# Compute the estimated (baseline/cumulative) hazard and (baseline) survival functions For a given vector of times, `hazards.fun` computes the estimated baseline hazard, cumulative baseline hazard, hazard, baseline survival, and survival functions. It can be used for prediction on a new sample. ```r hazards.fun(time, z = NULL, p, theta_hat, basehaz = c("weibul", "exp", "gomp", "poly", "pwexp"), q_max, timax) ``` ## Arguments - `time`: the vector containing the time values for which the hazard rate is computed. If the argument `z` is not `NULL`, then the length of the argument `time` should be the number of columns of `z`, which is $p$. - `z`: a new observation vector of length $p$. If `z = NULL` (the default), then the relative risk ($\boldsymbol{z}^{\top} \boldsymbol{\beta}$) is considered a vector of 1 with length $n$. - `p`: the number of coefficients. It is taken equal to the number of elements of the argument `z`, if `z` is not `NULL`. - `theta_hat`: a vector contains the values of the estimated parameters. The first $p$ values represent the coefficient parameters ($\boldsymbol{\beta}$), while the remaining values pertain to the parameters of the baseline hazard function ($\boldsymbol{\omega}$). - `basehaz`: a character string representing one of the available baseline hazard functions; `exponential` (`"exp"`), `Weibull` (`"weibul"`, the default), `Gompertz` (`"gomp"`), `exponentiated polynomial` (`"poly"`), and `piecewise exponential` (`"pwexp"`). Can be abbreviated. - `q_max`: a value represents the order of the exponentiated polynomial baseline hazard function. This argument should only be used when `basehaz = "poly"`. In the case of multiple centers, the maximum value of the orders should be used. `ql.LRT()` can be used for obtaining of the order of each center. - `timax`: a value represents the minimum (or maximum) value of the maximum times observed in the different centers. This argument should only be used when `basehaz = "pwexp"`. ## Details `hazards.fun` computes the estimated baseline hazard, cumulative baseline hazard, hazard, baseline survival, and survival functions at different time points specified in the argument `time`. The function `hazards.fun()` can be used for prediction purposes with new sample. The arguments `time` and `z` should be provided for the new data. ## Returns `hazards.fun` returns a list containing the following components: - **bhazard**: the vector of estimates of the baseline hazard function at the time points given by the argument `time`; - **cbhazard**: the vector of estimates of the cumulative baseline hazard function at the time points specified in the argument `time`; - **bsurvival**: the vector of estimates of the baseline survival function at the time points given by the argument `time`; - **hazard**: the vector of estimates of the hazard function at the time points given by the argument `time`; - **chazard**: the vector of estimates of the cumulative hazard function at the time points specified in the argument `time`; - **survival**: the vector of estimates of the survival function at the time points given by the argument `time`. ## References Pazira H., Massa E., Weijers J.A.M., Coolen A.C.C. and Jonker M.A. (2025b). **Bayesian Federated Inference for Survival Models**, **Journal of Applied Statistics (Accepted)**. ## Author(s) Hassan Pazira Maintainer: Hassan Pazira hassan.pazira@radboudumc.nl ## See Also `MAP.estimation` ## Examples ```r # Setting a seed for reproducibility set.seed(1123) ##------------------------- ## Simulating Survival data ##------------------------- n <- 40 p <- 7 Original_data <- data.frame(matrix(rnorm((n+1) * p), (n+1), p)) X <- Original_data[1:n,] X_new <- Original_data[(n+1),] # Simulating survival data from Exponential distribution # with a predefined censoring rate of 0.2: Orig_y <- surv.simulate(Z = Original_data, beta = rep(1,p), a = exp(1), cen_rate = 0.2, gen_data_from = "exp")$D[[1]][,1:2] y <- Orig_y[1:n,] y_new <- Orig_y[(n+1),] time_points <- seq(0, max(y$time), length.out=20) #------------------------ # Weibull baseline hazard #------------------------ Lambda <- inv.prior.cov(X, lambda = c(0.5, 1), family = 'survival', basehaz = 'weibul') fit_weib <- MAP.estimation(y, X, family = 'survival', Lambda = Lambda, basehaz = "weibul") # reltive risk is 1: hazards.fun(time = time_points, p = p, theta_hat = fit_weib$theta_hat, basehaz = "weibul") #------------------------- # Gompertz baseline hazard #------------------------- fit_gomp <- MAP.estimation(y, X, family = 'survival', Lambda = Lambda, basehaz = "gomp") # different time points hazards.fun(time=1:max(y*2), p = p, theta_hat = fit_gomp$theta_hat, basehaz = "gomp") ##---------------------------- ## Prediction for a new sample ##---------------------------- ## Exponentiated polynomial (poly) baseline hazard: Lambda <- inv.prior.cov(X, lambda = c(0.5, 1), family = 'survival', basehaz = "poly") fit_poly <- MAP.estimation(y, X, family = 'survival', Lambda = Lambda, basehaz = "poly") hazards.fun(time = y_new$time, z = X_new, theta_hat = fit_poly$theta_hat, basehaz = "poly", q_max = fit_poly$q_l) ## Piecewise Exponential (pwexp) baseline hazard: Lambda <- inv.prior.cov(X, lambda = c(0.5, 1), family = 'survival', basehaz = "pwexp") fit_pw <- MAP.estimation(y, X, family='survival', Lambda=Lambda, basehaz="pwexp", min_max_times = max(y)) hazards.fun(time = y_new$time, z = X_new, theta_hat = fit_pw$theta_hat, basehaz = "pwexp", timax = max(y)) ```

hazards.fun function