F.prediction {joint.Cox}

Dynamic prediction of death

Description

Dynamic prediction of death using a joint frailty-copula model. Probability of death between t and t+w is calculated given a tumour progression time X and covariates Z1 and Z2. If X<=t, the prediction probability is F(t,t+w|X=x, Z1, Z2). If X>t, the prediction probability is F(t,t+w|X>t, Z1, Z2). This function is a simpler version of F.windows. The guide for using this function shall be explained by Emura et al. (2019).

Usage

F.prediction(time, widths, X, Z1, Z2, beta1, beta2, eta, theta, alpha,
 g, h, xi1, xi3, Fplot = TRUE)

Arguments

time

prediction time (=t)

widths

length of window (=w)

X

time of tumour progression; if tumour progression does not occur before time t, one can set an arbitrary value X greater than t

Z1

a vector of covariates for progression

Z2

a vector of covariates for death

beta1

a vector of regression coefficients for progression

beta2

a vector of regression coefficients for death

eta

frailty variance

theta

copula parameter

alpha

parameter related to frailty; usually alpha=1

g

parameters related to the baseline hazard for progression

h

parameters related to the baseline hazard for death

xi1

lower bound for time-to-event

xi3

upper bound for time-to-death

Fplot

if FALSE, the plot is not shown

Details

Predicted probability of death is calculated given the event status (X<=t or X>t) and covariates (Z1 and Z2).

Value

time

t

widths

w

X

X

F

F(t,t+w|X=x, Z1, Z2) or F(t,t+w|X>t, Z1, Z2)

Author(s)

Takeshi Emura

References

Emura T, Nakatochi M, Matsui S, Michimae H, Rondeau V (2018), Personalized dynamic prediction of death according to tumour progression and high-dimensional genetic factors: meta-analysis with a joint model, Stat Methods Med Res 27(9):2842-58

Emura T, Michimae H, Matsui S (2019-), A clinician's guide for dynamic risk prediction of death using an R package joint.Cox, submitted for publication.

Examples

w=c(0,0.5,1,1.5,2)
par(mfrow=c(1,2))
F.prediction(time=1,X=0.8,widths=w,Z1=1,Z2=1,beta1=1,beta2=1,eta=0.5,theta=8,
         alpha=1,g=rep(1,5),h=rep(1,5),xi1=0,xi3=3)
F.prediction(time=1,X=1.5,widths=w,Z1=1,Z2=1,beta1=1,beta2=1,eta=0.5,theta=8,
         alpha=1,g=rep(1,5),h=rep(1,5),xi1=0,xi3=3)