intensity: M-spline estimate of the transition intensity function

In tagteam/SmoothHazard: Estimation of Smooth Hazard Models for Interval-Censored Data with Applications to Survival and Illness-Death Models

M-spline estimate of the transition intensity function

Description

M-spline estimate of the transition intensity function and the cumulative transition intensity function for survival and illness-death models

Usage

intensity(times, knots, number.knots, theta, linear.predictor = 0)

Arguments

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 exp(linear.predictor). Default is zero.

Details

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.

Value

times	The time points at which the following estimates are evaluated.
intensity	The transition intensity function evaluated at times.
cumulative.intensity	The cumulative transition intensity function evaluated at times
survival	The "survival" function, i.e., exp(-cumulative.intensity)

Author(s)

R: Celia Touraine <[e-mail]> and Thomas Alexander Gerds <[e-mail]> Fortran: Pierre Joly <[e-mail]>

See Also

shr, idm

Examples

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)

tagteam/SmoothHazard documentation built on April 5, 2024, 6:32 a.m.