includes covariates, then only the baseline (log-)hazard is returned. It is possible to provide values that define a new grid for evaluation of the estimated hazard. If not specified, the hazard is evaluated on the same grid used for the binning of the data, and therefore the estimation of the model. The function will check if the parameters for the new grid provided by the user are compatible with those originally used to construct the B-splines for estimating the model. If not, the grid will be adjusted accordingly and a warning will be returned.

Usage

get_hazard_1d(fitted_model, plot_grid = NULL)

Arguments

Value

A list with the following elements:

• new_plot_grid A list of parameters that specify the new grid, of the form list("ints", "smin", "smax", "ds")

• hazard A vector containing the estimated hazard values.

• loghazard A vector containing the estimated log-hazard values.

• log10hazard A vector containing the estimated log10-hazard values.

• SE_hazard A vector containing the estimated SEs for the hazard.

• SE_loghazard A vector containing the estimated SEs for the log-hazard.

• SE_log10hazard A vector containing the estimated SEs for the log10-hazard.

Examples

## preparing data - no covariates
dt1ts <- prepare_data(
  data = reccolon2ts,
  s_in = "entrys",
  s_out = "timesr",
  events = "status",
  ds = 180
)

## fitting the model with fit1ts() - default options

mod1 <- fit1ts(dt1ts)
# Obtain 1d hazard
get_hazard_1d(mod1)
# Change grid
get_hazard_1d(mod1,
  plot_grid = c(smin = 0, smax = 2730, ds = 30)
)

Description

get_hazard_1d_LMM() takes as input the results of a model estimated by fit1ts() and it returns the estimated values of the smooth log-hazard and the smooth hazard together with their standard errors. This function is specific for objects of class "haz1tsLMM".

If the model includes covariates, then only the baseline (log-)hazard is returned. It is possible to provide values that define a new grid for evaluation of the estimated hazard. If not specified, the hazard is evaluated on the same grid used for the binning of the data, and therefore the estimation of the model. The function will check if the parameters for the new grid provided by the user are compatible with those originally used to construct the B-splines for estimating the model. If not, the grid will be adjusted accordingly and a warning will be returned.

Usage

get_hazard_1d_LMM(fitted_model, plot_grid = NULL)

Arguments

Value

A list with the following elements:

• new_plot_grid A list of parameters that specify the new grid, of the form list("ints", "smin", "smax", "ds")

• hazard A vector containing the estimated hazard values.

• loghazard A vector containing the estimated log-hazard values.

• log10hazard A vector containing the estimated log10-hazard values.

• SE_hazard A vector containing the estimated SEs for the hazard.

• SE_loghazard A vector containing the estimated SEs for the log-hazard.

• SE_log10hazard A vector containing the estimated SEs for the log10-hazard.

Examples

## preparing data - no covariates
dt1ts <- prepare_data(
  data = reccolon2ts,
  s_in = "entrys",
  s_out = "timesr",
  events = "status",
  ds = 180
)

## fitting the model with fit1ts()

mod1 <- fit1ts(dt1ts,
  optim_method = "LMMsolver"
)
# Obtain 1d hazard
get_hazard_1d_LMM(mod1)
# Change grid
get_hazard_1d_LMM(mod1,
  plot_grid = c(smin = 0, smax = 2730, ds = 30)
)

Description

get_hazard_2d() takes as input the results of a model estimated by fit2ts(), fitpgam() or fitvcm() and it returns the estimated smooth log-hazard and the smooth hazard together with their standard errors.

It is possible to provide values that define a new grid for evaluation of the estimated hazard. If not specified, the hazard is evaluated on the same grid used for the binning of the data, and therefore the estimation of the model. The function will check if the parameters for the new grid provided by the user are compatible with those originally used to construct the B-splines for estimating the model. If not, the grid will be adjusted accordingly and a warning will be returned.

Usage

get_hazard_2d(
  fitted_model,
  plot_grid = NULL,
  where_slices = NULL,
  direction = c(NULL, "u", "s"),
  tmax = NULL,
  midpoints = FALSE
)

Arguments

Value

A list with the following elements:

• new_plot_grid A list of parameters that specify the new grid, of the form list("intu", "umin", "umax", "du", "ints", "smin", "smax", "ds")

• nBu The B-spline basis for u, evaluated over the new grid.

