| Title: | Penalized Mixture Cure Models for High-Dimensional Data |
|---|---|
| Description: | Provides functions for fitting various penalized parametric and semi-parametric mixture cure models with different penalty functions, testing for a significant cure fraction, and testing for sufficient follow-up as described in Fu et al (2022)<doi:10.1002/sim.9513> and Archer et al (2024)<doi:10.1186/s13045-024-01553-6>. False discovery rate controlled variable selection is provided using model-X knock-offs. |
| Authors: | Han Fu [aut],
Kellie J. Archer [aut, cre] |
| Maintainer: | Kellie J. Archer <[email protected]> |
| License: | MIT + file LICENSE |
| Version: | 0.0.2 |
| Built: | 2024-10-31 05:37:18 UTC |
| Source: | https://github.com/kelliejarcher/hdcuremodels |
Duration of complete response for 40 cytogenetically normal AML patients and a subset of 320 transcript expression from RNA-sequencing.
amltestamltest
A data frame with 40 rows (subjects) and 322 columns:
duration of complete response in years
censoring indicator: 1 = relapsed or died; 0 = alive at last follow=up
normalized expression for indicated transcript
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doi:10.1186/s13045-024-01553-6
Duration of complete response for 306 cytogenetically normal AML patients and a subset of 320 transcript expression from RNA-sequencing.
amltrainamltrain
A data frame with 306 rows (subjects) and 322 columns:
duration of complete response in years
censoring indicator: 1 = relapsed or died; 0 = alive at last follow=up
normalized expression for indicated transcript
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doi:10.1186/s13045-024-01553-6
This function calculates the AUC for cure prediction using the mean score imputation (MSI) method proposed by Asano et al.
auc_mcm(object, newdata, cure_cutoff = 5, model_select = "AIC")auc_mcm(object, newdata, cure_cutoff = 5, model_select = "AIC")
object |
a |
newdata |
an optional data.frame that minimally includes the incidence and/or latency variables to use for predicting the response. If omitted, the training data are used. |
cure_cutoff |
cutoff value for cure, used to produce a proxy for the unobserved cure status; default is 5. |
model_select |
for models fit using |
Returns the AUC value for cure prediction using the mean score imputation (MSI) method.
Asano, J., Hirakawa, H., Hamada, C. (2014) Assessing the prediction accuracy of cure in the Cox proportional hazards cure model: an application to breast cancer data. Pharmaceutical Statistics, 13:357–363.
library(survival) set.seed(1234) temp <- generate_cure_data(n = 100, j = 10, n_true = 10, a = 1.8) training <- temp$training testing <- temp$testing fit <- curegmifs(Surv(Time, Censor) ~ ., data = training, x_latency = training, model = "weibull", thresh = 1e-4, maxit = 2000, epsilon = 0.01, verbose = FALSE) auc_mcm(fit, model_select = "cAIC") auc_mcm(fit, newdata = testing)library(survival) set.seed(1234) temp <- generate_cure_data(n = 100, j = 10, n_true = 10, a = 1.8) training <- temp$training testing <- temp$testing fit <- curegmifs(Surv(Time, Censor) ~ ., data = training, x_latency = training, model = "weibull", thresh = 1e-4, maxit = 2000, epsilon = 0.01, verbose = FALSE) auc_mcm(fit, model_select = "cAIC") auc_mcm(fit, newdata = testing)
coef.mixturecure is a generic function which extracts the model
coefficients from a fitted mixture cure model object fit using
curegmifs, cureem, cv_curegmifs, or cv_cureem.
## S3 method for class 'mixturecure' coef(object, model_select = "AIC", ...)## S3 method for class 'mixturecure' coef(object, model_select = "AIC", ...)
object |
a |
model_select |
for models fit using |
... |
other arguments. |
a list of estimated parameters extracted from the model object using the model selection criterion
curegmifs, cureem,
summary.mixturecure, plot.mixturecure,
predict.mixturecure
library(survival) set.seed(1234) temp <- generate_cure_data(n = 100, j = 10, n_true = 10, a = 1.8) training <- temp$training fit <- curegmifs(Surv(Time, Censor) ~ ., data = training, x_latency = training, model = "weibull", thresh = 1e-4, maxit = 2000, epsilon = 0.01, verbose = FALSE) coef(fit)library(survival) set.seed(1234) temp <- generate_cure_data(n = 100, j = 10, n_true = 10, a = 1.8) training <- temp$training fit <- curegmifs(Surv(Time, Censor) ~ ., data = training, x_latency = training, model = "weibull", thresh = 1e-4, maxit = 2000, epsilon = 0.01, verbose = FALSE) coef(fit)
This function calculates the C-statistic using the cure status weighting (CSW) method proposed by Asano and Hirakawa.
concordance_mcm(object, newdata, cure_cutoff = 5, model_select = "AIC")concordance_mcm(object, newdata, cure_cutoff = 5, model_select = "AIC")
object |
a |
newdata |
an optional data.frame that minimally includes the incidence and/or latency variables to use for predicting the response. If omitted, the training data are used. |
cure_cutoff |
cutoff value for cure, used to produce a proxy for the unobserved cure status; default is 5. |
model_select |
for models fit using |
value of C-statistic for the cure models.
