Package 'curesurv' reference manual

Title:	Mixture and Non Mixture Parametric Cure Models to Estimate Cure Indicators
Description:	Fits a variety of cure models using excess hazard modeling methodology such as the mixture model proposed by Phillips et al. (2002) <doi:10.1002/sim.1101> The Weibull distribution is used to represent the survival function of the uncured patients; Fits also non-mixture cure model such as the time-to-null excess hazard model proposed by Boussari et al. (2020) <doi:10.1111/biom.13361>.
Authors:	Juste Goungounga [aut, cre] , Judith Breaud [aut] , Olayide Boussari [aut] , Valerie Jooste [aut]
Maintainer:	Juste Goungounga <[email protected]>
License:	GPL (>= 3)
Version:	0.1.1
Built:	2024-11-17 05:11:26 UTC
Source:	https://github.com/cran/curesurv

Akaike's An Information Criterion for cure models

Description

Calculates the Akaike's "An Information Criterion" for fitted models from curesurv

Usage

## S3 method for class 'curesurv'
AIC(object, ..., k = 2)
## S3 method for class 'curesurv'
AIC(object, ..., k = 2)

Arguments

`object`	a fitted model object obtained from `curesurv`
`...`	optionally more fitted model objects obtained from `curesurv`.
`k`	numeric, the penalty per parameter to be used; the default k = 2 is the classical AIC.

Details

When comparing models fitted by maximum likelihood to the same data, the smaller the AIC, the better the fit.

However in our case, one should be careful when comparing the AIC. Specifically, when one implements a mixture cure model with curesurv without correcting the rate table (pophaz.alpha=FALSE), one is not obligated to specify cumpophaz. However, you cannot compare a model where cumpophaz is not specified with a model where cumpophaz is specified. If one wants to compare different models using AIC, one should always specify cumpophaz when using the curesurv function.

Value

the value corresponds to the AIC calculated from the log-likelihood of the fitted model if just one object is provided. If multiple objects are provided, a data.frame with columns corresponding to the objects and row representing the AIC

Examples



library("curesurv")
library("survival")

 testiscancer$age_crmin <- (testiscancer$age- min(testiscancer$age)) /
              sd(testiscancer$age)

fit_m1_ad_tneh <- curesurv(Surv(time_obs, event) ~ z_tau(age_crmin) +
                          z_alpha(age_crmin),
                          pophaz = "ehazard",
                          cumpophaz = "cumehazard",
                          model = "nmixture", dist = "tneh",
                          link_tau = "linear",
                          data = testiscancer,
                          method_opt = "L-BFGS-B")

 AIC(fit_m1_ad_tneh)

 
library("curesurv")
library("survival")

 testiscancer$age_crmin <- (testiscancer$age- min(testiscancer$age)) /
              sd(testiscancer$age)

fit_m1_ad_tneh <- curesurv(Surv(time_obs, event) ~ z_tau(age_crmin) +
                          z_alpha(age_crmin),
                          pophaz = "ehazard",
                          cumpophaz = "cumehazard",
                          model = "nmixture", dist = "tneh",
                          link_tau = "linear",
                          data = testiscancer,
                          method_opt = "L-BFGS-B")

 AIC(fit_m1_ad_tneh)

anova.curesurv function for likelihood-ratio test of two nested models from curesurv function

Description

This function computes an analysis of deviance table for two excess hazard models fitted using the curesurv R package.

Usage

## S3 method for class 'curesurv'
anova(object, ..., test = "LRT")
## S3 method for class 'curesurv'
anova(object, ..., test = "LRT")

Arguments

`object`	An object of class curesurv.
`...`	Additional object of class curesurv.
`test`	A character string. Computes the likelihood-ratio test for value `"LRT"`. In case the two models are the same, but one with the correction of mortality tables and one without, the likelihood ratio test is computed for value `"LRT_alpha"` These are the only tests available for now.

Value

An object of class anova inheriting from class matrix. The different columns contain respectively the degrees of freedom and the log-likelihood values of the two nested models, the degree of freedom of the chi-square statistic, the chi-square statistic, and the p-value of the likelihood ratio test.

Note

The comparison between two or more models by anova or more excess hazard models will only be valid if they are fitted to the same dataset, and if the compared models are nested. This may be a problem if there are missing values.

Examples


library("curesurv")
library("survival")

testiscancer$age_crmin <- (testiscancer$age - min(testiscancer$age)) / sd(testiscancer$age)

fit_m0 <- curesurv(Surv(time_obs, event) ~ 1 | 1,
                          pophaz = "ehazard",
                          cumpophaz = "cumehazard",
                          model = "nmixture", dist = "tneh",
                          link_tau = "linear",
                          data = testiscancer,
                          method_opt = "L-BFGS-B")

fit_m1 <- curesurv(Surv(time_obs, event) ~ age_crmin | 1,
                          pophaz = "ehazard",
                          cumpophaz = "cumehazard",
                          model = "nmixture", dist = "tneh",
                          link_tau = "linear",
                          data = testiscancer,
                          method_opt = "L-BFGS-B")

anova(fit_m0, fit_m1)


library("curesurv")
library("survival")

testiscancer$age_crmin <- (testiscancer$age - min(testiscancer$age)) / sd(testiscancer$age)

fit_m0 <- curesurv(Surv(time_obs, event) ~ 1 | 1,
                          pophaz = "ehazard",
                          cumpophaz = "cumehazard",
                          model = "nmixture", dist = "tneh",
                          link_tau = "linear",
                          data = testiscancer,
                          method_opt = "L-BFGS-B")

fit_m1 <- curesurv(Surv(time_obs, event) ~ age_crmin | 1,
                          pophaz = "ehazard",
                          cumpophaz = "cumehazard",
                          model = "nmixture", dist = "tneh",
                          link_tau = "linear",
                          data = testiscancer,
                          method_opt = "L-BFGS-B")

anova(fit_m0, fit_m1)

cumLexc_mul function

Description

returns the cumulative excess hazard for an TNEH model in case of parametrization of log the of the time to null excess hazard as function to fit the data

Usage

cumLexc_mul(z_tau, z_alpha, x, theta)
cumLexc_mul(z_tau, z_alpha, x, theta)

Arguments

`z_tau`	covariates depending on tau
`z_alpha`	covariates depending on alpha
`x`	time value
`theta`	of the coefficient of tneh parameters

Value

An object of class numeric containing the cumulative excess hazard with the same length as the time.

Fitting cure models using curesurv

Description

Fits the non-mixture cure model proposed by Boussari et al. (2020), or mixture cure model such as proposed by De Angelis et al. (1999) with the possibility to correct the background mortality as proposed by Phillips et al. (2002) in the net survival framework.