• nBs The B-spline basis for s, evaluated over the new grid.

• hazard A matrix containing the estimated hazard values.

• loghazard A matrix containing the estimated log-hazard values.

• log10hazardA matrix containing the estimated log10-hazard values.

• SE_hazard A matrix containing the estimated SEs for the hazard.

• SE_loghazard A matrix containing the estimated SEs for the log-hazard.

• SE_log10haz A matrix containing the estimated SEs for the log10-hazard.

Examples

# Create some fake data - the bare minimum
id <- 1:20
u <- c(
  5.43, 3.25, 8.15, 5.53, 7.28, 6.61, 5.91, 4.94, 4.25, 3.86, 4.05, 6.86,
  4.94, 4.46, 2.14, 7.56, 5.55, 7.60, 6.46, 4.96
)
s <- c(
  0.44, 4.89, 0.92, 1.81, 2.02, 1.55, 3.16, 6.36, 0.66, 2.02, 1.22, 3.96,
  7.07, 2.91, 3.38, 2.36, 1.74, 0.06, 5.76, 3.00
)
ev <- c(1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1) #'

fakedata <- as.data.frame(cbind(id, u, s, ev))
fakedata2ts <- prepare_data(
  data = fakedata,
  u = "u",
  s_out = "s",
  ev = "ev",
  ds = .5
)
# Fit a fake model - not optimal smoothing
fakemod <- fit2ts(fakedata2ts,
  optim_method = "grid_search",
  lrho = list(
    seq(1, 1.5, .5),
    seq(1, 1.5, .5)
  )
)
# Obtain 2d hazard
get_hazard_2d(fakemod)

get_hazard_2d(fakemod,
  plot_grid = list(
    c(umin = 3, umax = 8.5, du = .1),
    c(smin = 0, smax = 7.1, ds = .1)
  )
)

Description

get_hazard_2d_LMM() takes as input an object of class 'haz2tsLMM' and it returns the estimated smooth log-hazard, the log10-hazard and the hazard surface together with their standard errors.

It is possible to provide values that define a new grid for evaluation of the estimated hazard. If not specified, the hazard is evaluated on the same grid used for the binning of the data, and therefore the estimation of the model. The function will check if the parameters for the new grid provided by the user are compatible with those originally used to construct the B-splines for estimating the model. If not, the grid will be adjusted accordingly and a warning will be returned.

Usage

get_hazard_2d_LMM(
  fitted_model,
  plot_grid = NULL,
  where_slices = NULL,
  direction = c("u", "s", NULL),
  tmax = NULL
)

Arguments

Value

A list with the following elements:

• new_plot_grid A list of parameters that specify the new grid, of the form list("intu", "umin", "umax", "du", "ints", "smin", "smax", "ds")

• hazard A matrix containing the estimated hazard values.

• loghazard A matrix containing the estimated log-hazard values.

• log10hazardA matrix containing the estimated log10-hazard values.

• SE_hazard A matrix containing the estimated SEs for the hazard.

• SE_loghazard A matrix containing the estimated SEs for the log-hazard.

• SE_log10haz A matrix containing the estimated SEs for the log10-hazard.

Examples

# Create some fake data - the bare minimum
id <- 1:20
u <- c(
  5.43, 3.25, 8.15, 5.53, 7.28, 6.61, 5.91, 4.94, 4.25, 3.86, 4.05, 6.86,
  4.94, 4.46, 2.14, 7.56, 5.55, 7.60, 6.46, 4.96
)
s <- c(
  0.44, 4.89, 0.92, 1.81, 2.02, 1.55, 3.16, 6.36, 0.66, 2.02, 1.22, 3.96,
  7.07, 2.91, 3.38, 2.36, 1.74, 0.06, 5.76, 3.00
)
ev <- c(1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1) #'

fakedata <- as.data.frame(cbind(id, u, s, ev))
fakedata2ts <- prepare_data(data = fakedata,
                            u = "u",
                            s_out = "s",
                            ev = "ev",
                            ds = .5)
# Fit a fake model - not optimal smoothing
fakemod <- fit2ts(fakedata2ts,
  optim_method = "LMMsolver"
)

# Get hazard
get_hazard_2d_LMM(fakemod)

# Use a finer grid of points
get_hazard_2d_LMM(fakemod,
                 plot_grid = list(c(umin = 3, umax = 8.5, du = .1),
                                  c(smin = 0, smax = 7.1, ds = .1)))

Description

get_hr() takes as input the results of a model with covariates estimated by fit2ts() or fit1ts() and returns the estimated hazard ratios together with their standard errors.

