Description Usage Arguments Value References See Also Examples
For rightcensored data, fit a regular Cox cure rate model (Kuk and Chen, 1992; Sy and Taylor, 2000) via an EM algorithm. For rightcensored data with uncertain event status, fit the Cox cure model proposed by Wang et al. (2020).
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55  cox_cure(
surv_formula,
cure_formula,
time,
event,
data,
subset,
contrasts = NULL,
bootstrap = 0,
firth = FALSE,
surv_start = NULL,
cure_start = NULL,
surv_offset = NULL,
cure_offset = NULL,
em_max_iter = 200,
em_rel_tol = 1e05,
surv_max_iter = 30,
surv_rel_tol = 1e05,
cure_max_iter = 30,
cure_rel_tol = 1e05,
tail_completion = c("zero", "exp", "zerotau"),
tail_tau = NULL,
pmin = 1e05,
early_stop = TRUE,
verbose = FALSE,
...
)
cox_cure.fit(
surv_x,
cure_x,
time,
event,
cure_intercept = TRUE,
bootstrap = 0,
firth = FALSE,
surv_start = NULL,
cure_start = NULL,
surv_offset = NULL,
cure_offset = NULL,
surv_standardize = TRUE,
cure_standardize = TRUE,
em_max_iter = 200,
em_rel_tol = 1e05,
surv_max_iter = 30,
surv_rel_tol = 1e05,
cure_max_iter = 30,
cure_rel_tol = 1e05,
tail_completion = c("zero", "exp", "zerotau"),
tail_tau = NULL,
pmin = 1e05,
early_stop = TRUE,
verbose = FALSE,
...
)

surv_formula 
A formula object starting with 
cure_formula 
A formula object starting with 
time 
A numeric vector for the observed survival times. 
event 
A numeric vector for the event indicators. 
data 
An optional data frame, list, or environment that contains the
covariates and response variables ( 
subset 
An optional logical vector specifying a subset of observations to be used in the fitting process. 
contrasts 
An optional list, whose entries are values (numeric
matrices or character strings naming functions) to be used as
replacement values for the contrasts replacement function and whose
names are the names of columns of data containing factors. See

bootstrap 
An integer representing the number of bootstrap samples for
estimating standard errors of the coefficient estimates. The bootstrap
procedure will not run with 
firth 
A logical value indicating whether to use Firth's
biasreduction method (Firth, 1993) in the logistic model component.
The default value is 
surv_start, cure_start 
An optional numeric vector representing the
starting values for the survival model component or the incidence model
component. If 
surv_offset, cure_offset 
An optional numeric vector representing the
offset term in the survival model compoent or the incidence model
component. The function will internally try to find values of the
specified variable in the 
em_max_iter 
A positive integer specifying the maximum iteration
number of the EM algorithm. The default value is 
em_rel_tol 
A positive number specifying the tolerance that determines
the convergence of the EM algorithm in terms of the convergence of the
covariate coefficient estimates. The tolerance is compared with the
relative change between estimates from two consecutive iterations, which
is measured by ratio of the L1norm of their difference to the sum of
their L1norm. The default value is 
surv_max_iter, cure_max_iter 
A positive integer specifying the maximum
iteration number of the Mstep routine related to the survival model
component or the incidence model component. The default value is

surv_rel_tol, cure_rel_tol 
A positive number specifying the tolerance
that determines the convergence of the Mstep related to the survival
model component or the incidence model component in terms of the
convergence of the covariate coefficient estimates. The tolerance is
compared with the relative change between estimates from two consecutive
iterations, which is measured by ratio of the L1norm of their
difference to the sum of their L1norm. The default value is

tail_completion 
A character string specifying the tail completion
method for conditional survival function. The available methods are