Non-mixture cure model

The Boussari model

This model allows for direct estimation of time-to-null-excess-hazard which can be interpreted as time-to-cure. The parametrization offers various link functions for the covariates effects on the time-to-null-excess-hazard: τ(z_k) = g(τ₀ + z_k τ_k). If link_tau=linear, then g is the identity function. If link_tau=loglinear then g is the exponential function. In this model, the cure proportion is expressed as: π(z;θ) = exp(−g(τ₀ + z_k τ_k) \text{Beta}((\alpha_{0} + Z_{k} \alpha_{k}), \beta)).

Mixture cure model

The user can choose the survival function modeling the uncured patients net survival among Weibull (default) and exponentiated Weibull. The parametrization for weibull distribution is S_u(t) = exp(−λt^γ)^exp(δZ). The related hazard function is expressed as: λ_u(t) = γλt^{γ− 1} exp(δz) The net survival and the excess hazard functions can be respectively expressed as S_E(t) = π(z;β) + (1 − π(z;β)) * S_u(t). and λ_E(t)=[((1−π(z;β))fu(t))/(π(z;β) + (1 − π(z;β))S_u(t))], with π(z;β) = [1/((1 + exp(−[β₀ + Zβ])))].

Correction of background mortality

Usually, in the net survival framework the expected hazard is directly obtained from life tables. However some patients in cancer registries can have some factors impacting their expected mortality rates (such as comorbidities, deprivation) that are not always accounted #' for in the available life tables, and there is a need to account for this problem. The correction proposed by Phillips et al (2002) assumes that λ_exp(t,z)=αλ_pop(t,z_k) with λ_exp(t,z) the patient expected hazard and λ_pop(t,z_k) the population hazard obtained from life table.

Usage

curesurv(
  formula,
  data,
  pophaz = NULL,
  cumpophaz = NULL,
  pophaz.alpha = FALSE,
  model = "nmixture",
  dist = "weib",
  link_tau = "linear",
  ncoor_des = NULL,
  init = NULL,
  maxit_opt = 10000,
  gradient = FALSE,
  hessian_varcov = TRUE,
  optim_func = "optim",
  optimizer = "optim",
  method_opt = "L-BFGS-B",
  trace = 0,
  nvalues = 10,
  iter_eps = 1e-08,
  optim_fixed = NULL,
  clustertype = NULL,
  nproc = 1,
  subset,
  na.action,
  sign_delta,
  ...
)
curesurv(
  formula,
  data,
  pophaz = NULL,
  cumpophaz = NULL,
  pophaz.alpha = FALSE,
  model = "nmixture",
  dist = "weib",
  link_tau = "linear",
  ncoor_des = NULL,
  init = NULL,
  maxit_opt = 10000,
  gradient = FALSE,
  hessian_varcov = TRUE,
  optim_func = "optim",
  optimizer = "optim",
  method_opt = "L-BFGS-B",
  trace = 0,
  nvalues = 10,
  iter_eps = 1e-08,
  optim_fixed = NULL,
  clustertype = NULL,
  nproc = 1,
  subset,
  na.action,
  sign_delta,
  ...
)

Arguments

`formula`	a formula object of the `Surv` function with the response on the left of a `~` operator and the terms on the right. The response must be a survival object as returned by the `Surv` function (`time` in first and `status` in second).
`data`	a data frame in which to interpret the variables named in the formula
`pophaz`	corresponds to the name of the column in the data representing the values of the population instantaneous mortality rates. If the `pophaz` argument is not specified, overall survival is fitted.
`cumpophaz`	corresponds to the name of the column in the data representing the values of the instantaneous population cumulative mortality rates. If not specified, the model cannot be compared with model with `pophaz.alpha = TRUE` using AIC.
`pophaz.alpha`	to be specified if user want an excess hazard model with correction of mortality rates by a scale parameter
`model`	To fit a mixture model, specify `model = "mixture"`. To fit Time-To-Null Excess Hazard model the argument is `model = "tneh"`.
`dist`	For mixture model, it corresponds to the function used to fit the uncured patients survival. By default, `("weib")` is used. Another option is the exponentiated Weibull function `("eweib")`. For non-mixture models, this argument corresponds to the name of the model. By default, `("tneh")` is used to fit the time to null excess hazard model proposed by Boussari et al..
`link_tau`	must be specified only for `model ="tneh"`. Default is linear link `("linear")`. Another link is loglinear `("loglinear")`.
`ncoor_des`	if null, the initial parameters are defaults. If else, the initials parameters are obtained via coordinates descent algorithms
`init`	a list containing the vector of initial values `theta_init`, the vector of upper bounds `theta_upper` and the vector of the lower bounds `theta_lower` for the parameters to estimate. For each elements of the list, give the name of the covariate followed by the vector of the fixed initials values
`maxit_opt`	option for maximum of iteration in optimization function
`gradient`	True if optimization process requires gradient to be provided
`hessian_varcov`	TRUE if user wants variance covariance matrix using hessian function
`optim_func`	specify which function to be used for optimization purposes.
`optimizer`	only use this argument when `optim_func="bbmle"`
`method_opt`	optimization method used in `optim` function. The default algorithm is "L-BFGS-B".
`trace`	Non-negative integer corresponding to the `trace` argument as in `optim`
`nvalues`	number of set of initial values when using multiple initials values
`iter_eps`	this parameter only works when `ncoor_des = "iter"`; It allows to run coordinates descent algorithm until the stooping criteria equal at least to the specified value.
`optim_fixed`	to specify with parameter to not estimated in the estimation process
`clustertype`	related to cluster type in `marqLevAlg` package
`nproc`	number of processors for parallel computing as in `marqLevAlg`
`subset`	an expression indicating which subset of the data should be used in the modeling. All observations are included by default
`na.action`	as in the coxph function, a missing-data filter function.
`sign_delta`	only used for mixture cure rate models to specify if the effects or minus the effects of covariates acting on uncured survival to be considered. Default will be sign_delta = "1". The alternative is sign_delta = "-1".
`...`	additional parameters such `z_alpha`, and `z_tau`. For more details, use the help function.