Usage

get_hr(fitted_model)

Arguments

Value

A list with the following elements:

• HR A vector of hazard ratios (calculated as $\exp(\hat\beta)$).

• SE_HR A vector of Standard Errors for the hazard ratios calculated via the delta method.

• beta A vector of the estimated $\hat\beta$ coefficients.

• SE_beta A vector of the Standard Errors for the beta coefficients.

Examples

# Create some fake data - the bare minimum
id <- 1:20
u <- c(5.43, 3.25, 8.15, 5.53, 7.28, 6.61, 5.91, 4.94, 4.25, 3.86, 4.05, 6.86,
       4.94, 4.46, 2.14, 7.56, 5.55, 7.60, 6.46, 4.96)
s <- c(0.44, 4.89, 0.92, 1.81, 2.02, 1.55, 3.16, 6.36, 0.66, 2.02, 1.22, 3.96,
       7.07, 2.91, 3.38, 2.36, 1.74, 0.06, 5.76, 3.00)
ev <- c(1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1)
x1 <- c(0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0)

fakedata <- as.data.frame(cbind(id, u, s, ev, x1))
fakedata2ts <- prepare_data(data = fakedata,
                            u = "u",
                            s_out = "s",
                            ev = "ev",
                            ds = .5,
                            individual = TRUE,
                            covs = "x1")
# Fit a fake model - not optimal smoothing
fakemod <- fit2ts(fakedata2ts,
                  optim_method = "grid_search",
                  lrho = list(seq(1, 1.5, .5),
                              seq(1, 1.5, .5)))
get_hr(fakemod)

Description

Summary function for object of class 'haz2ts'

Usage

haz2ts_summary(x, ...)

Arguments

Value

a printed summary of the fitted model

Examples

# Create some fake data - the bare minimum
id <- 1:20
u <- c(5.43, 3.25, 8.15, 5.53, 7.28, 6.61, 5.91, 4.94, 4.25, 3.86, 4.05, 6.86,
       4.94, 4.46, 2.14, 7.56, 5.55, 7.60, 6.46, 4.96)
s <- c(0.44, 4.89, 0.92, 1.81, 2.02, 1.55, 3.16, 6.36, 0.66, 2.02, 1.22, 3.96,
       7.07, 2.91, 3.38, 2.36, 1.74, 0.06, 5.76, 3.00)
ev <- c(1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1)#'

fakedata <- as.data.frame(cbind(id, u, s, ev))
fakedata2ts <- prepare_data(data = fakedata,
                            u = "u",
                            s_out = "s",
                            ev = "ev",
                            ds = .5)
# Fit a fake model - not optimal smoothing
fakemod <- fit2ts(fakedata2ts,
                  optim_method = "grid_search",
                  lrho = list(seq(1, 1.5, .5),
                              seq(1, 1.5, .5)))
summary(fakemod)

Description

Summary function for object of class 'haz2tsLMM'

Usage

haz2tsLMM_summary(x, ...)

Arguments

Value

a printed summary of the fitted model, including optimal smoothing paramters, the effective dimension ED and the AIC/BIC. For model with covariates, a regression table is also returned.

