R/rootweibull.R

In spatsurv: Bayesian Spatial Survival Analysis with Parametric Proportional Hazards Models

##' rootWeibullHaz function
##'
##' A function to define a parametric proportional hazards model where the baseline hazard is taken from the Weibull model.
##' This function returns an object inheriting class 'basehazardspec', list of functions 'distinfo', 'basehazard', 'gradbasehazard', 'hessbasehazard',
##' 'cumbasehazard', 'gradcumbasehazard', 'hesscumbasehazard' and 'densityquantile'
##'
##' The \code{distinfo} function is used to provide basic distribution specific information to other \code{spatsurv} functions. The user is required
##' to provide the following information in the returned list: \code{npars}, the number of parameters in this distribution; \code{parnames},
##' the names of the parameters; \code{trans}, the transformation scale on which the priors will be provided; \code{itrans}, the inverse
##' transformation function that will be applied to the parameters before the hazard, and other functions are evaluated; \code{jacobian},
##' the derivative of the inverse transformation function with respect to each of the parameters; and \code{hessian}, the second derivatives
##' of the inverse transformation function with respect to each of the parameters -- note that currently the package \code{spatsurv}
##' only allows the use of functions where the parameters are transformed independently.
##'
##' The \code{basehazard} function is used to evaluate the baseline hazard function for the distribution of interest. It returns a
##' function that accepts as input a vector of times, \code{t} and returns a vector.
##'
##' The \code{gradbasehazard} function is used to evaluate the gradient of the baseline hazard function with respect to the parameters,
##' this typically returns a vector. It returns a function that accepts as input a vector of times, \code{t}, and returns a matrix.
##'
##' The \code{hessbasehazard} function is used to evaluate the Hessian of the baseline hazard function. It returns a function that accepts
##' as input a vector of times, \code{t} and returns a list of hessian matrices corresponding to each \code{t}.
##'
##' The \code{cumbasehazard} function is used to evaluate the cumulative baseline hazard function for the distribution of interest.
##' It returns a function that accepts as input a vector of times, \code{t} and returns a vector.
##'
##' The \code{gradcumbasehazard} function is used to evaluate the gradient of the cumulative baseline hazard function with respect
##' to the parameters, this typically returns a vector. It returns a function that accepts as input a vector of times, \code{t}, and returns a matrix.
##'
##' The \code{hesscumbasehazard} function is used to evaluate the Hessian of the cumulative baseline hazard function. It returns a
##' function that accepts as input a vector of times, \code{t} and returns a list of hessian matrices corresponding to each \code{t}.
##'
##' The \code{densityquantile} function is used to return quantiles of the density function. This is NOT REQUIRED for running the MCMC,
##' merely for us in post-processing with the \code{predict} function where \code{type} is 'densityquantile'. In the case of the Weibull
##' model for the baseline hazard, it can be shown that the q-th quantile is:
##'
##' @return an object inheriting class 'basehazardspec'
##' @param MLinits initial values for optim, default is NULL
##' @seealso \link{tpowHaz}, \link{exponentialHaz}, \link{gompertzHaz}, \link{makehamHaz}
##' @export

rootWeibullHaz <- function(MLinits=NULL){

    flist <- list()

    flist$distinfo <- function(){
        retlist <- list()
        retlist$npars <- 2
        retlist$parnames <- c("alpha","lambda")
        retlist$trans <- log
        retlist$itrans <- exp
        retlist$jacobian <- exp
        retlist$hessian <- list(exp,exp)
        retlist$MLinits <- MLinits
        return(retlist)
    }

    flist$basehazard <- function(pars){
        fun <- function(t,...){
            #browser()
            return(0.5*pars[2]^0.5*pars[1]*t^(pars[1]/2-1)) # in this case alpha=pars[1], lambda=pars[2]
        }
        return(fun)
    }

    flist$gradbasehazard <- function(pars){
        fun <- function(t,...){
            return(0.5*t^(pars[1]/2-1)*cbind(pars[2]^0.5*(1+0.5*pars[1]*log(t)),0.5*pars[1]*pars[2]^(-0.5))) # in this case alpha=pars[1], lambda=pars[2]
        }
        return(fun)

    }

    flist$hessbasehazard <- function(pars){
        funfun <- function(t,pars){
            m <- matrix(0,2,2) # note m[2,2]=0 i.e. d2h_0/dlambda^2 = 0
            m[1,2] <- m[2,1] <- 0.25*t^(pars[1]/2-1) * (pars[2]^(-0.5)*(1+0.5*pars[1]))
            m[1,1] <- 0.25*t^(pars[1]/2-1) * (2*pars[2]^0.5*log(t) + 0.5*pars[1]*pars[2]^0.5*log(t)^2)
            m[2,2] <- 0.25*t^(pars[1]/2-1) * (0.5*pars[1]*pars[2]^(-3/2))
            return(m) # in this case alpha=pars[1], lambda=pars[2]
        }

        fun <- function(t,...){
            return(lapply(t,funfun,pars=pars))
        }
        return(fun)

    }

    flist$cumbasehazard <- function(pars){
        fun <- function(t,...){
            #browser()
            return(pars[2]^0.5*t^(pars[1]/2)) # in this case alpha=pars[1], lambda=pars[2]
        }
        return(fun)
    }

    flist$gradcumbasehazard <- function(pars){
        fun <- function(t,...){
            return(0.5*t^(pars[1]/2)*cbind(pars[2]^0.5*log(t),pars[2]^(-0.5))) # in this case alpha=pars[1], lambda=pars[2]
        }
        return(fun)
    }

    flist$hesscumbasehazard <- function(pars){
        funfun <- function(t,pars){
            m <- matrix(0,2,2) # note m[2,2]=0 i.e. d2H_0/dlambda^2 = 0
            m[1,2] <- m[2,1] <- 0.25*t^(pars[1]/2) * (pars[2]^(-0.5)*log(t))
            m[1,1] <- 0.25*t^(pars[1]/2) * (pars[2]^(0.5)*log(t)^2)
            m[2,2] <- 0.25*t^(pars[1]/2) * (-pars[2]^(-3/2))
            return(m) # in this case alpha=pars[1], lambda=pars[2]
        }

        fun <- function(t,...){
            return(lapply(t,funfun,pars=pars))
        }
        return(fun)
    }

    flist$densityquantile <- function(pars,other){
        fun <- function(probs,...){
            stop("densityquantile not available yet")
        }
        return(fun)
    }


    class(flist) <- c("basehazardspec","list")
    return(flist)
}