Value

An object of class curesurv. This object is a list containing the following components:

`iter_coords`	number of iterations performed to obtain initial values of the parameters in tneh model only
`coefficients`	estimates found for the model
`estimates`	estimates in the appropriate scale for the model
`loglik`	corresponds to the log-likelihood computed; if only the pophaz is provided, the log-likelihood doesn't correspond to the total log-likelihood. The part of the cumulative population hazard is a constant and is dropped for the computation as presented in Esteve et al. (1990); The total log-likekihood is calculed if the user specifies a column name equal expected cumulative mortality (cumpophaz)
`iteractions`	the number iterations attained to estimate the parameters of the related model
`evaluations`	the number of times the log-likelihood function was evaluated until to reach the convergence
`convergence`	an integer code as in optim when `L-BFGS-B` method is used in optim.
`message`	a character string returned by the optimizer
`varcov`	the variance covariance matrix of the parameters estimated
`varcov_star`	the variance covariance matrix of the coefficients of the model of interest
`std_err`	the standard errors of the estimated parameters
`std_err_star`	the standard errors of the coefficients of the model of interest
`AIC`	the Akaike information criteria from the model of interest
`n.events`	the number of events in the dataset. Events are considered
`n.obs`	the number of observations in the dataset.
`model`	if fitted model is a mixture model, it returns "mixture". If fitted model is Time-To-Null Excess Hazard model, it returns "nmixture".
`Terms`	the representation of the terms in the model
`pophaz.alpha`	logical value to indicate if fitted cure model requires correction of mortality rates by a scale parameter
`pophaz`	corresponds to the the population instantaneous mortality rates.
`cumpophaz`	corresponds to the population cumulative mortality rates.
`frailtyhp`	a booleen to be specified if a frailty correction is needed for the population hazard.
`dist`	For mixture model, it corresponds to the function used to fit the uncured patients survival. By default, ("weib") is used. Another option is the exponentiated Weibull function ("eweib"). For non-mixture models, this argument corresponds to the name of the model. By default, ("tneh") is used to fit the time to null excess hazard model proposed by Boussari et al.
`xmax`	maximum follow-up time to evaluate the TTC
`z_tau`	Covariates acting on parameter tau in non mixture cure model tneh
`link_tau`	returned only for model ="tneh"; returned by default is "linear" or "loglinear" for linear or loglinear link function of covariates acting on tau parameter.
`z_alpha`	Covariates acting on parameter alpha in non mixture cure model tneh
`z_c`	Covariates acting on cure fraction in mixture cure model
`z_ucured`	covariates acting on survival of uncured in mixture cure model
`z_pcured`	Covariates acting on cure fraction in mixture cure model
`z_ucured`	covariates acting on survival of uncured in mixture cure model
`data`	the dataset used to run the model
`call`	the function call based on model
`formula`	the formula as a formula object

Note

Note that all these models can be fitted in the overall survival setting.

time is OBLIGATORY in years

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Valerie Jooste

References

Boussari O, Bordes L, Romain G, Colonna M, Bossard N, Remontet L, Jooste V. Modeling excess hazard with time-to-cure as a parameter. Biometrics. 2021 Dec;77(4):1289-1302. doi: 10.1111/biom.13361. Epub 2020 Sep 12. PMID: 32869288. (pubmed)

Boussari O, Romain G, Remontet L, Bossard N, Mounier M, Bouvier AM, Binquet C, Colonna M, Jooste V. A new approach to estimate time-to-cure from cancer registries data. Cancer Epidemiol. 2018 Apr;53:72-80. doi: 10.1016/j.canep.2018.01.013. Epub 2018 Feb 4. PMID: 29414635. (pubmed)

Phillips N, Coldman A, McBride ML. Estimating cancer prevalence using mixture models for cancer survival. Stat Med. 2002 May 15;21(9):1257-70. doi: 10.1002/sim.1101. PMID: 12111877. (pubmed)

De Angelis R, Capocaccia R, Hakulinen T, Soderman B, Verdecchia A. Mixture models for cancer survival analysis: application to population-based data with covariates. Stat Med. 1999 Feb 28;18(4):441-54. doi: 10.1002/(sici)1097-0258(19990228)18:4<441::aid-sim23>3.0.co;2-m. PMID: 10070685. (pubmed)

Botta L, Caffo O, Dreassi E, Pizzoli S, Quaglio F, Rugge M, Valsecchi MG. A new cure model that corrects for increased risk of non-cancer death: analysis of reliability and robustness, and application to real-life data. BMC Med Res Methodol. 2023 Mar 25;23(1):70. doi: 10.1186/s12874-023-01876-x. PMID: N/A. (pubmed)

Examples


library("curesurv")
library("survival")



# Net survival setting
# Mixture cure model with Weibull function for the uncured patients survival:
# no covariate

theta_init2 <- rep(0, 3)
theta_lower2 <- c(-Inf,-Inf,-Inf)
theta_upper2 <- c(Inf, Inf, Inf)


fit_m0_ml <- curesurv(Surv(time_obs, event) ~ 1 | 1,
             pophaz = "ehazard",
             cumpophaz = "cumehazard",
             model = "mixture", dist = "weib",
             data = testiscancer,
             init = list(theta_init = theta_init2,
             theta_lower = theta_lower2,
             theta_upper = theta_upper2),
             method_opt = "L-BFGS-B")
fit_m0_ml



# Mixture cure model with Weibull function for the uncured patients survival:
#standardized age as covariate


fit_m2_ml <- curesurv(Surv(time_obs, event) ~ age_cr | age_cr,
                   pophaz = "ehazard",
                   cumpophaz = "cumehazard",
                   model = "mixture", dist = "weib",
                   data = testiscancer,
                   method_opt = "L-BFGS-B")

 fit_m2_ml



## Non mixture cure model
### TNEH Null model
#### loglinear effect of covariates on time-to-null excess hazard

theta_init2 <- rep(0, 3)
theta_lower2 <- c(-Inf,-Inf,-Inf)
theta_upper2 <- c(Inf, Inf, Inf)

fit_m0_mult_tneh <- curesurv(Surv(time_obs, event) ~ 1,
                          pophaz = "ehazard",
                          cumpophaz = "cumehazard",
                          model = "nmixture",
                          dist = "tneh", link_tau = "loglinear",
                          data = testiscancer,
                          init = list(theta_init = theta_init2,
                                      theta_lower = theta_lower2,
                                      theta_upper = theta_upper2),
                          method_opt = "L-BFGS-B")


fit_m0_mult_tneh

#### Additive parametrization
theta_init2 <- c(1, 6, 6)
theta_lower2 <- c(0,1,0)
theta_upper2 <- c(Inf, Inf, Inf)

fit_m0_ad_tneh <- curesurv(Surv(time_obs, event) ~ 1,
                          pophaz = "ehazard",
                          cumpophaz = "cumehazard",
                          model = "nmixture",
                          dist = "tneh", link_tau = "linear",
                          data = testiscancer,
                          init = list(theta_init = theta_init2,
                                      theta_lower = theta_lower2,
                                      theta_upper = theta_upper2),
                          method_opt = "L-BFGS-B")



 fit_m0_ad_tneh

#### Additive parametrization, with covariates
fit_m1_ad_tneh <- curesurv(Surv(time_obs, event) ~ z_alpha(age_cr) +
                          z_tau(age_cr),
                          pophaz = "ehazard",
                          cumpophaz = "cumehazard",
                          model = "nmixture",
                          dist = "tneh", link_tau = "linear",
                          data = testiscancer,
                          method_opt = "L-BFGS-B")



 fit_m1_ad_tneh




library("curesurv")
library("survival")