Examples

# Create some fake data - the bare minimum
id <- 1:20
u <- c(
  5.43, 3.25, 8.15, 5.53, 7.28, 6.61, 5.91, 4.94, 4.25, 3.86, 4.05, 6.86,
  4.94, 4.46, 2.14, 7.56, 5.55, 7.60, 6.46, 4.96
)
s <- c(
  0.44, 4.89, 0.92, 1.81, 2.02, 1.55, 3.16, 6.36, 0.66, 2.02, 1.22, 3.96,
  7.07, 2.91, 3.38, 2.36, 1.74, 0.06, 5.76, 3.00
)
ev <- c(1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1) #'

fakedata <- as.data.frame(cbind(id, u, s, ev))
fakedata2ts <- prepare_data(data = fakedata,
                            u = "u",
                            s_out = "s",
                            ev = "ev",
                            ds = .5)
# Fit a fake model - not optimal smoothing
fakemod <- fit2ts(fakedata2ts,
  optim_method = "LMMsolver"
)
summary(fakemod)

Description

Summary function for object of class 'haz2tsPGAM'

Usage

haz2tsPGAM_summary(x, ...)

Arguments

Value

a printed summary of the fitted model

Examples

# Create some fake data - the bare minimum
id <- 1:20
u <- c(5.43, 3.25, 8.15, 5.53, 7.28, 6.61, 5.91, 4.94, 4.25, 3.86, 4.05, 6.86,
       4.94, 4.46, 2.14, 7.56, 5.55, 7.60, 6.46, 4.96)
s <- c(0.44, 4.89, 0.92, 1.81, 2.02, 1.55, 3.16, 6.36, 0.66, 2.02, 1.22, 3.96,
       7.07, 2.91, 3.38, 2.36, 1.74, 0.06, 5.76, 3.00)
ev <- c(1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1)#'

fakedata <- as.data.frame(cbind(id, u, s, ev))
fakedata2ts <- prepare_data(data = fakedata,
                            u = "u",
                            s_out = "s",
                            ev = "ev",
                            ds = .5)
# Fit a fake model - not optimal smoothing
fakemod <- fitpgam(fakedata2ts,
                  optim_method = "grid_search",
                  lrho = list(seq(1, 1.5, .5),
                              seq(1, 1.5, .5)))
summary(fakemod)

Description

Summary function for object of class 'haz2tsVCM'

Usage

haz2tsVCM_summary(x, ...)

Arguments

Value

a printed summary of the fitted model

Examples

# Create some fake data - the bare minimum
id <- 1:20
u <- c(5.43, 3.25, 8.15, 5.53, 7.28, 6.61, 5.91, 4.94, 4.25, 3.86, 4.05, 6.86,
       4.94, 4.46, 2.14, 7.56, 5.55, 7.60, 6.46, 4.96)
s <- c(0.44, 4.89, 0.92, 1.81, 2.02, 1.55, 3.16, 6.36, 0.66, 2.02, 1.22, 3.96,
       7.07, 2.91, 3.38, 2.36, 1.74, 0.06, 5.76, 3.00)
ev <- c(1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1)#'

fakedata <- as.data.frame(cbind(id, u, s, ev))
fakedata2ts <- prepare_data(data = fakedata,
                            u = "u",
                            s_out = "s",
                            ev = "ev",
                            ds = .5)
# Fit a fake model - not optimal smoothing
fakemod <- fitvcm(fakedata2ts)
summary(fakemod)

Description

imageplot_2ts() plots an image of the two time scales hazard (or survival or cumulative hazard) with contour lines. This is the default call implemented in plot.haz2ts and other functions.

Usage

imageplot_2ts(x, y, z, plot_options = list(), ...)

Arguments

Value

An image plot of an estimated surface.

Description

imageplot_SE() plots an image of the SEs of the two time scales hazard with contour lines.

Usage

imageplot_SE(x, y, z, plot_options = list(), ...)

Arguments

Value

An image plot of the SEs for the (log-) hazard surface.

Description

make_bins() constructs the bins over the time axes and saves the extremes of the bins in a vector.

Usage

make_bins(
  t_in = NULL,
  t_out = NULL,
  u = NULL,
  s_in = NULL,
  s_out,
  min_t = NULL,
  max_t = NULL,
  min_u = NULL,
  max_u = NULL,
  min_s = NULL,
  max_s = NULL,
  dt = NULL,
  du = NULL,
  ds
)

Arguments

Details

It allows construction of bins over the time scales t and s and/or over the fixed-time axis u. The time scale s is always required. See also prepare_data() to conveniently prepare individual data for the analysis with one, or two time scales.