Asano, J. and Hirakawa, H. (2017) Assessing the prediction accuracy of a cure model for censored survival data with long-term survivors: Application to breast cancer data. Journal of Biopharmaceutical Statistics, 27:6, 918–932.
library(survival) set.seed(1234) temp <- generate_cure_data(n = 100, j = 10, n_true = 10, a = 1.8) training <- temp$training testing <- temp$testing fit <- curegmifs(Surv(Time, Censor) ~ ., data = training, x_latency = training, model = "weibull", thresh = 1e-4, maxit = 2000, epsilon = 0.01, verbose = FALSE) concordance_mcm(fit, model_select = "cAIC") concordance_mcm(fit, newdata = testing, model_select = "cAIC")library(survival) set.seed(1234) temp <- generate_cure_data(n = 100, j = 10, n_true = 10, a = 1.8) training <- temp$training testing <- temp$testing fit <- curegmifs(Surv(Time, Censor) ~ ., data = training, x_latency = training, model = "weibull", thresh = 1e-4, maxit = 2000, epsilon = 0.01, verbose = FALSE) concordance_mcm(fit, model_select = "cAIC") concordance_mcm(fit, newdata = testing, model_select = "cAIC")
Estimates the cured fraction using a Kaplan-Meier fitted object.
cure_estimate(object)cure_estimate(object)
object |
a |
estimated proportion of cured observations
survfit, sufficient_fu_test,
nonzerocure_test
library(survival) set.seed(1234) temp <- generate_cure_data(n = 100, j = 10, n_true = 10, a = 1.8) training <- temp$training km_fit <- survfit(Surv(Time, Censor) ~ 1, data = training) cure_estimate(km_fit)library(survival) set.seed(1234) temp <- generate_cure_data(n = 100, j = 10, n_true = 10, a = 1.8) training <- temp$training km_fit <- survfit(Surv(Time, Censor) ~ 1, data = training) cure_estimate(km_fit)
Fits a penalized parametric and semi-parametric mixture cure model (MCM) using the E-M algorithm with user-specified penalty parameters. The lasso (L1), MCP, and SCAD penalty is supported for the Cox MCM while only lasso is currently supported for parametric MCMs.
cureem( formula, data, subset, x_latency = NULL, model = c("cox", "weibull", "exponential"), penalty = c("lasso", "MCP", "SCAD"), penalty_factor_inc = NULL, penalty_factor_lat = NULL, thresh = 0.001, scale = TRUE, maxit = NULL, inits = NULL, lambda_inc = 0.1, lambda_lat = 0.1, gamma_inc = 3, gamma_lat = 3, ... )cureem( formula, data, subset, x_latency = NULL, model = c("cox", "weibull", "exponential"), penalty = c("lasso", "MCP", "SCAD"), penalty_factor_inc = NULL, penalty_factor_lat = NULL, thresh = 0.001, scale = TRUE, maxit = NULL, inits = NULL, lambda_inc = 0.1, lambda_lat = 0.1, gamma_inc = 3, gamma_lat = 3, ... )
formula |
an object of class " |
data |
a data.frame in which to interpret the variables named in the
|
subset |
an optional expression indicating which subset of observations to be used in the fitting process, either a numeric or factor variable should be used in subset, not a character variable. All observations are included by default. |
x_latency |
specifies the variables to be included in the latency
portion of the model and can be either a matrix of predictors, a model
formula with the right hand side specifying the latency variables, or the
same data.frame passed to the |
model |
type of regression model to use for the latency portion of mixture cure model. Can be "cox", "weibull", or "exponential" (default is "cox"). |
penalty |
type of penalty function. Can be "lasso", "MCP", or "SCAD" (default is "lasso"). |
penalty_factor_inc |
vector of binary indicators representing the penalty to apply to each incidence coefficient: 0 implies no shrinkage and 1 implies shrinkage. If not supplied, 1 is applied to all incidence variables. |
penalty_factor_lat |
vector of binary indicators representing the penalty to apply to each latency coefficient: 0 implies no shrinkage and 1 implies shrinkage. If not supplied, 1 is applied to all latency variables. |
thresh |
small numeric value. The iterative process stops when the differences between successive expected penalized complete-data log-likelihoods for both incidence and latency components are less than this specified level of tolerance (default is 10^-3). |
scale |
logical, if TRUE the predictors are centered and scaled. |
maxit |
integer specifying the maximum number of passes over the data
for each lambda. If not specified, 100 is applied when
|
inits |
an optional list specifiying the initial value for the
incidence intercept ( |
lambda_inc |
numeric value for the penalization parameter |
lambda_lat |
numeric value for the penalization parameter |
gamma_inc |
numeric value for the penalization parameter |
gamma_lat |
numeric value for the penalization parameter |
... |
additional arguments. |
b_path |
Matrix representing the solution path of the coefficients in the incidence portion of the model. Row is step and column is variable. |
beta_path |
Matrix representing the solution path of lthe coefficients in the latency portion of the model. Row is step and column is variable. |
b0_path |
Vector representing the solution path of the intercept in the incidence portion of the model. |
logLik_inc |
Vector representing the expected penalized complete-data log-likelihood for the incidence portion of the model for each step in the solution path. |
logLik_lat |
Vector representing the expected penalized complete-data log-likelihood for the latency portion of the model for each step in the solution path. |
x_incidence |
Matrix representing the design matrix of the incidence predictors. |
x_latency |
Matrix representing the design matrix of the latency predictors. |
y |
Vector representing the survival object response as
returned by the |
model |
Character string indicating the type of regression model used for the latency portion of mixture cure model ("weibull" or "exponential"). |
scale |
Logical value indicating whether the predictors were centered and scaled. |
method |
Character string indicating the EM alogoritm was used in fitting the mixture cure model. |
rate_path |
Vector representing the solution path of the rate parameter for the Weibull or exponential density in the latency portion of the model. |
alpha_path |
Vector representing the solution path of the shape parameter for the Weibull density in the latency portion of the model. |
call |
the matched call. |
Archer, K. J., Fu, H., Mrozek, K., Nicolet, D., Mims, A. S., Uy, G. L., Stock, W., Byrd, J. C., Hiddemann, W., Braess, J., Spiekermann, K., Metzeler, K. H., Herold, T., Eisfeld, A.-K. (2024) Identifying long-term survivors and those at higher or lower risk of relapse among patients with cytogenetically normal acute myeloid leukemia using a high-dimensional mixture cure model. Journal of Hematology & Oncology, 17:28.