# Net survival setting
# Mixture cure model with Weibull function for the uncured patients survival:
# no covariate

theta_init2 <- rep(0, 3)
theta_lower2 <- c(-Inf,-Inf,-Inf)
theta_upper2 <- c(Inf, Inf, Inf)


fit_m0_ml <- curesurv(Surv(time_obs, event) ~ 1 | 1,
             pophaz = "ehazard",
             cumpophaz = "cumehazard",
             model = "mixture", dist = "weib",
             data = testiscancer,
             init = list(theta_init = theta_init2,
             theta_lower = theta_lower2,
             theta_upper = theta_upper2),
             method_opt = "L-BFGS-B")
fit_m0_ml



# Mixture cure model with Weibull function for the uncured patients survival:
#standardized age as covariate


fit_m2_ml <- curesurv(Surv(time_obs, event) ~ age_cr | age_cr,
                   pophaz = "ehazard",
                   cumpophaz = "cumehazard",
                   model = "mixture", dist = "weib",
                   data = testiscancer,
                   method_opt = "L-BFGS-B")

 fit_m2_ml



## Non mixture cure model
### TNEH Null model
#### loglinear effect of covariates on time-to-null excess hazard

theta_init2 <- rep(0, 3)
theta_lower2 <- c(-Inf,-Inf,-Inf)
theta_upper2 <- c(Inf, Inf, Inf)

fit_m0_mult_tneh <- curesurv(Surv(time_obs, event) ~ 1,
                          pophaz = "ehazard",
                          cumpophaz = "cumehazard",
                          model = "nmixture",
                          dist = "tneh", link_tau = "loglinear",
                          data = testiscancer,
                          init = list(theta_init = theta_init2,
                                      theta_lower = theta_lower2,
                                      theta_upper = theta_upper2),
                          method_opt = "L-BFGS-B")


fit_m0_mult_tneh

#### Additive parametrization
theta_init2 <- c(1, 6, 6)
theta_lower2 <- c(0,1,0)
theta_upper2 <- c(Inf, Inf, Inf)

fit_m0_ad_tneh <- curesurv(Surv(time_obs, event) ~ 1,
                          pophaz = "ehazard",
                          cumpophaz = "cumehazard",
                          model = "nmixture",
                          dist = "tneh", link_tau = "linear",
                          data = testiscancer,
                          init = list(theta_init = theta_init2,
                                      theta_lower = theta_lower2,
                                      theta_upper = theta_upper2),
                          method_opt = "L-BFGS-B")



 fit_m0_ad_tneh

#### Additive parametrization, with covariates
fit_m1_ad_tneh <- curesurv(Surv(time_obs, event) ~ z_alpha(age_cr) +
                          z_tau(age_cr),
                          pophaz = "ehazard",
                          cumpophaz = "cumehazard",
                          model = "nmixture",
                          dist = "tneh", link_tau = "linear",
                          data = testiscancer,
                          method_opt = "L-BFGS-B")



 fit_m1_ad_tneh

Simulated data with vital status information from Weibull mixture cure model

Description

Simulated data

Usage

data(dataweib)
data(dataweib)

Format

This dataset contains the following variables:

age: Age at diagnosis
age_cr: centered and scaled age at diagnosis
age_classe: "<45", "45_59" and ">=60" age groups
sexe: "male", "female" gender groups
stage: "<0", "1" , "2" and "3" for stage I-IV groups
time_obs: Follow-up time (years)
event: Vital status
cumehazard: individual cumulative expected hazard
ehazard: individual instantaneous expected hazard

Examples

data(dataweib)
summary(dataweib)
data(dataweib)
summary(dataweib)

Simulated pancreas data with vital status information

Description

Simulated data

Usage

data(pancreas_data)
data(pancreas_data)

Format

This dataset contains the following variables:

age: Age at diagnosis
age_cr: centered and scaled age at diagnosis
age_classe: "<45", "45_59" and ">=60" age groups
time_obs: Follow-up time (years)
event: Vital status
cumehazard: individual cumulative expected hazard
ehazard: individual instantaneous expected hazard

Examples

data(pancreas_data)
summary(pancreas_data)
data(pancreas_data)
summary(pancreas_data)

plot method for curesurv prediction objects

Description

Produces figures of (excess) hazard, (net) survival and probability P(t) of being cured at a given time t after diagnosis knowing that he/she was alive up to time t.

Usage

## S3 method for class 'predCuresurv'
plot(
  x,
  fun = "all",
  conf.int = FALSE,
  conf.type = c("log", "log-log", "plain"),
  legend.out = TRUE,
  xlab = "Time since diagnosis",
  ylab.haz = "excess hazard",
  ylab.surv = "net survival",
  ylab.ptcure = "P(t)",
  ylab.cumhaz = "cumulative excess hazard",
  ylab.logcumhaz = "logarithm of cumulative excess hazard",
  col.haz = "black",
  col.surv = "black",
  col.ptcure = "black",
  col.cumhaz = "black",
  col.logcumhaz = "black",
  col.tau = "red",
  col.ttc = "green4",
  col.p95 = "black",
  col.pi = "blue",
  lty.surv = 1,
  lty.haz = 1,
  lty.ptcure = 1,
  lty.cumhaz = 1,
  lty.logcumhaz = 1,
  lty.pi = 2,
  lty.tau = 2,
  lty.ttc = 3,
  lty.p95 = 4,
  lty.ic = 5,
  lwd.main = 1,
  lwd.sub = 1,
  lwd.ic = 1,
  ...
)
## S3 method for class 'predCuresurv'
plot(
  x,
  fun = "all",
  conf.int = FALSE,
  conf.type = c("log", "log-log", "plain"),
  legend.out = TRUE,
  xlab = "Time since diagnosis",
  ylab.haz = "excess hazard",
  ylab.surv = "net survival",
  ylab.ptcure = "P(t)",
  ylab.cumhaz = "cumulative excess hazard",
  ylab.logcumhaz = "logarithm of cumulative excess hazard",
  col.haz = "black",
  col.surv = "black",
  col.ptcure = "black",
  col.cumhaz = "black",
  col.logcumhaz = "black",
  col.tau = "red",
  col.ttc = "green4",
  col.p95 = "black",
  col.pi = "blue",
  lty.surv = 1,
  lty.haz = 1,
  lty.ptcure = 1,
  lty.cumhaz = 1,
  lty.logcumhaz = 1,
  lty.pi = 2,
  lty.tau = 2,
  lty.ttc = 3,
  lty.p95 = 4,
  lty.ic = 5,
  lwd.main = 1,
  lwd.sub = 1,
  lwd.ic = 1,
  ...
)