A few words about constructing the grid of bins. There is no 'golden rule' or optimal strategy for setting the number of bins over each time axis, or deciding on the bins' width. It very much depends on the data structure, however, we try to give some directions here. First, in most cases, more bins is better than less bins. A good number is about 30 bins. However, if data are scarce, the user might want to find a compromise between having a larger number of bins, and having many bins empty. Second, the chosen width of the bins (that is du and ds) does depend on the time unit over which the time scales are measured. For example, if the time is recorded in days, as in the example below, and several years of follow-up are available, the user can split the data in bins of width 30 (corresponding to about one month), 60 (about two months), 90 (about three months), etc. If the time scale is measured in years, then appropriate width could be 0.25 (corresponding to a quarter of a year), or 0.5 (that is half year). However, in some cases, time might be measure in completed years, as is often the case for age. In this scenario, an appropriate bin width is 1.

Finally, it is always a good idea to plot your data first, and explore the range of values over which the time scale(s) are recorded. This will give insight about reasonable values for the arguments min_s, min_u, max_s and max_u (that in any case are optional).

Value

A list with the following elements:

• bins_t if t_out is provided, this is a vector of bins extremes for the time scale t

• midt if t_out is provided, this is a vector with the midpoints of the bins over t

• nt if t_out is provided, this is the number of bins over t

• bins_u if u is provided, this is a vector of bins extremes for u axis

• midu if u is provided, this is a vector with the midpoints of the bins over u

• nu if u is provided, this is the number of bins over u

• bins_s is a vector of bins extremes for the time scale s

• mids is a vector with the midpoints of the bins over s

• ns is the number of bins over s

Examples

# Make bins for colon cancer data by time at randomization and time since recurrence
bins <- make_bins(u = reccolon2ts$timer, s_out = reccolon2ts$timesr,
                 du = 30, ds = 30)
# Make bins for colon cancer data only over time since recurrence
bins <- make_bins(s_out = reccolon2ts$timesr, ds = 60)

Description

Make a grid of points to evaluate B-splines

Usage

make_grid(
  plot_grid,
  model_specifications,
  class_fitmodel,
  where_slices = NULL,
  direction = c(NULL, "u", "s"),
  tmax = NULL,
  midpoints = FALSE
)

Arguments

Value

A list of specification for the grid

Examples

make_grid(plot_grid = list(
    c(umin = 3, umax = 8.5, du = .1),
    c(smin = 0, smax = 7.1, ds = .1)
  ),
  model_specification = list(umin = 2, umax = 8.5, smin = 0, smax = 7.5),
  class_fitmodel = "haz2ts")

Description

plot_slices() plots slices of the (log-)hazard with two time scales, at selected values of one of the two time dimensions.

Usage

plot_slices(x, y, direction, plot_options = list())

Arguments

Value

A plot of the slices of the hazard cut at selected points.

Description

plot.haz1ts() is a plot method for objects of class haz1ts.

Usage

## S3 method for class 'haz1ts'
plot(
  x,
  which_plot = c("hazard", "covariates"),
  plot_grid = NULL,
  plot_options = list(),
  ...
)

Arguments

Value

A plot of the type required.

Examples

## preparing data - no covariates
dt1ts <- prepare_data(
  data = reccolon2ts,
  s_in = "entrys",
  s_out = "timesr",
  events = "status",
  ds = 180
)

## fitting the model with fit1ts() - default options

mod1 <- fit1ts(dt1ts)

plot(mod1)

Description

plot.haz1tsLMM() is a plot method for objects of class haz1tsLMM.

Usage

## S3 method for class 'haz1tsLMM'
plot(
  x,
  which_plot = c("hazard", "covariates"),
  plot_grid = NULL,
  plot_options = list(),
  ...
)

Arguments

Details

The function obtainSmoothTrend from the R-package LMMsolver is used here. We refer the interested readers to https://biometris.github.io/LMMsolver/ for more details on LMMsolver and its usage.

Value

A plot of the type required.

