% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/cox_helpers.R
\name{cox_family}
\alias{cox_family}
\title{Cox Proportional Hazards Family for lgspline}
\usage{
cox_family()
}
\value{
A list with family components used by \code{lgspline}.
}
\description{
Creates a family-like object for Cox PH models. The link function is
\code{log} (the linear predictor is log-relative-hazard), but unlike
standard GLM families there is no dispersion parameter and no closed-form
mean-variance relationship.

The family provides \code{$loglik} and \code{$aic} methods compatible
with \code{\link{logLik.lgspline}}.
}
\details{
Cox PH is semiparametric: the baseline hazard is unspecified. The
partial log-likelihood depends only on the order of event times and the
linear predictor \eqn{\eta = \mathbf{X}\boldsymbol{\beta}}. Consequently:
\itemize{
  \item No dispersion parameter is estimated (\code{sigmasq_tilde} is
        fixed at 1).
  \item \code{dev.resids} returns martingale-style residuals for GCV
        tuning compatibility.
  \item The response variable is survival time (positive), and the link
        is \code{log}.
}
}
\examples{
fam <- cox_family()
fam$family
fam$link

}