Arguments

`x`	result of the `predCuresurv` function
`fun`	in "haz" or "surv" or "pt_cure", "cumhaz", "logcumhaz", the plot produced is that of (excess) hazard, or that of (net) survival, or that of the probability P(t) of being cured at a given time t after diagnosis knowing that he/she was alive up to time t is provided, or that of cumulative hazard or that of the logarithm of the cumulative hazard; if `fun = "all"`, the plots of the three first indicators are produced.
`conf.int`	an argument expected to be TRUE if the confidence intervals of the related-indicator specified by the argument "fun" are needed. The default option is FALSE. Confidence intervals are not available for `fun="cumhaz"` and `fun="logcumhaz"`
`conf.type`	One of "plain", "log", "log-log". The first option causes the standard intervals curve +- k *se(curve), where k is determined from conf.int. The log option calculates intervals based on log(curve). The log-log option bases the intervals on the log(-log(curve)).
`legend.out`	an argument deciding the place of the legend if `fun="all"`. The default value is TRUE and forces most of the legend on the empty bottom-right plot slot. If value is FALSE, the legend will be printed entirely in each subplot.
`xlab`	label for the x-axis of the plot.
`ylab.haz`	optional label for the y-axis of the plot of excess hazard
`ylab.surv`	optional label for the y-axis of the plot of net survival
`ylab.ptcure`	optional label for the y-axis of the plot of the probability `P(t)` of being cured at a given time t after diagnosis knowing that he/she was alive up to time t
`ylab.cumhaz`	optional label for the y-axis of the plot of cumulative excess hazard
`ylab.logcumhaz`	optional label for the y-axis of the plot of logarithm of cumulative excess hazard
`col.haz`	optional argument to specify the color of curve of the excess hazard
`col.surv`	optional argument to specify the color of curve of the net survival
`col.ptcure`	optional argument to specify the color of curve of probability `P(t)` of being cured at a given time t after diagnosis knowing that he/she was alive up to time `t`.
`col.cumhaz`	optional argument to specify the color of curve of cumulative excess hazard
`col.logcumhaz`	optional argument to specify the color of curve of the logarithm of cumulative excess hazard
`col.tau`	optional argument to specify the color of curve of time-to-null excess hazard
`col.ttc`	optional argument to specify the color of curve of time-to-cure
`col.p95`	optional argument to specify the color for the line highlighting $\epsilon$ when $P(t) \ge 1-\epsilon$
`col.pi`	optional argument to specify the color of cure proportion
`lty.surv`	stands for line types for net survival
`lty.haz`	stands for line types for excess hazard
`lty.ptcure`	stands for line types for probability P(t) of being cured at a given time t after diagnosis knowing that he/she was alive up to time t.
`lty.cumhaz`	stands for line types for cumulative excess hazard
`lty.logcumhaz`	stands for line types for logarithm cumulative excess hazard
`lty.pi`	stands for line types for cure proportion
`lty.tau`	stands for line types for time-to-null excess hazard
`lty.ttc`	stands for line types for time-to-cure
`lty.p95`	stands for line types for the line highlighting $\epsilon$ when $P(t) \ge 1-\epsilon$
`lty.ic`	stands for line types for confidence intervals
`lwd.main`	line width for the main line (haz, surv, pt_cure, cumhaz, logcumhaz)
`lwd.sub`	line width for the additionnal lines (ttc, p95, tau...)
`lwd.ic`	line width for the confidence intervals lines
`...`	additional options as in the classical plot method.
`ylab`	optional label for the y-axis of the plot. Depending to the curve of interest (hazard, survival, probability of being cured at a given time t, or all),the argument must be named `ylab.haz, ylab.surv, ylab.ptcure`. If missing some default labels are provided depending on the curve of interest. This name can be found in the data.frame from the result of the `predict.curesurv` function.

Value

No value is returned.

Author(s)

Juste Goungounga, Judith Breaud, Eugenie Blandin, Olayide Boussari, Valerie Jooste

Examples




library("curesurv")
library("survival")

 testiscancer$age_crmin <- (testiscancer$age- min(testiscancer$age)) /
              sd(testiscancer$age)

fit_m1_ad_tneh <- curesurv(Surv(time_obs, event) ~ z_tau(age_crmin) +
                          z_alpha(age_crmin),
                          pophaz = "ehazard",
                          cumpophaz = "cumehazard",
                          model = "nmixture", dist = "tneh",
                          link_tau = "linear",
                          data = testiscancer,
                          method_opt = "L-BFGS-B")

 fit_m1_ad_tneh


#'  #mean of age
 newdata1 <- with(testiscancer,
 expand.grid(event = 0, age_crmin = mean(age_crmin), time_obs  = seq(0.001,10,0.1)))

 pred_agemean <- predict(object = fit_m1_ad_tneh, newdata = newdata1)


 #max of age
 newdata2 <- with(testiscancer,
 expand.grid(event = 0,
 age_crmin = max(age_crmin),
  time_obs  = seq(0.001,10,0.1)))

 pred_agemax <- predict(object = fit_m1_ad_tneh, newdata = newdata2)

   # predictions at time 2 years and  of age

   newdata3 <- with(testiscancer,
      expand.grid(event = 0,
      age_crmin = seq(min(testiscancer$age_crmin),max(testiscancer$age_crmin), 0.1),
      time_obs  = 2))

   pred_age_val <- predict(object = fit_m1_ad_tneh, newdata = newdata3)

 #plot of 3 indicators for mean age

 plot(pred_agemean, fun="all")