library(survival) set.seed(1234) temp <- generate_cure_data(n = 80, j = 100, n_true = 10, a = 1.8) training <- temp$training fit <- cureem(Surv(Time, Censor) ~ ., data = training, x_latency = training, model = "cox", penalty = "lasso", lambda_inc = 0.1, lambda_lat = 0.1, gamma_inc = 6, gamma_lat = 10)library(survival) set.seed(1234) temp <- generate_cure_data(n = 80, j = 100, n_true = 10, a = 1.8) training <- temp$training fit <- cureem(Surv(Time, Censor) ~ ., data = training, x_latency = training, model = "cox", penalty = "lasso", lambda_inc = 0.1, lambda_lat = 0.1, gamma_inc = 6, gamma_lat = 10)
Fits a penalized Weibull or exponential mixture cure model using the generalized monotone incremental forward stagewise (GMIFS) algorithm and yields solution paths for parameters in the incidence and latency portions of the model.
curegmifs( formula, data, subset, x_latency = NULL, model = c("weibull", "exponential"), penalty_factor_inc = NULL, penalty_factor_lat = NULL, epsilon = 0.001, thresh = 1e-05, scale = TRUE, maxit = 10000, inits = NULL, verbose = TRUE, ... )curegmifs( formula, data, subset, x_latency = NULL, model = c("weibull", "exponential"), penalty_factor_inc = NULL, penalty_factor_lat = NULL, epsilon = 0.001, thresh = 1e-05, scale = TRUE, maxit = 10000, inits = NULL, verbose = TRUE, ... )
formula |
an object of class " |
data |
a data.frame in which to interpret the variables named in the
|
subset |
an optional expression indicating which subset of observations to be used in the fitting process, either a numeric or factor variable should be used in subset, not a character variable. All observations are included by default. |
x_latency |
specifies the variables to be included in the latency
portion of the model and can be either a matrix of predictors, a model
formula with the right hand side specifying the latency variables, or the
same data.frame passed to the |
model |
type of regression model to use for the latency portion of mixture cure model. Can be "weibull" or "exponential"; default is "weibull". |
penalty_factor_inc |
vector of binary indicators representing the penalty to apply to each incidence coefficient: 0 implies no shrinkage and 1 implies shrinkage. If not supplied, 1 is applied to all incidence variables. |
penalty_factor_lat |
vector of binary indicators representing the penalty to apply to each latency coefficient: 0 implies no shrinkage and 1 implies shrinkage. If not supplied, 1 is applied to all latency variables. |
epsilon |
small numeric value reflecting the incremental value used to update a coefficient at a given step (default is 0.001). |
thresh |
small numeric value. The iterative process stops when the differences between successive expected penalized complete-data log-likelihoods for both incidence and latency components are less than this specified level of tolerance (default is 10^-5). |
scale |
logical, if TRUE the predictors are centered and scaled. |
maxit |
integer specifying the maximum number of steps to run in the iterative algorithm (default is 10^4). |
inits |
an optional list specifiying the initial value for the incidence
intercept ( |
verbose |
logical, if TRUE running information is printed to the console (default is FALSE). |
... |
additional arguments. |
b_path |
Matrix representing the solution path of the coefficients in the incidence portion of the model. Row is step and column is variable. |
beta_path |
Matrix representing the solution path of the coefficients in the latency portion of the model. Row is step and column is variable. |
b0_path |
Vector representing the solution path of the intercept in the incidence portion of the model. |
rate_path |
Vector representing the solution path of the rate parameter for the Weibull or exponential density in the latency portion of the model. |
logLik |
Vector representing the log-likelihood for each step in the solution path. |
x_incidence |
Matrix representing the design matrix of the incidence predictors. |
x_latency |
Matrix representing the design matrix of the latency predictors. |
y |
Vector representing the survival object response as returned
by the |
model |
Character string indicating the type of regression model used for the latency portion of mixture cure model ("weibull" or "exponential"). |
scale |
Logical value indicating whether the predictors were centered and scaled. |
alpha_path |
Vector representing the solution path of the shape parameter for the Weibull density in the latency portion of the model. |
call |
the matched call. |
Fu, H., Nicolet, D., Mrozek, K., Stone, R. M., Eisfeld, A. K., Byrd, J. C., Archer, K. J. (2022) Controlled variable selection in Weibull mixture cure models for high-dimensional data. Statistics in Medicine, 41(22), 4340–4366.
