
@article{Bagust.2014,
author = {Adrian Bagust and Sophie Beale},
title ={Survival Analysis and Extrapolation Modeling of Time-to-Event Clinical Trial Data for Economic Evaluation: An Alternative Approach},
journal = {Medical Decision Making},
volume = {34},
number = {3},
pages = {343-351},
year = {2014},
doi = {10.1177/0272989X13497998},
    note ={PMID: 23901052}
}

@article{Spiegelhalter.2003,
author = {Spiegelhalter, David J. and Best, Nicola G. and Carlin, Bradley P. and Van Der Linde, Angelika},
title = {Bayesian measures of model complexity and fit},
journal = {Journal of the Royal Statistical Society: Series B (Statistical Methodology)},
volume = {64},
number = {4},
pages = {583-639},
keywords = {Bayesian model comparison, Decision theory, Deviance information criterion, Effective number of parameters, Hierarchical models, Information theory, Leverage, Markov chain Monte Carlo methods, Model dimension},
doi = {https://doi.org/10.1111/1467-9868.00353},
url = {https://rss.onlinelibrary.wiley.com/doi/abs/10.1111/1467-9868.00353},
eprint = {https://rss.onlinelibrary.wiley.com/doi/pdf/10.1111/1467-9868.00353},
abstract = {Summary. We consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined. Using an information theoretic argument we derive a measure pD for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest. In general pD approximately corresponds to the trace of the product of Fisher's information and the posterior covariance, which in normal models is the trace of the ‘hat’ matrix projecting observations onto fitted values. Its properties in exponential families are explored. The posterior mean deviance is suggested as a Bayesian measure of fit or adequacy, and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages. Adding pD to the posterior mean deviance gives a deviance information criterion for comparing models, which is related to other information criteria and has an approximate decision theoretic justification. The procedure is illustrated in some examples, and comparisons are drawn with alternative Bayesian and classical proposals. Throughout it is emphasized that the quantities required are trivial to compute in a Markov chain Monte Carlo analysis.},
year = {2002}
}

@misc{Ouwens.2018, title={Use of clinical opinion in the estimation of survival extrapolation distributions}, url={https://www.ispor.org/docs/default-source/presentations/91714pdf.pdf?sfvrsn=a5b2756f_0}, journal={ISPOR EU 2018 - Use of clinical opinion in the estimation of survival extrapolation distributions}, publisher={ISPOR}, author={Ouwens, Mario}, year={2018}, month={Nov}}


@article{Watanabe.2010,
author = {Watanabe, Sumio},
title = {Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory},
year = {2010},
issue_date = {3/1/2010},
publisher = {JMLR.org},
volume = {11},
issn = {1532-4435},
journal = {J. Mach. Learn. Res.},
month = dec,
pages = {3571–3594},
numpages = {24}
}
@article{Jackson.2010,
   author = {Jackson, C. H. and Sharples, L. D. and Thompson, S. G.},
   title = {{Structural and parameter uncertainty in Bayesian cost-effectiveness models}},
   journal = {J R Stat Soc Ser C Appl Stat},
   volume = {59},
   number = {2},
   pages = {233-253},
   ISSN = {0035-9254 (Print)
0035-9254},
   DOI = {10.1111/j.1467-9876.2009.00684.x},
   year = {2010},
   type = {Journal Article}
}

@article{Gelfand.1994,
 ISSN = {00359246},
 abstract = {Model determination is a fundamental data analytic task. Here we consider the problem of choosing among a finite (without loss of generality we assume two) set of models. After briefly reviewing classical and Bayesian model choice strategies we present a general predictive density which includes all proposed Bayesian approaches that we are aware of. Using Laplace approximations we can conveniently assess and compare the asymptotic behaviour of these approaches. Concern regarding the accuracy of these approximations for small to moderate sample sizes encourages the use of Monte Carlo techniques to carry out exact calculations. A data set fitted with nested non-linear models enables comparisons between proposals and between exact and asymptotic values.},
 author = {A. E. Gelfand and D. K. Dey},
 journal = {Journal of the Royal Statistical Society. Series B (Methodological)},
 number = {3},
 pages = {501--514},
 publisher = {[Royal Statistical Society, Wiley]},
 title = {{Bayesian Model Choice: Asymptotics and Exact Calculations}},
 volume = {56},
 year = {1994}
}
 @Misc{loo.2020,
    title = {loo: Efficient leave-one-out cross-validation and WAIC for Bayesian models},
    author = {Aki Vehtari and Jonah Gabry and Mans Magnusson and Yuling Yao and Paul-Christian Bürkner and Topi Paananen and Andrew Gelman},
    year = {2020},
    note = {R package version 2.4.1},
    url = {https://mc-stan.org/loo/},
  }