 #plot of net survival for mean and maximum age (comparison)

oldpar <- par(no.readonly = TRUE)

par(mfrow = c(2, 2),
    cex = 1.0)
plot(pred_agemax$time,
    pred_agemax$ex_haz,
    type = "l",
    lty = 1,
    lwd = 2,
    xlab = "Time since diagnosis",
    ylab = "excess hazard")
lines(pred_agemean$time,
     pred_agemean$ex_haz,
     type = "l",
     lty = 2,
     lwd = 2)

legend("topright",
      horiz = FALSE,
      legend = c("hE(t) age.max = 79.9", "hE(t) age.mean = 50.8"),
      col = c("black", "black"),
      lty = c(1, 2, 1, 1, 2, 2))
grid()

plot(pred_agemax$time,
    pred_agemax$netsurv,
    type = "l",
    lty = 1,
    lwd = 2,
    ylim = c(0, 1),
    xlab = "Time since diagnosis",
    ylab = "net survival")
lines(pred_agemean$time,
     pred_agemean$netsurv,
     type = "l",
     lty = 2,
     lwd = 2)
legend("bottomleft",
       horiz = FALSE,
       legend = c("Sn(t) age.max = 79.9", "Sn(t) age.mean = 50.8"),
       col = c("black", "black"),
      lty = c(1, 2, 1, 1, 2, 2))
grid()

plot(pred_agemax$time,
    pred_agemax$pt_cure,
    type = "l",
    lty = 1,
    lwd = 2,
    ylim = c(0, 1), xlim = c(0,30),
    xlab = "Time since diagnosis",
    ylab = "probability of being cured P(t)")

lines(pred_agemean$time,
     pred_agemean$pt_cure,
     type = "l",
     lty = 2,
     lwd = 2)


abline(v = pred_agemean$tau[1],
      lty = 2,
      lwd = 2,
      col = "blue")
abline(v = pred_agemean$TTC[1],
       lty = 2,
       lwd = 2,
       col = "red")
abline(v = pred_agemax$tau[1],
       lty = 1,
       lwd = 2,
       col = "blue")
abline(v = pred_agemax$TTC[1],
       lty = 1,
       lwd = 2,
      col = "red")
grid()

legend("bottomright",
       horiz = FALSE,
       legend = c("P(t) age.max = 79.9",
                 "P(t) age.mean = 50.8",
                 "TNEH age.max = 79.9",
                 "TTC age.max = 79.9",
                 "TNEH age.mean = 50.8",
                 "TTC age.mean = 50.8"),
      col = c("black", "black", "blue", "red", "blue", "red"),
      lty = c(1, 2, 1, 1, 2, 2))


 val_age <- seq(min(testiscancer$age_crmin),
                max(testiscancer$age_crmin), 0.1) * sd(testiscancer$age) +
                min(testiscancer$age)


 pred_age_val <- predict(object = fit_m1_ad_tneh, newdata = newdata3)


par(mfrow=c(2,2))
 plot(val_age,
     pred_age_val$ex_haz, type = "l",
     lty=1, lwd=2,
     xlab = "age",
     ylab = "excess hazard")
grid()

 plot(val_age,
     pred_age_val$netsurv, type = "l", lty=1,
     lwd=2, xlab = "age", ylab = "net survival")
     grid()

 plot(val_age,
     pred_age_val$pt_cure, type = "l", lty=1, lwd=2,
     xlab = "age",
     ylab = "P(t)")
     grid()
par(oldpar)
 

library("curesurv")
library("survival")

 testiscancer$age_crmin <- (testiscancer$age- min(testiscancer$age)) /
              sd(testiscancer$age)

fit_m1_ad_tneh <- curesurv(Surv(time_obs, event) ~ z_tau(age_crmin) +
                          z_alpha(age_crmin),
                          pophaz = "ehazard",
                          cumpophaz = "cumehazard",
                          model = "nmixture", dist = "tneh",
                          link_tau = "linear",
                          data = testiscancer,
                          method_opt = "L-BFGS-B")

 fit_m1_ad_tneh


#'  #mean of age
 newdata1 <- with(testiscancer,
 expand.grid(event = 0, age_crmin = mean(age_crmin), time_obs  = seq(0.001,10,0.1)))

 pred_agemean <- predict(object = fit_m1_ad_tneh, newdata = newdata1)


 #max of age
 newdata2 <- with(testiscancer,
 expand.grid(event = 0,
 age_crmin = max(age_crmin),
  time_obs  = seq(0.001,10,0.1)))

 pred_agemax <- predict(object = fit_m1_ad_tneh, newdata = newdata2)

   # predictions at time 2 years and  of age

   newdata3 <- with(testiscancer,
      expand.grid(event = 0,
      age_crmin = seq(min(testiscancer$age_crmin),max(testiscancer$age_crmin), 0.1),
      time_obs  = 2))

   pred_age_val <- predict(object = fit_m1_ad_tneh, newdata = newdata3)

 #plot of 3 indicators for mean age

 plot(pred_agemean, fun="all")


 #plot of net survival for mean and maximum age (comparison)

oldpar <- par(no.readonly = TRUE)

par(mfrow = c(2, 2),
    cex = 1.0)
plot(pred_agemax$time,
    pred_agemax$ex_haz,
    type = "l",
    lty = 1,
    lwd = 2,
    xlab = "Time since diagnosis",
    ylab = "excess hazard")
lines(pred_agemean$time,
     pred_agemean$ex_haz,
     type = "l",
     lty = 2,
     lwd = 2)

legend("topright",
      horiz = FALSE,
      legend = c("hE(t) age.max = 79.9", "hE(t) age.mean = 50.8"),
      col = c("black", "black"),
      lty = c(1, 2, 1, 1, 2, 2))
grid()

plot(pred_agemax$time,
    pred_agemax$netsurv,
    type = "l",
    lty = 1,
    lwd = 2,
    ylim = c(0, 1),
    xlab = "Time since diagnosis",
    ylab = "net survival")
lines(pred_agemean$time,
     pred_agemean$netsurv,
     type = "l",
     lty = 2,
     lwd = 2)
legend("bottomleft",
       horiz = FALSE,
       legend = c("Sn(t) age.max = 79.9", "Sn(t) age.mean = 50.8"),
       col = c("black", "black"),
      lty = c(1, 2, 1, 1, 2, 2))
grid()

plot(pred_agemax$time,
    pred_agemax$pt_cure,
    type = "l",
    lty = 1,
    lwd = 2,
    ylim = c(0, 1), xlim = c(0,30),
    xlab = "Time since diagnosis",
    ylab = "probability of being cured P(t)")

lines(pred_agemean$time,
     pred_agemean$pt_cure,
     type = "l",
     lty = 2,
     lwd = 2)