library(survival) set.seed(1234) temp <- generate_cure_data(n = 100, j = 10, n_true = 10, a = 1.8) training <- temp$training fit <- curegmifs(Surv(Time, Censor) ~ ., data = training, x_latency = training, model = "weibull", thresh = 1e-4, maxit = 2000, epsilon = 0.01, verbose = FALSE)library(survival) set.seed(1234) temp <- generate_cure_data(n = 100, j = 10, n_true = 10, a = 1.8) training <- temp$training fit <- curegmifs(Surv(Time, Censor) ~ ., data = training, x_latency = training, model = "weibull", thresh = 1e-4, maxit = 2000, epsilon = 0.01, verbose = FALSE)
Fits a penalized parametric and semi-parametric mixture cure model (MCM) using the E-M algorithm with with k-fold cross-validation for parameter tuning. The lasso (L1), MCP and SCAD penalty are supported for the Cox MCM while only lasso is currently supported for parametric MCMs. When FDR controlled variable selection is used, the model-X knockoffs method is applied and indices of selected variables are returned.
cv_cureem( formula, data, subset, x_latency = NULL, model = c("cox", "weibull", "exponential"), penalty = c("lasso", "MCP", "SCAD"), penalty_factor_inc = NULL, penalty_factor_lat = NULL, fdr_control = FALSE, fdr = 0.2, grid_tuning = FALSE, thresh = 0.001, scale = TRUE, maxit = NULL, inits = NULL, lambda_inc_list = NULL, lambda_lat_list = NULL, nlambda_inc = NULL, nlambda_lat = NULL, gamma_inc = 3, gamma_lat = 3, lambda_min_ratio_inc = 0.1, lambda_min_ratio_lat = 0.1, n_folds = 5, measure_inc = c("c", "auc"), one_se = FALSE, cure_cutoff = 5, parallel = FALSE, seed = NULL, verbose = TRUE, ... )cv_cureem( formula, data, subset, x_latency = NULL, model = c("cox", "weibull", "exponential"), penalty = c("lasso", "MCP", "SCAD"), penalty_factor_inc = NULL, penalty_factor_lat = NULL, fdr_control = FALSE, fdr = 0.2, grid_tuning = FALSE, thresh = 0.001, scale = TRUE, maxit = NULL, inits = NULL, lambda_inc_list = NULL, lambda_lat_list = NULL, nlambda_inc = NULL, nlambda_lat = NULL, gamma_inc = 3, gamma_lat = 3, lambda_min_ratio_inc = 0.1, lambda_min_ratio_lat = 0.1, n_folds = 5, measure_inc = c("c", "auc"), one_se = FALSE, cure_cutoff = 5, parallel = FALSE, seed = NULL, verbose = TRUE, ... )
formula |
an object of class " |
data |
a data.frame in which to interpret the variables named in
the |
subset |
an optional expression indicating which subset of observations to be used in the fitting process, either a numeric or factor variable should be used in subset, not a character variable. All observations are included by default. |
x_latency |
specifies the variables to be included in the latency
portion of the model and can be either a matrix of predictors, a model
formula with the right hand side specifying the latency variables, or the
same data.frame passed to the |
model |
type of regression model to use for the latency portion of mixture cure model. Can be "cox", "weibull", or "exponential" (default is "cox"). |
penalty |
type of penalty function. Can be "lasso", "MCP", or "SCAD" (default is "lasso"). |
penalty_factor_inc |
vector of binary indicators representing the penalty to apply to each incidence coefficient: 0 implies no shrinkage and 1 implies shrinkage. If not supplied, 1 is applied to all incidence variables. |
penalty_factor_lat |
vector of binary indicators representing the penalty to apply to each latency coefficient: 0 implies no shrinkage and 1 implies shrinkage. If not supplied, 1 is applied to all latency variables. |
fdr_control |
logical, if TRUE, model-X knockoffs are used for FDR-controlled variable selection and indices of selected variables are returned (default is FALSE). |
fdr |
numeric value in (0, 1) range specifying the target FDR level to
use for variable selection when |
grid_tuning |
logical, if TRUE a 2-D grid tuning approach is used to
select the optimal pair of |
thresh |
small numeric value. The iterative process stops when the differences between successive expected penalized complete-data log-likelihoods for both incidence and latency components are less than this specified level of tolerance (default is 10^-3). |
scale |
logical, if TRUE the predictors are centered and scaled. |
maxit |
maximum number of passes over the data for each lambda. If not
specified, 100 is applied when |
inits |
an optional list specifiying the initial value for the incidence
intercept ( |
lambda_inc_list |
a numeric vector used to search for the optimal
|
lambda_lat_list |
a numeric vector used to search for the optimal
|
nlambda_inc |
an integer specifying the number of values to search for
the optimal |
nlambda_lat |
an integer specifying the number of values to search
for the optimal |
gamma_inc |
numeric value for the penalization parameter |
gamma_lat |
numeric value for the penalization parameter |
lambda_min_ratio_inc |
numeric value in (0,1) representing the smallest
value for |
lambda_min_ratio_lat |
numeric value in (0.1) representing the smallest
value for |
n_folds |
an integer specifying the number of folds for the k-fold cross-valiation procedure (default is 5). |
measure_inc |
character string specifying the evaluation criterion used
in selecting the optimal |
one_se |
logical, if TRUE then the one standard error rule is applied for selecting the optimal parameters. The one standard error rule selects the most parsimonious model having evaluation criterion no more than one standard error worse than that of the best evaluation criterion (default is FALSE). |
cure_cutoff |
numeric value representing the cutoff time value that represents subjects not experiencing the event by this time are cured. This value is used to produce a proxy for the unobserved cure status when calculating C-statistic and AUC (default is 5 representing 5 years). Users should be careful to note the time scale of their data and adjust this according to the time scale and clinical application. |
parallel |
logical. If TRUE, parallel processing is performed for K-fold
CV using |
seed |
optional integer representing the random seed. Setting the random seed fosters reproducibility of the results. |
