# Fast implementation of cumulative density function, survival function, ... for scenarios with progression ```r 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) ``` ## Arguments - `hazard_before`: hazard for death before progression - `prog_rate`: hazard rate for progression - `hazard_after`: hazard for death after progression ## Returns A function with one parameter, a vector of times/probabilities where the function should be evaluated. ## 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. ## 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 ## Examples ```r 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") ```

progression_cdf_fun function