tail_tau 
A numeric number specifying the time of zerotail
completion. It will be used only if 
pmin 
A numeric number specifying the minimum value of probabilities
for sake of numerical stability. The default value is 
early_stop 
A logical value specifying whether to stop the iteration
once the negative loglikelihood unexpectedly increases, which may
suggest convergence on likelihood, or indicate numerical issues or
implementation bugs. The default value is 
verbose 
A logical value. If 
... 
Other arguments for future usage. A warning will be thrown if any invalid argument is specified. 
surv_x 
A numeric matrix for the design matrix of the survival model component. 
cure_x 
A numeric matrix for the design matrix of the cure rate model
component. The design matrix should exclude an intercept term unless we
want to fit a model only including the intercept term. In that case, we
need further set 
cure_intercept 
A logical value specifying whether to add an intercept
term to the cure rate model component. If 
surv_standardize 
A logical value specifying whether to standardize
the covariates for the survival model part. If 
cure_standardize 
A logical value specifying whether to standardize
the covariates for the cure rate model part. If 
cox_cure
object for regular Cox cure rate model or
cox_cure_uncer
object for Cox cure rate model with uncertain events.
Firth, D. (1993). Bias reduction of maximum likelihood estimates. Biometrika, 80(1), 27–38.
Kuk, A. Y. C., & Chen, C. (1992). A mixture model combining logistic regression with proportional hazards regression. Biometrika, 79(3), 531–541.
Peng, Y. (2003). Estimating baseline distribution in proportional hazards cure models. Computational Statistics & Data Analysis, 42(12), 187–201.
Sy, J. P., & Taylor, J. M. (2000). Estimation in a Cox proportional hazards cure model. Biometrics, 56(1), 227–236.
Wang, W., Luo, C., Aseltine, R. H., Wang, F., Yan, J., & Chen, K. (2020). Suicide Risk Modeling with Uncertain Diagnostic Records. arXiv preprint arXiv:2009.02597.
cox_cure_net
for regularized Cox cure rate model with
elasticnet penalty.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76  library(intsurv)
### regular Cox cure rate model ======================================
## 1. simulate rightcensored data with a cure fraction
set.seed(123)
n_obs < 2e2
p < 5
x_mat < matrix(rnorm(n_obs * p), nrow = n_obs, ncol = p)
colnames(x_mat) < paste0("x", seq_len(p))
cure_beta < rep(0.5, p)
b0 <  1
expit < binomial()$linkinv
ncure_prob < expit(as.numeric(b0 + x_mat %*% cure_beta))
is_cure < 1  rbinom(n_obs, size = 1, prob = ncure_prob)
surv_beta < rep(0.5, p)
risk_score < as.numeric(x_mat %*% surv_beta)
event_time < rexp(n_obs, exp(as.numeric(x_mat %*% surv_beta)))
censor_time < 10
event < ifelse(event_time < censor_time & ! is_cure, 1, 0)
obs_time < ifelse(event > 0, event_time, censor_time)
## modelfitting from given design matrices
fit1 < cox_cure.fit(x_mat, x_mat, obs_time, event, bootstrap = 30)
summary(fit1)
## coefficient estimates from both model parts
coef(fit1)
## or a particular part
coef(fit1, "surv")
coef(fit1, "cure")
## weighted concordance index (Cindex)
fit1$model$c_index
## which also can be computed as follows
cIndex(time = obs_time, event = event,
risk_score = fit1$fitted$surv_xBeta,
weight = ifelse(event > 0, 1, fit1$fitted$susceptible_prob))
## 2. create a toy dataset
toy_dat < data.frame(time = obs_time, status = event)
toy_dat$group < cut(abs(x_mat[, 1L]), breaks = c(0, 0.5, 1, 3, Inf),
labels = LETTERS[1:4])
toy_dat < cbind(toy_dat, as.data.frame(x_mat[,  1L, drop = FALSE]))
## modelfitting from given model formula
fit2 < cox_cure(~ x3 + x4 + group, ~ group + x3 + offset(x2),
time = time, event = status, surv_offset = x2,
data = toy_dat, subset = group != "D", bootstrap = 30)
summary(fit2)
## get BIC's
BIC(fit1)
BIC(fit2)
BIC(fit1, fit2)
### Cox cure rate model with uncertain event status ==================
## simulate sample data
sim_dat < simData4cure(nSubject = 200, max_censor = 10, lambda_censor = 0.1,
survMat = x_mat, cureMat = x_mat, b0 = 1)
table(sim_dat$case)
table(sim_dat$obs_event, useNA = "ifany")
## use formula
fit3 < cox_cure(~ x1 + x2 + x3, ~ z1 + z2 + z3,
time = obs_time, event = obs_event, data = sim_dat)
summary(fit3)
## use design matrix
fit4 < cox_cure.fit(x_mat, x_mat, time = sim_dat$obs_time,
event = sim_dat$obs_event)
summary(fit4)
## get BIC's
BIC(fit3, fit4)

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