verbose |
logical, if TRUE running information is printed to the console (default is FALSE). |
... |
additional arguments. |
b0 |
Estimated intercept for the incidence portion of the model. |
b |
Estimated coefficients for the incidence portion of the model. |
beta |
Estimated coefficients for the latency portion of the model. |
alpha |
Estimated shape parameter if the Weibull model is fit. |
rate |
Estimated rate parameter if the Weibull or exponential model is fit. |
logLik_inc |
Expected penalized complete-data log-likelihood for the incidence portion of the model. |
logLik_lat |
Expected penalized complete-data log-likelihood for the latency portion of the model. |
selected_lambda_inc |
Value of |
selected_lambda_lat |
Value of |
max_c |
Maximum C-statistic achieved. |
max_auc |
Maximum AUC for cure prediction achieved; only output
when |
selected_index_inc |
Indices of selected variables for the
incidence portion of the model when |
selected_index_lat |
Indices of selected variables for the
latency portion of the model when |
call |
the matched call. |
Archer, K. J., Fu, H., Mrozek, K., Nicolet, D., Mims, A. S., Uy, G. L., Stock, W., Byrd, J. C., Hiddemann, W., Braess, J., Spiekermann, K., Metzeler, K. H., Herold, T., Eisfeld, A.-K. (2024) Identifying long-term survivors and those at higher or lower risk of relapse among patients with cytogenetically normal acute myeloid leukemia using a high-dimensional mixture cure model. Journal of Hematology & Oncology, 17:28.
library(survival) set.seed(1234) temp <- generate_cure_data(n = 200, j = 25, n_true = 5, a = 1.8) training <- temp$training fit.cv <- cv_cureem(Surv(Time, Censor) ~ ., data = training, x_latency = training, fdr_control = FALSE, grid_tuning = FALSE, nlambda_inc = 10, nlambda_lat = 10, n_folds = 2, seed = 23, verbose = TRUE) fit.cv.fdr <- cv_cureem(Surv(Time, Censor) ~ ., data = training, x_latency = training, model = "weibull", penalty = "lasso", fdr_control = TRUE, grid_tuning = FALSE, nlambda_inc = 10, nlambda_lat = 10, n_folds = 2, seed = 23, verbose = TRUE)library(survival) set.seed(1234) temp <- generate_cure_data(n = 200, j = 25, n_true = 5, a = 1.8) training <- temp$training fit.cv <- cv_cureem(Surv(Time, Censor) ~ ., data = training, x_latency = training, fdr_control = FALSE, grid_tuning = FALSE, nlambda_inc = 10, nlambda_lat = 10, n_folds = 2, seed = 23, verbose = TRUE) fit.cv.fdr <- cv_cureem(Surv(Time, Censor) ~ ., data = training, x_latency = training, model = "weibull", penalty = "lasso", fdr_control = TRUE, grid_tuning = FALSE, nlambda_inc = 10, nlambda_lat = 10, n_folds = 2, seed = 23, verbose = TRUE)
Fits a penalized Weibull or exponential mixture cure model using the generalized monotone incremental forward stagewise (GMIFS) algorithm with k-fold cross-validation to select the optimal iteration step along the solution path. When FDR controlled variable selection is used, the model-X knockoffs method is applied and indices of selected variables are returned.
cv_curegmifs( formula, data, subset, x_latency = NULL, model = c("weibull", "exponential"), penalty_factor_inc = NULL, penalty_factor_lat = NULL, fdr_control = FALSE, fdr = 0.2, epsilon = 0.001, thresh = 1e-05, scale = TRUE, maxit = 10000, inits = NULL, n_folds = 5, measure_inc = c("c", "auc"), one_se = FALSE, cure_cutoff = 5, parallel = FALSE, seed = NULL, verbose = TRUE, ... )cv_curegmifs( formula, data, subset, x_latency = NULL, model = c("weibull", "exponential"), penalty_factor_inc = NULL, penalty_factor_lat = NULL, fdr_control = FALSE, fdr = 0.2, epsilon = 0.001, thresh = 1e-05, scale = TRUE, maxit = 10000, inits = NULL, n_folds = 5, measure_inc = c("c", "auc"), one_se = FALSE, cure_cutoff = 5, parallel = FALSE, seed = NULL, verbose = TRUE, ... )
formula |
an object of class " |
data |
a data.frame in which to interpret the variables named in the
|
subset |
an optional expression indicating which subset of observations to be used in the fitting process, either a numeric or factor variable should be used in subset, not a character variable. All observations are included by default. |
x_latency |
specifies the variables to be included in the latency
portion of the model and can be either a matrix of predictors, a model
formula with the right hand side specifying the latency variables, or the
same data.frame passed to the |
model |
type of regression model to use for the latency portion of mixture cure model. Can be "weibull" or "exponential"; default is "weibull". |
penalty_factor_inc |
vector of binary indicators representing the penalty to apply to each incidence coefficient: 0 implies no shrinkage and 1 implies shrinkage. If not supplied, 1 is applied to all incidence variables. |
penalty_factor_lat |
vector of binary indicators representing the penalty to apply to each latency coefficient: 0 implies no shrinkage and 1 implies shrinkage. If not supplied, 1 is applied to all latency variables. |
fdr_control |
logical, if TRUE, model-X knockoffs are used for FDR-controlled variable selection and indices of selected variables are returned (default is FALSE). |
fdr |
numeric value in (0, 1) range specifying the target FDR level to
use for variable selection when |
epsilon |
small numeric value reflecting incremental value used to update a coefficient at a given step (default is 0.001). |
thresh |
small numeric value. The iterative process stops when the differences between successive expected penalized complete-data log-likelihoods for both incidence and latency components are less than this specified level of tolerance (default is 10^-5). |
scale |
logical, if TRUE the predictors are centered and scaled. |
maxit |
integer specifying the maximum number of steps to run in the iterative algorithm (default is 10^4). |
inits |
an optional list specifiying the initial value for the incidence
intercept ( |
n_folds |
an integer specifying the number of folds for the k-fold cross-valiation procedure (default is 5). |
measure_inc |
character string specifying the evaluation criterion used
