SmoothHazard (version 2024.04.10)

intensity: 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)

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)

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.

Author

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

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.

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)

# \donttest{
  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               
# }