BFI (version 2.0.1)

hazards.fun: Compute the estimated (baseline/cumulative) hazard and (baseline) survival functions

Description

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.

Usage

hazards.fun(time,
            z = NULL,
            p,
            theta_hat,
            basehaz = c("weibul", "exp", "gomp", "poly", "pwexp"),
            q_max,
            timax)

Value

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.

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".

Author

Hassan Pazira
Maintainer: Hassan Pazira

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.

References

Pazira H., Massa E., Weijers J.A.M., Coolen A.C.C. and Jonker M.A. (2024). Bayesian Federated Inference for Survival Models, arXiv. <https://arxiv.org/abs/2404.17464>

See Also

MAP.estimation

Examples

# 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))