in selecting the optimal |
one_se |
logical, if TRUE then the one standard error rule is applied for selecting the optimal parameters. The one standard error rule selects the most parsimonious model having evaluation criterion no more than one standard error worse than that of the best evaluation criterion (default is FALSE). |
cure_cutoff |
numeric value representing the cutoff time value that represents subjects not experiencing the event by this time are cured. This value is used to produce a proxy for the unobserved cure status when calculating C-statistic and AUC (default is 5 representing 5 years). Users should be careful to note the time scale of their data and adjust this according to the time scale and clinical application. |
parallel |
logical. If TRUE, parallel processing is performed for K-fold
CV using |
seed |
optional integer representing the random seed. Setting the random seed fosters reproducibility of the results. |
verbose |
logical, if TRUE running information is printed to the console (default is FALSE). |
... |
additional arguments. |
b0 |
Estimated intercept for the incidence portion of the model. |
b |
Estimated coefficients for the incidence portion of the model. |
beta |
Estimated coefficients for the latency portion of the model. |
alpha |
Estimated shape parameter if the Weibull model is fit. |
rate |
Estimated rate parameter if the Weibull or exponential model is fit. |
logLik |
Log-likelihood value. |
selected.step.inc |
Iteration step selected for the incidence portion of the model using cross-validation. NULL when fdr_control is TRUE. |
selected.step.lat |
Iteration step selected for the latency portion of the model using cross-validation. NULL when fdr_control is TRUE. |
max.c |
Maximum C-statistic achieved |
max.auc |
Maximum AUC for cure prediction achieved; only output
when |
selected_index_inc |
Indices of selected variables for the
incidence portion of the model when |
selected_index_lat |
Indices of selected variables for the
latency portion of the model when |
call |
the matched call. |
Fu, H., Nicolet, D., Mrozek, K., Stone, R. M., Eisfeld, A. K., Byrd, J. C., Archer, K. J. (2022) Controlled variable selection in Weibull mixture cure models for high-dimensional data. Statistics in Medicine, 41(22), 4340–4366.
library(survival) set.seed(123) temp <- generate_cure_data(n = 100, j = 15, n_true = 3, a = 1.8, rho = 0.2) training <- temp$training fit.cv <- cv_curegmifs(Surv(Time, Censor) ~ ., data = training, x_latency = training, fdr_control = FALSE, maxit = 450, epsilon = 0.01 ,n_folds = 2, seed = 23, verbose = TRUE)library(survival) set.seed(123) temp <- generate_cure_data(n = 100, j = 15, n_true = 3, a = 1.8, rho = 0.2) training <- temp$training fit.cv <- cv_curegmifs(Surv(Time, Censor) ~ ., data = training, x_latency = training, fdr_control = FALSE, maxit = 450, epsilon = 0.01 ,n_folds = 2, seed = 23, verbose = TRUE)
Simulate data under a mixture cure model
generate_cure_data( n = 400, j = 500, nonp = 2, train_prop = 0.75, n_true = 10, a = 1, rho = 0.5, itct_mean = 0.5, cens_ub = 20, alpha = 1, lambda = 2, same_signs = FALSE, model = "weibull" )generate_cure_data( n = 400, j = 500, nonp = 2, train_prop = 0.75, n_true = 10, a = 1, rho = 0.5, itct_mean = 0.5, cens_ub = 20, alpha = 1, lambda = 2, same_signs = FALSE, model = "weibull" )
n |
an integer denoting the total sample size. |
j |
an integer denoting the number of penalized predictors which is the same for both the incidence and latency portions of the model. |
nonp |
an integer less than j denoting the number of unpenalized predictors (which is the same for both the incidence and latency portions of the model. |
train_prop |
a numeric value in 0, 1 representing the fraction of n to be used in forming the training dataset. |
n_true |
an integer denoting the number of variables truly associated with the outcome (i.e., the number of covariates with nonzero parameter values) among the penalized predictors. |
a |
a numeric value denoting the effect size which is the same for both the incidence and latency portions of the model. |
rho |
a numeric value in 0, 1 representing the correlation between adjacent covariates in the same block. See details below. |
itct_mean |
a numeric value representing the expectation of the incidence intercept which controls the cure rate. |
cens_ub |
a numeric value representing the upper bound on the censoring
time distribition which follows a uniform distribution on 0, |
alpha |
a numeric value representing the shape parameter in the Weibull density. |
lambda |
a numeric value representing the rate parameter in the Weibull density. |
same_signs |
logical, if TRUE the incidence and latency coefficients have the same signs. |
model |
type of regression model to use for the latency portion of mixture cure model. Can be "weibull", "GG", "Gompertz", "nonparametric", or "GG_baseline". |
training |
training data.frame which includes Time, Censor, and covariates. |
testing |
testing data.frame which includes Time, Censor, and covariates. |
parameters |
a list including: the indices of true incidence
signals ( |
library(survival) set.seed(1234) data <- generate_cure_data(n = 200, j = 50, n_true = 10, a = 1.8, rho = 0.2) training <- data$training testing <- data$testing fit <- cureem(Surv(Time, Censor) ~ ., data = training, x_latency = training, model = "cox", penalty = "lasso", lambda_inc = 0.05, lambda_lat = 0.05, gamma_inc = 6, gamma_lat = 10)library(survival) set.seed(1234) data <- generate_cure_data(n = 200, j = 50, n_true = 10, a = 1.8, rho = 0.2) training <- data$training testing <- data$testing fit <- cureem(Surv(Time, Censor) ~ ., data = training, x_latency = training, model = "cox", penalty = "lasso", lambda_inc = 0.05, lambda_lat = 0.05, gamma_inc = 6, gamma_lat = 10)
Tests the null hypothesis that the proportion of observations susceptible to the event = 1 against the alternative that the proportion of observations susceptible to the event is < 1. If the null hypothesis is rejected, there is a significant cured fraction.
nonzerocure_test(object, reps = 1000, seed = NULL, plot = FALSE, b = NULL)nonzerocure_test(object, reps = 1000, seed = NULL, plot = FALSE, b = NULL)
object |
a |
reps |
number of simulations on which to base the p-value (default = 1000). |
seed |
optional random seed. |
plot |
logical. If TRUE a histogram of the estimated susceptible proportions over all simulations is produced. |
b |
optional. If specified the maximum observed time for the uniform distribution for generating the censoring times. If not specified, an exponential model is used for generating the censoring times (default). |
proportion_susceptible |
estimated proportion of susceptibles |
proportion_cured |
estimated proportion of those cured |
p_value |
p-value testing the null hypothesis that the proportion of susceptibles = 1 (cured fraction = 0) against the alternative that the proportion of susceptibles < 1 (non-zero cured fraction) |
time_95_percent_of_events |
estimated time at which 95% of events should have occurred |
Maller, R. A. and Zhou, X. (1996) Survival Analysis with Long-Term Survivors. John Wiley & Sons.
survfit, cure_estimate,
sufficient_fu_test
library(survival) set.seed(1234) temp <- generate_cure_data(n = 100, j = 10, n_true = 10, a = 1.8) training <- temp$training km_fit <- survfit(Surv(Time, Censor) ~ 1, data = training) nonzerocure_test(km_fit)library(survival) set.seed(1234) temp <- generate_cure_data(n = 100, j = 10, n_true = 10, a = 1.8) training <- temp$training km_fit <- survfit(Surv(Time, Censor) ~ 1, data = training) nonzerocure_test(km_fit)
This function plots either the coefficient path, the AIC, the cAIC, the BIC,
or the log-likelihood for a fitted curegmifs or cureem object.
This function produces a lollipop plot of the coefficient estimates for a
fitted cv_curegmifs or cv_cureem object.
## S3 method for class 'mixturecure' plot( x, type = c("trace", "AIC", "BIC", "logLik", "cAIC", "mAIC", "mBIC", "EBIC"), xlab = NULL, ylab = NULL, main = NULL, ... )## S3 method for class 'mixturecure' plot( x, type = c("trace", "AIC", "BIC", "logLik", "cAIC", "mAIC", "mBIC", "EBIC"), xlab = NULL, ylab = NULL, main = NULL, ... )
x |
a |
type |
default is |
xlab |
a default x-axis label will be used which can be changed by specifying a user-defined x-axis label. |
ylab |
a default y-axis label will be used which can be changed by specifying a user-defined y-axis label. |
main |
a default main title will be used which can be changed by
specifying a user-defined main title. This option is not used for
|
... |
other arguments. |
this function has no returned value but is called for its side effects
curegmifs, cureem,
coef.mixturecure, summary.mixturecure,
predict.mixturecure
library(survival) set.seed(1234) temp <- generate_cure_data(n = 100, j = 10, n_true = 10, a = 1.8) training <- temp$training fit <- curegmifs(Surv(Time, Censor) ~ ., data = training, x_latency = training, model = "weibull", thresh = 1e-4, maxit = 2000, epsilon = 0.01, verbose = FALSE) plot(fit)library(survival) set.seed(1234) temp <- generate_cure_data(n = 100, j = 10, n_true = 10, a = 1.8) training <- temp$training fit <- curegmifs(Surv(Time, Censor) ~ ., data = training, x_latency = training, model = "weibull", thresh = 1e-4, maxit = 2000, epsilon = 0.01, verbose = FALSE) plot(fit)
This function returns a list the includes the predicted probabilities for
susceptibles as well as the linear predictor for the latency distribution
and a dichotomous risk for latency for a curegmifs, cureem,
cv_curegmifs or cv_cureem fitted object.