abline(v = pred_agemean$tau[1],
      lty = 2,
      lwd = 2,
      col = "blue")
abline(v = pred_agemean$TTC[1],
       lty = 2,
       lwd = 2,
       col = "red")
abline(v = pred_agemax$tau[1],
       lty = 1,
       lwd = 2,
       col = "blue")
abline(v = pred_agemax$TTC[1],
       lty = 1,
       lwd = 2,
      col = "red")
grid()

legend("bottomright",
       horiz = FALSE,
       legend = c("P(t) age.max = 79.9",
                 "P(t) age.mean = 50.8",
                 "TNEH age.max = 79.9",
                 "TTC age.max = 79.9",
                 "TNEH age.mean = 50.8",
                 "TTC age.mean = 50.8"),
      col = c("black", "black", "blue", "red", "blue", "red"),
      lty = c(1, 2, 1, 1, 2, 2))


 val_age <- seq(min(testiscancer$age_crmin),
                max(testiscancer$age_crmin), 0.1) * sd(testiscancer$age) +
                min(testiscancer$age)


 pred_age_val <- predict(object = fit_m1_ad_tneh, newdata = newdata3)


par(mfrow=c(2,2))
 plot(val_age,
     pred_age_val$ex_haz, type = "l",
     lty=1, lwd=2,
     xlab = "age",
     ylab = "excess hazard")
grid()

 plot(val_age,
     pred_age_val$netsurv, type = "l", lty=1,
     lwd=2, xlab = "age", ylab = "net survival")
     grid()

 plot(val_age,
     pred_age_val$pt_cure, type = "l", lty=1, lwd=2,
     xlab = "age",
     ylab = "P(t)")
     grid()
par(oldpar)

Prediction for a curesurv cure model

Description

return predicted (excess) hazard, (net) survival, cure fraction and time to null excess hazard or time to cure.

Usage

## S3 method for class 'curesurv'
predict(
  object,
  newdata = NULL,
  xmax = 10^9,
  level = 0.975,
  epsilon = 0.05,
  sign_delta = 1,
  ...
)
## S3 method for class 'curesurv'
predict(
  object,
  newdata = NULL,
  xmax = 10^9,
  level = 0.975,
  epsilon = 0.05,
  sign_delta = 1,
  ...
)

Arguments

`object`	Output from `curesurv` function
`newdata`	the new data to be specified for predictions; If else, predictions are made using the data provided during the estimation step in order to obtain the output from curesurv function.
`xmax`	maximum time at which Time-to-Cure is evaluated numerically.
`level`	$1-\frac{\alpha}{2}$ -order quantile of a normal distribution for the confidence intervals
`epsilon`	value fixed by user to estimate the TTC $Pi(t) \ge 1-\epsilon$ . By default epsilon = 0.05.
`sign_delta`	sign of effect of delta on covariates acting on survival function, positive by default "sign_delta = 1" and alternative is "sign_delta = -1"
`...`	additional parameters

Value

An object of class c("pred_curesurv", "data.frame"). This object is a list containing the following components:

`time`	time in the input new data
`ex_haz`	predicted excess hazard at the time provided in the new data
`netsurv`	predicted net survival at the time provided in the new data
`pt_cure`	probability to be cured
`tau`	time to null in model TNEH when object corresponds to the results from Boussari model or its extension.
`netsurv_tau`	pi or net survival at time tau when object corresponds to the results from Boussari model or its extension.
`time_to_cure_ttc`	time to cure (TTC)

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Valerie Jooste

References

Phillips N, Coldman A, McBride ML. Estimating cancer prevalence using mixture models for cancer survival. Stat Med. 2002 May 15;21(9):1257-70. doi: 10.1002/sim.1101. PMID: 12111877. (pubmed)

Examples


library("curesurv")
library("survival")

fit_m2_ml <- curesurv(Surv(time_obs, event) ~ age_cr|age_cr,
                   pophaz = "ehazard",
                   cumpophaz = "cumehazard",
                   model = "mixture",
                   data = pancreas_data,
                   method_opt = "L-BFGS-B")

 fit_m2_ml

 newdata <- pancreas_data[2,]

 predict(object = fit_m2_ml, newdata = newdata)

## Non mixture cure model
### TNEH model

#### Additive parametrization

testiscancer$age_crmin <- (testiscancer$age- min(testiscancer$age)) /
              sd(testiscancer$age)

fit_m1_ad_tneh <- curesurv(Surv(time_obs, event) ~ z_tau(age_crmin) +
                          z_alpha(age_crmin),
                          pophaz = "ehazard",
                          cumpophaz = "cumehazard",
                          model = "nmixture", dist = "tneh",
                          link_tau = "linear",
                          data = testiscancer,
                          method_opt = "L-BFGS-B")

 fit_m1_ad_tneh

 predict(object = fit_m1_ad_tneh, newdata = testiscancer[3:6,])

 #mean of age
 newdata1 <- with(testiscancer,
 expand.grid(event = 0, age_crmin = mean(age_crmin), time_obs  = seq(0.001,10,0.1)))

 pred_agemean <- predict(object = fit_m1_ad_tneh, newdata = newdata1)


 #max of age
 newdata2 <- with(testiscancer,
 expand.grid(event = 0,
 age_crmin = max(age_crmin),
  time_obs  = seq(0.001,10,0.1)))

 pred_agemax <- predict(object = fit_m1_ad_tneh, newdata = newdata2)
 head(pred_agemax)




library("curesurv")
library("survival")

fit_m2_ml <- curesurv(Surv(time_obs, event) ~ age_cr|age_cr,
                   pophaz = "ehazard",
                   cumpophaz = "cumehazard",
                   model = "mixture",
                   data = pancreas_data,
                   method_opt = "L-BFGS-B")

 fit_m2_ml

 newdata <- pancreas_data[2,]

 predict(object = fit_m2_ml, newdata = newdata)

## Non mixture cure model
### TNEH model

#### Additive parametrization

testiscancer$age_crmin <- (testiscancer$age- min(testiscancer$age)) /
              sd(testiscancer$age)

fit_m1_ad_tneh <- curesurv(Surv(time_obs, event) ~ z_tau(age_crmin) +
                          z_alpha(age_crmin),
                          pophaz = "ehazard",
                          cumpophaz = "cumehazard",
                          model = "nmixture", dist = "tneh",
                          link_tau = "linear",
                          data = testiscancer,
                          method_opt = "L-BFGS-B")

 fit_m1_ad_tneh

 predict(object = fit_m1_ad_tneh, newdata = testiscancer[3:6,])

 #mean of age
 newdata1 <- with(testiscancer,
 expand.grid(event = 0, age_crmin = mean(age_crmin), time_obs  = seq(0.001,10,0.1)))

 pred_agemean <- predict(object = fit_m1_ad_tneh, newdata = newdata1)


 #max of age
 newdata2 <- with(testiscancer,
 expand.grid(event = 0,
 age_crmin = max(age_crmin),
  time_obs  = seq(0.001,10,0.1)))

 pred_agemax <- predict(object = fit_m1_ad_tneh, newdata = newdata2)
 head(pred_agemax)

print a curesurv object

Description

Print an object of class "curesurv"

Usage

## S3 method for class 'curesurv'
print(x, digits = max(1L, getOption("digits") - 3L), signif.stars = FALSE, ...)
## S3 method for class 'curesurv'
print(x, digits = max(1L, getOption("digits") - 3L), signif.stars = FALSE, ...)

