Survival Distributions with piece-wise Constant Hazards and multiple states (function factories)

Densitiy, distribution function, hazard function, cumulative hazard function and survival function of multi-state survival functions.

Those functions return functions of one parameter that can be evaluated to give the density, distribution function, ... The parameters t, Q, pi and abs are checked only once and not at every function evaluation.

Usage

dmstate_fun(t, Q, pi, abs)

pmstate_fun(t, Q, pi, abs)

hmstate_fun(t, Q, pi, abs)

chmstate_fun(t, Q, pi, abs)

smstate_fun(t, Q, pi, abs)

multistate_functions(t, Q, pi, abs)

Arguments

t

vector of left interval borders

Q

Q-matrices of the process, see details

pi

initial distribution

abs

indicator vector of absorbing states, see details

Value

dmstate_fun gives the density.

pmstate_fun gives the distribution function

hmstate_fun gives the hazard function.

chmstate_fun gives the cumulative hazard function.

smstate_fun gives the survival function.

multistate_functions gives an object of class "miniPCH"

Functions

• dmstate_fun(): density of survival distributions with piece-wise constant hazards and multiple states

• pmstate_fun(): distribution function of survival distributions with piece-wise constant hazards and multiple states

• hmstate_fun(): hazard function of survival distributions with piece-wise constant hazards and multiple states

• chmstate_fun(): cumulative hazard function of survival distributions with piece-wise constant hazards and multiple states

• smstate_fun(): survival function of survival distributions with piece-wise constant hazards and multiple states

See also

dmstate

Examples

Tint <- 0
Q <- matrix(
  c(
    -0.3, 0.2, 0.1,
    0  ,-0.4, 0.4,
    0  ,   0,   0
  ), 3, 3, byrow = TRUE
)
dim(Q) <- c(3,3,1)
pi <- c(1,0,0)
abs <- c(0,0,1)

my_density           <-  dmstate_fun(Tint, Q, pi, abs)
my_distribution      <-  pmstate_fun(Tint, Q, pi, abs)
my_hazard            <-  hmstate_fun(Tint, Q, pi, abs)
my_cumulative_hazard <- chmstate_fun(Tint, Q, pi, abs)
my_survival          <-  smstate_fun(Tint, Q, pi, abs)

t <- seq(0,20, by=0.1)
par(mfrow=c(3,2))
plot(t, my_density(t), type="l")
plot(t, my_distribution(t), type="l")
plot(t, my_hazard(t), type="l", ylim=c(0,1))
plot(t, my_cumulative_hazard(t), type="l")
plot(t, my_survival(t), type="l")
Tint <- 0
Q <- matrix(
  c(
    -0.3, 0.2, 0.1,
    0  ,-0.4, 0.4,
    0  ,   0,   0
  ), 3, 3, byrow = TRUE
)
dim(Q) <- c(3,3,1)
pi <- c(1,0,0)
abs <- c(0,0,1)

my_obj <- multistate_functions(Tint, Q, pi, abs)
t <- seq(0,20, by=0.1)
plot(t, my_obj$d(t), type="l")