Introduction
In health economic evaluations, the choice of intervention typically has consequences for lifetime survival. Therefore we often want to estimate the expected survival over a lifetime horizon,
\[ \mbox{E}[T \mid \boldsymbol{\theta}]= \int_0^\infty S(t)dt. \]
This implies that the expected (i.e. mean) survival time can be computed as the “area under the survival curve”. More importantly, this clarifies why applications of survival modelling in HTA requires a full extrapolation of the survival curve: the focus of the economic analysis is on the mean survival time and in order to obtain it, we need to be able to derive the full survival curve in the range of times \(t = 0, \ldots, \infty\).
A challenge with estimating lifetime survival based on trial data is that we can only observe death times \(T\) that are shorter than the follow-up time of the trial. For people still alive at the end of the trial, the survival times are right-censored. To estimate \(E(T)\), we need to know the distribution of \(T\) over all plausible values of \(T\).
The basis of the structure of these pages is take from the NICE DSU report 14 (Latimer 2011).
R packages
There are many R package available for doing survival analysis, both on CRAN and on other site such as GitHub. Those we will make most use of for the exercises will be
survHE: Survival analysis in health economic evaluation contains a suite of functions to systematise the workflow involving survival analysis in health economic evaluation. survHE can fit a large range of survival models using both a frequentist approach (by calling the R package flexsurv) and a Bayesian perspective.flexsurv: Flexible parametric models for time-to-event data, including the Royston-Parmar spline model, generalized gamma and generalized F distributions. Any user-defined parametric distribution can be fitted, given at least an R function defining the probability density or hazard. There are also tools for fitting and predicting from fully parametric multi-state models, based on either cause-specific hazards or mixture models.INLA: R-INLA is a more general package in R that do approximate Bayesian inference for Latent Gaussian Models.survival: Contains the core survival analysis routines, including definition of Surv objects, Kaplan-Meier and Aalen-Johansen (multi-state) curves, Cox models, and parametric accelerated failure time models.