Arguments

`x`	an object of class "curesurv".
`digits`	minimum number of significant digits to be used for most numbers.
`signif.stars`	logical; if TRUE, P-values are additionally encoded visually as "significance stars" in order to help scanning of long coefficient tables.
`...`	additional options

Value

an object of class "curesurv" representing the fit. See curesurv for details.

Author(s)

Juste Goungounga, Judith Breaud, Eugenie Blandin, Olayide Boussari, Valerie Jooste

References

Boussari O, Bordes L, Romain G, Colonna M, Bossard N, Remontet L, Jooste V. Modeling excess hazard with time-to-cure as a parameter. Biometrics. 2020 Aug 31. doi: 10.1111/biom.13361. Epub ahead of print. PMID: 32869288. (pubmed)

Phillips N, Coldman A, McBride ML. Estimating cancer prevalence using mixture models for cancer survival. Stat Med. 2002 May 15;21(9):1257-70. doi: 10.1002/sim.1101. PMID: 12111877. (pubmed)

Examples


library("curesurv")
library("survival")



# overall survival setting
# Mixture cure model with Weibull function for the uncured patients survival:
# no covariate



fit_ml0 <- curesurv(Surv(time_obs, event) ~ 1 | 1,
             model = "mixture", dist = "weib",
             data = testiscancer,
             method_opt = "L-BFGS-B")


print(fit_ml0)

library("curesurv")
library("survival")



# overall survival setting
# Mixture cure model with Weibull function for the uncured patients survival:
# no covariate



fit_ml0 <- curesurv(Surv(time_obs, event) ~ 1 | 1,
             model = "mixture", dist = "weib",
             data = testiscancer,
             method_opt = "L-BFGS-B")


print(fit_ml0)

summary for a curesurv cure model

Description

summary an object of class "curesurv"

Usage

## S3 method for class 'curesurv'
summary(
  object,
  digits = max(1L, getOption("digits") - 3L),
  signif.stars = FALSE,
  ...
)
## S3 method for class 'curesurv'
summary(
  object,
  digits = max(1L, getOption("digits") - 3L),
  signif.stars = FALSE,
  ...
)

Arguments

`object`	an object of class "curesurv".
`digits`	minimum number of significant digits to be used for most numbers.
`signif.stars`	logical; if TRUE, P-values are additionally encoded visually as "significance stars" in order to help scanning of long coefficient tables.
`...`	additional options

Value

an object of class "curesurv" representing the fit. See curesurv for details.

Author(s)

Juste Goungounga, Judith Breaud, Eugenie Blandin, Olayide Boussari, Valerie Jooste

References

Phillips N, Coldman A, McBride ML. Estimating cancer prevalence using mixture models for cancer survival. Stat Med. 2002 May 15;21(9):1257-70. doi: 10.1002/sim.1101. PMID: 12111877. (pubmed)

Examples


library("curesurv")
library("survival")



# overall survival setting
# Mixture cure model with Weibull function for the uncured patients survival:
# no covariate



fit_ml0 <- curesurv(Surv(time_obs, event) ~ 1 | 1,
             model = "mixture", dist = "weib",
             data = testiscancer,
             method_opt = "L-BFGS-B")


 summary(fit_ml0)

library("curesurv")
library("survival")



# overall survival setting
# Mixture cure model with Weibull function for the uncured patients survival:
# no covariate



fit_ml0 <- curesurv(Surv(time_obs, event) ~ 1 | 1,
             model = "mixture", dist = "weib",
             data = testiscancer,
             method_opt = "L-BFGS-B")


 summary(fit_ml0)

Simulated testis cancer data using a cure model

Description

Simulated dataset of 2000 individuals as in Boussari et al. (2020), following setting 1 sub-scenario design.

Usage

data(testiscancer)
data(testiscancer)

Format

This dataset contains the following variables:

age: Age at diagnosis
age_cr: centered and scaled age at diagnosis
age_classe: "<40", "40_65" and ">=65" age groups
time_obs: Follow-up time (years)
event: Vital status
cumehazard: individual cumulative expected hazard
ehazard: individual instantaneous expected hazard
weisurvpop: individual expected survival

Examples

data(testiscancer)
summary(testiscancer)
data(testiscancer)
summary(testiscancer)

z_alpha function identifying variables acting on alpha parameter

Description

variables adjusted on alpha parameter in non-mixture cure model with "tneh" specified for the distribution.

Usage

z_alpha(x)
z_alpha(x)

Arguments

`x`	a simple formula.

Value

the variable x

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Gaelle Romain, Valerie Jooste

References

z_tau function identifying variables acting on tau parameter

Description

variables adjusted on tau parameter in non-mixture cure model with "tneh" specified for the distribution.

Usage

z_tau(x)
z_tau(x)

Arguments

`x`	the name of the column in the dataset representing the variable that will act on tau parameter of the "tneh" model

Value

the variable x

Author(s)

Juste Goungounga, Judith Breaud, Eugenie Blandin, Olayide Boussari, Valerie Jooste

Package 'curesurv'

Help Index

Akaike's An Information Criterion for cure models

Description

Usage

Arguments

Details

Value

Examples

anova.curesurv function for likelihood-ratio test of two nested models from curesurv function

Description

Usage

Arguments

Value

Note

Examples

cumLexc_mul function

Description

Usage

Arguments

Value

Fitting cure models using curesurv

Description

Non-mixture cure model

The Boussari model

Mixture cure model

Correction of background mortality

Usage

Arguments

Value

Note

Author(s)

References

See Also

Examples

Simulated data with vital status information from Weibull mixture cure model

Description

Usage

Format

Examples

Simulated pancreas data with vital status information

Description

Usage

Format

Examples

plot method for curesurv prediction objects

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Prediction for a curesurv cure model

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

print a curesurv object

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

summary for a curesurv cure model

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples