F.window.Weibull {joint.Cox}

Dynamic prediction of death under the joint frailty-copula model (the Weibull baseline hazard functions)

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).

Usage

F.window.Weibull(time, width, X, Z1, Z2, beta1, beta2, eta, theta, alpha, 
                  scale1, shape1,scale2,shape2, xi1, xi3, Fplot = TRUE)

Arguments

time

prediction time (=t)

width

length of window (=w)

X

time of tumour progression < time

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

scale1

scale parameter related to the baseline hazard for progression

shape1

shape parameter related to the baseline hazard for progression

scale2

scale parameter related to the baseline hazard for death

shape2

shape parameter 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

width

w

X

X

F_event_at_X

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

F_noevent

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

Author(s)

Sayaka Shinohara, 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

Shinohara S, Lin YH, Michimae H, Emura T (2020), Dynamic lifetime prediction using a Weibull-based bivariate failure time model: a meta-analysis of individual-patient data, Comm Stat Simul, DOI:10.1080/03610918.2020.1855449

Examples

w=1
par(mfrow=c(1,2))
F.window.Weibull(time=1,X=0.2,width=w,Z1=1,Z2=1,beta1=1,beta2=1,eta=0.5,theta=8,
                 alpha=1,scale1=1,shape1=1,scale2=1,shape2=1,xi1=0,xi3=3)
F.window.Weibull(time=1,X=0.8,width=w,Z1=1,Z2=1,beta1=1,beta2=1,eta=0.5,theta=8,
                 alpha=1,scale1=1,shape1=1,scale2=1,shape2=1,xi1=0,xi3=3)