Examples

## preparing data - no covariates
dt1ts <- prepare_data(data = reccolon2ts,
                      s_in = "entrys",
                      s_out = "timesr",
                      events = "status",
                      ds = 180)

## fitting the model with fit1ts() - default options

mod1 <- fit1ts(dt1ts,
optim_method = "LMMsolver")
plot(mod1)

Description

plot.haz2ts() is the plot method for objects of class haz2ts. It produces several kinds of plots of the fitted model with two time scales (see fit2ts()), either in the original (t,s) plane, while respecting the constraint imposed by the relation of the two time scales, or in the transformed (u,s) plane.

Usage

## S3 method for class 'haz2ts'
plot(
  x,
  plot_grid = NULL,
  which_plot = c("hazard", "covariates", "SE", "slices", "survival", "cumhaz"),
  where_slices = NULL,
  direction = c(NULL, "u", "s"),
  plot_options = list(),
  ...
)

Arguments

Details

The vignette "visualization" presents and discusses all the different plotting options for the fitted model over two time scales. In most of the cases, the user will want to visualize the hazard surface over the two time scales. This can be plotted on the hazard scale, the log-hazard scale or the log10-hazard scale, by switching to TRUE the corresponding argument in plot_options. The survival and cumulative hazard functions can be plotted as two-dimensional surfaces over u and s or t and s. However, it is also very informative to plot them as one-dimensional curves over s (cross-sections or slices). This is done by selecting which_plot = "survival" and surv_slices = TRUE in plot_options. Additionally, a vector of values for the cutting points over the u-axis should be passed to the argument where_slices, together with setting direction = u. Similar plot is obtained for the cumulative hazard by selecting which_plot = "cumhaz", cumhaz_slices = TRUE, see examples section. Please, notice that for the survival function and the cumulative hazard, only cross-sections of the surface for selected values of u (over the s time) can be plotted.

Value

A plot of the fitted model.

Examples

# Create some fake data - the bare minimum
id <- 1:20
u <- c(
  5.43, 3.25, 8.15, 5.53, 7.28, 6.61, 5.91, 4.94, 4.25, 3.86, 4.05, 6.86,
  4.94, 4.46, 2.14, 7.56, 5.55, 7.60, 6.46, 4.96
)
s <- c(
  0.44, 4.89, 0.92, 1.81, 2.02, 1.55, 3.16, 6.36, 0.66, 2.02, 1.22, 3.96,
  7.07, 2.91, 3.38, 2.36, 1.74, 0.06, 5.76, 3.00
)
ev <- c(1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1) #'

fakedata <- as.data.frame(cbind(id, u, s, ev))
fakedata2ts <- prepare_data(
  u = fakedata$u,
  s_out = fakedata$s,
  ev = fakedata$ev,
  ds = .5
)
# Fit a fake model - not optimal smoothing
fakemod <- fit2ts(fakedata2ts,
  optim_method = "grid_search",
  lrho = list(
    seq(1, 1.5, .5),
    seq(1, 1.5, .5)
  )
)

# plot the hazard surface
plot(fakemod)

# plot the survival function as one-dimension curves over `s`
plot(fakemod,
  which_plot = "survival",
  direction = "u",
  where_slices = c(4, 6, 8),
  plot_options = list(
    surv_slices = TRUE
  )
)

# Plot cross-sections of the hazard over `s` for selected values of `u`

plot(fakemod,
  which_plot = "slices",
  where_slices = c(4, 6, 8),
  direction = "u",
  plot_options = list(
    main = "Cross-sections of the hazard",
    xlab = "Time",
    ylab = "Hazard"
  )
)

Description

plot.haz2tsLMM() is the plot method for objects of class haz2tsLMM. It produces plots of the fitted model with two time scales (see fit2ts()), fitted via LMMsolver. The two-dimensional plots are limited to the transformed plane, that is only plots over u and s axes are produced.

Usage

## S3 method for class 'haz2tsLMM'
plot(
  x,
  plot_grid = NULL,
  which_plot = c("hazard", "covariates", "SE", "slices", "survival", "cumhaz"),
  where_slices = NULL,
  direction = c(NULL, "u", "s"),
  plot_options = list(),
  ...
)

Arguments