SimNPH (version 0.5.7)

progression_cdf_fun: Fast implementation of cumulative density function, survival function, ... for scenarios with progression

Description

Fast implementation of cumulative density function, survival function, ... for scenarios with progression

Usage

progression_cdf_fun(hazard_before, prog_rate, hazard_after)
progression_surv_fun(hazard_before, prog_rate, hazard_after)
progression_pdf_fun(hazard_before, prog_rate, hazard_after)
progression_haz_fun(hazard_before, prog_rate, hazard_after)
progression_quant_fun(hazard_before, prog_rate, hazard_after)

Value

A function with one parameter, a vector of times/probabilities where the function should be evaluated.

Arguments

hazard_before

hazard for death before progression

prog_rate

hazard rate for progression

hazard_after

hazard for death after progression

Functions

• progression_cdf_fun(): cumulative density function for progression scenario

• progression_surv_fun(): survival function for progression scenario

• progression_pdf_fun(): probability density function for progression scenario

• progression_haz_fun(): hazard function for progression scenario

• progression_quant_fun(): quantile function for progression scenario

Details

Calculations are done by viewing the disease process as a three state (non-progressed disease, progressed disease, death) continuous time markov chain. Calculations can then easily be done using the matrix exponential function and Q-matrices.

Examples

cdf <- progression_cdf_fun(
  hazard_before = m2r(48),
  prog_rate = m2r(18),
  hazard_after = m2r(6)
)
t <- 0:1000
plot(t, cdf(t), type="l")
surv <- progression_surv_fun(
  hazard_before = m2r(48),
  prog_rate = m2r(18),
  hazard_after = m2r(6)
)
t <- 0:1000
plot(t, surv(t), type="l")
pdf <- progression_pdf_fun(
  hazard_before = m2r(48),
  prog_rate = m2r(18),
  hazard_after = m2r(6)
)
t <- 0:1000
plot(t, pdf(t), type="l")
haz <- progression_haz_fun(
  hazard_before = m2r(48),
  prog_rate = m2r(18),
  hazard_after = m2r(6)
)
t <- 0:1000
plot(t, haz(t), type="l")
quant <- progression_quant_fun(
  hazard_before = m2r(48),
  prog_rate = m2r(18),
  hazard_after = m2r(6)
)
p <- seq(0,0.99, by=.01)
plot(p, quant(p), type="l")