predict.PHcure {penPHcure}

Predict method for PHcure.object

Description

Compute probabilities to be susceptible and survival probabilities (conditional on being susceptible) for a model fitted by penPHcure with the argument pen.type = "none".

Usage

## S3 method for class 'PHcure'
predict(object, newdata, X = NULL,...)

Arguments

object

an object of class PHcure.object.

newdata

a data.frame in counting process format.

X

[optional] a matrix of time-invariant covariates. It is not required, unless argument X was supplied in the call to the penPHcure function.

...

ellipsis to pass extra arguments.

Details

If argument X was not supplied in the call to the penPHcure function, the probabilities to be susceptible are computed using the covariates retrieved using the same which.X method as in the penPHcure function call.

Value

An object of class predict.PHcure, a list including the following elements:

CURE

a numeric vector containing the probabilities to be susceptible to the event of interest:

P(Y_i=1|x_i) = \frac{ e^{\mathbf{x}_i'\hat{\mathbf{b}}} }{1+e^{\mathbf{x}_i'\hat{\mathbf{b}}}},

where \mathbf{x}_i is a vector of time-invariant covariates and \hat{\mathbf{b}} is a vector of estimated coefficients.

SURV

a numeric vector containing the survival probabilities (conditional on being susceptible to the event of interest):

S(t_i|Y_i=1,\bar{\mathbf{z}}_i(t))=\exp\left(-\sum_{j=1}^K (t_{(j-1)}-t_{(j)}) \hat{\lambda}_{0j} I(t_{(j)}\leq t_i) e^{\mathbf{z}_i(t_{(j)})\hat{\boldsymbol{\beta}}}\right),

where t_{(1)}<t_{(2)}<...<t_{(K)} denotes the K ordered event-times, \mathbf{z}_i(t) is a vector of time-varying covariates, \hat{\boldsymbol{\beta}} is a vector of estimated coefficients and \hat{\lambda}_{0j} is the estimated baseline hazard function (constant in the interval (t_{(j-1)},t_{(j)}]).

Examples

# Generate some data (for more details type ?penPHcure.simulate in your console)
set.seed(12) # For reproducibility
data <- penPHcure.simulate(N=250)
 
# Fit standard cure model (without inference)
fit <- penPHcure(Surv(time = tstart,time2 = tstop,
                      event = status) ~ z.1 + z.2 + z.3 + z.4,
                 cureform = ~ x.1 + x.2 + x.3 + x.4,data = data)

# Use the predict method to obtain the probabilities for the fitted model
pred.fit <- predict(fit,data)

# Use the predict method to make prediction for new observations.
#  For example, two individuals censored at time 0.5 and 1.2, respectively,
#  and all cavariates equal to 1.
newdata <- data.frame(tstart=c(0,0),tstop=c(0.5,1.2),status=c(0,0),
                      z.1=c(1,1),z.2=c(1,1),z.3=c(1,1),z.4=c(1,1),
                      x.1=c(1,1),x.2=c(1,1),x.3=c(1,1),x.4=c(1,1))
pred.fit.newdata <- predict(fit,newdata)
# The probabilities to be susceptible are:
pred.fit.newdata$CURE
# [1] 0.6761677 0.6761677
# The survival probabilities (conditional on being susceptible) are:
pred.fit.newdata$SURV
# [1] 0.5591570 0.1379086