## S3 method for class 'mixturecure' predict(object, newdata, model_select = "AIC", ...)## S3 method for class 'mixturecure' predict(object, newdata, model_select = "AIC", ...)
object |
a |
newdata |
an optional data.frame that minimally includes the incidence and/or latency variables to use for predicting the response. If omitted, the training data are used. |
model_select |
for models fit using |
... |
other arguments |
p_uncured |
a vector of probabilities from the incidence portion of the fitted model representing the P(uncured). |
linear_latency |
a vector for the linear predictor from the latency portion of the model. |
latency_risk |
a dichotomous class representing low (below the median) versus high risk for the latency portion of the model. |
curegmifs, cureem,
coef.mixturecure, summary.mixturecure,
plot.mixturecure
library(survival) set.seed(1234) temp <- generate_cure_data(n = 100, j = 10, n_true = 10, a = 1.8) training <- temp$training fit <- curegmifs(Surv(Time, Censor) ~ ., data = training, x_latency = training, model = "weibull", thresh = 1e-4, maxit = 2000, epsilon = 0.01, verbose = FALSE) predict_train <- predict(fit) names(predict_train) testing <- temp$testing predict_test <- predict(fit, newdata = testing)library(survival) set.seed(1234) temp <- generate_cure_data(n = 100, j = 10, n_true = 10, a = 1.8) training <- temp$training fit <- curegmifs(Surv(Time, Censor) ~ ., data = training, x_latency = training, model = "weibull", thresh = 1e-4, maxit = 2000, epsilon = 0.01, verbose = FALSE) predict_train <- predict(fit) names(predict_train) testing <- temp$testing predict_test <- predict(fit, newdata = testing)
This function prints the names of the list objects from a curegmifs,
cureem, cv_cureem, or cv_curegmifs fitted model.
## S3 method for class 'mixturecure' print(x, ...)## S3 method for class 'mixturecure' print(x, ...)
x |
a |
... |
other arguments. |
names of the objects in a mixturecure object fit using cureem,
curegmifs, cv_cureem, or cv_curegmifs.
The contents of an mixturecure fitted object differ depending
upon whether the EM (cureem) or GMIFS (curegmifs) algorithm is
used for model fitting. Also, the output differs depending upon whether
x_latency is specified in the model (i.e., variables are included in
the latency portion of the model fit) or only terms on the right hand
side of the equation are included (i.e., variables are included in the
incidence portion of the model).
curegmifs, cureem,
coef.mixturecure, summary.mixturecure,
plot.mixturecure, predict.mixturecure
library(survival) set.seed(1234) temp <- generate_cure_data(n = 100, j = 10, n_true = 10, a = 1.8) training <- temp$training fit <- curegmifs(Surv(Time, Censor) ~ ., data = training, x_latency = training, model = "weibull", thresh = 1e-4, maxit = 2000, epsilon = 0.01, verbose = FALSE) print(fit)library(survival) set.seed(1234) temp <- generate_cure_data(n = 100, j = 10, n_true = 10, a = 1.8) training <- temp$training fit <- curegmifs(Surv(Time, Censor) ~ ., data = training, x_latency = training, model = "weibull", thresh = 1e-4, maxit = 2000, epsilon = 0.01, verbose = FALSE) print(fit)
Tests for sufficient follow-up using a Kaplan-Meier fitted object.
sufficient_fu_test(object)sufficient_fu_test(object)
object |
a |
p_value |
p-value from testing the null hypothesis that there was not sufficient follow-up against the alternative that there was sufficient follow-up |
n_n |
total number of events that occurred at time > pmax(0, 2*(last observed event time)-(last observed time)) and < the last observed event time |
N |
number of observations in the dataset |
Maller, R. A. and Zhou, X. (1996) Survival Analysis with Long-Term Survivors. John Wiley & Sons.
survfit, cure_estimate,
nonzerocure_test
library(survival) set.seed(1234) temp <- generate_cure_data(n = 100, j = 10, n_true = 10, a = 1.8) training <- temp$training km_fit <- survfit(Surv(Time, Censor) ~ 1, data = training) sufficient_fu_test(km_fit)library(survival) set.seed(1234) temp <- generate_cure_data(n = 100, j = 10, n_true = 10, a = 1.8) training <- temp$training km_fit <- survfit(Surv(Time, Censor) ~ 1, data = training) sufficient_fu_test(km_fit)
summary method for a mixturecure object fit using curegmifs,
cureem, cv_curegmifs, or cv_cureem.
## S3 method for class 'mixturecure' summary(object, ...)## S3 method for class 'mixturecure' summary(object, ...)
object |
a |
... |
other arguments. |
prints the following items extracted from the object fit using
curegmifs or cureem: the step and value that maximizes the
log-likelihood; the step and value that minimizes the AIC, modified AIC
(mAIC), corrected AIC (cAIC), BIC, modified BIC (mBIC), and extended BIC
(EBIC). Returns log-likelihood, AIC, and BIC if the object was fit using
cv_curegmifs or cv_cureem at the optimal cross-validated values
if no FDR control; the number of non-zero incidence and latency variables is
returned when cross-validation is used together with FDR control.
curegmifs, cureem,
coef.mixturecure, plot.mixturecure,
predict.mixturecure
library(survival) set.seed(1234) temp <- generate_cure_data(n = 100, j = 10, n_true = 10, a = 1.8) training <- temp$training fit <- curegmifs(Surv(Time, Censor) ~ ., data = training, x_latency = training, model = "weibull", thresh = 1e-4, maxit = 2000, epsilon = 0.01, verbose = FALSE) summary(fit)library(survival) set.seed(1234) temp <- generate_cure_data(n = 100, j = 10, n_true = 10, a = 1.8) training <- temp$training fit <- curegmifs(Surv(Time, Censor) ~ ., data = training, x_latency = training, model = "weibull", thresh = 1e-4, maxit = 2000, epsilon = 0.01, verbose = FALSE) summary(fit)