intensity {SmoothHazard} | R Documentation |
M-spline estimate of the transition intensity function and the cumulative transition intensity function for survival and illness-death models
intensity(times, knots, number.knots, theta, linear.predictor = 0)
times |
Time points at which to estimate the intensity function |
knots |
Knots for the M-spline |
number.knots |
Number of knots for the M-splines (and I-splines see details) |
theta |
The coefficients for the linear combination of M-splines (and I-splines see details) |
linear.predictor |
Linear predictor beta*Z. When it is non-zero,
transition and cumulative transition are multiplied by |
The estimate of the transition intensity function is a linear
combination of M-splines and the estimate of the cumulative transition
intensity function is a linear combination of I-splines (the integral of a
M-spline is called I-spline). The coefficients theta
are the same for
the M-splines and I-splines.
Important: the theta parameters returned by idm
and shr
are in fact
the square root of the splines coefficients. See examples.
This function is a R-translation of a corresponding Fortran function called susp
. susp
is
used internally by idm
and shr
.
times |
The time points at which the following estimates are evaluated. |
intensity |
The transition intensity function evaluated at |
cumulative.intensity |
The cumulative transition intensity function evaluated at |
survival |
The "survival" function, i.e., exp(-cumulative.intensity) |
R: Celia Touraine <Celia.Touraine@isped.u-bordeaux2.fr> and Thomas Alexander Gerds <tag@biostat.ku.dk> Fortran: Pierre Joly <Pierre.Joly@isped.u-bordeaux2.fr>
data(testdata) fit.su <- shr(Hist(time=list(l, r), id) ~ cov, data = testdata,method = "Splines",CV = TRUE) intensity(times = fit.su$time, knots = fit.su$knots, number.knots = fit.su$nknots, theta = fit.su$theta^2) ## Not run: data(Paq1000) fit.idm <- idm(formula02 = Hist(time = t, event = death, entry = e) ~ certif, formula01 = Hist(time = list(l,r), event = dementia) ~ certif, formula12 = ~ certif, method = "Splines", data = Paq1000) # Probability of survival in state 0 at age 80 for a subject with no cep given that he is in state 0 at 70 su0 <- (intensity(times = 80, knots = fit.idm$knots01, number.knots = fit.idm$nknots01, theta = fit.idm$theta01^2)$survival *intensity(times = 80, knots = fit.idm$knots02, number.knots = fit.idm$nknots02, theta = fit.idm$theta02^2)$survival)/ (intensity(times = 70, knots = fit.idm$knots01, number.knots = fit.idm$nknots01, theta = fit.idm$theta01^2)$survival *intensity(times = 70, knots = fit.idm$knots02, number.knots = fit.idm$nknots02, theta = fit.idm$theta02^2)$survival) # Same result as: predict(fit.idm, s = 70, t = 80, conf.int = FALSE) # see first element ## End(Not run)