 @Manual{muhaz.2019,
    title = {muhaz: Hazard Function Estimation in Survival Analysis},
    author = {Kenneth Hess and  R. Gentleman},
    year = {2019},
    note = {R package version 1.2.6.1 (accessed Feb 01, 2021)},
    url = {https://CRAN.R-project.org/package=muhaz},
     }
 @Manual{hesim.2020,
    title = {{hesim: Health-Economic Simulation Modeling and Decision Analysis}},
    author = {Devin Incerti and Jeroen P. Jansen},
    year = {2020},
    note = {R package version 0.3.1 (accessed Feb 01, 2021)}
  }
  @Manual{bshazard.2018,
    title = {{bshazard: Nonparametric Smoothing of the Hazard Function}},
    author = {Paola Rebora,Agus Salim and Marie Reilly},
    year = {2018},
    note = {R package version 1.1 (accessed Feb 01, 2021)}
  }

  @Manual{RTCGA,
    title = {RTCGA: The Cancer Genome Atlas Data Integration},
    author = {Marcin Kosinski and Przemyslaw Biecek},
    year = {2020},
    note = {R package version 1.18.0 (accessed Feb 01, 2021)},
   }


@article{Green.1995,
  title={Reversible jump Markov chain Monte Carlo computation and Bayesian model determination},
  author={Green, Peter J},
  journal={Biometrika},
  volume={82},
  number={4},
  pages={711--732},
  year={1995},
  publisher={Oxford University Press}
}
@article{Depaoli.2016,
 ISSN = {10769986, 19351054},
 URL = {http://www.jstor.org/stable/26447820},
 abstract = {A review of the software Just Another Gibbs Sampler (JAGS) is provided. We cover aspects related to history and development and the elements a user needs to know to get started with the program, including (a) definition of the data, (b) definition of the model, (c) compilation of the model, and (d) initialization of the model. An example using a latent class model with large-scale education data is provided to illustrate how easily JAGS can be implemented in R. We also cover details surrounding the many programs implementing JAGS. We conclude with a discussion of the newest features and upcoming developments. JAGS is constantly evolving and is developing into a flexible, user-friendly program with many benefits for Bayesian inference.},
 author = {Sarah Depaoli and James P. Clifton and Patrice R. Cobb},
 journal = {Journal of Educational and Behavioral Statistics},
 number = {6},
 pages = {628--649},
 publisher = {[American Educational Research Association, Sage Publications, Inc., American Statistical Association]},
 title = {Just Another Gibbs Sampler (JAGS): Flexible Software for MCMC Implementation},
 volume = {41},
 year = {2016}
}

@article{Plummer.2003,
author = {Plummer, Martyn},
year = {2003},
month = {04},
pages = {},
title = {JAGS: A Program for Analysis of Bayesian Graphical Models using Gibbs Sampling},
volume = {124},
journal = {3rd International Workshop on Distributed Statistical Computing (DSC 2003); Vienna, Austria}
}


@article{Cooney.2023,
author = {Philip Cooney and Arthur White},
title ={Direct Incorporation of Expert Opinion into Parametric Survival Models to Inform Survival Extrapolation},
journal = {Medical Decision Making},
volume = {1},
number = {1},
pages = {0272989X221150212},
year = {2023},
doi = {10.1177/0272989X221150212},
    note ={PMID: 36647200},

URL = { 
        https://doi.org/10.1177/0272989X221150212
    
},
eprint = { 
        https://doi.org/10.1177/0272989X221150212
    
}
,
    abstract = { BackgroundIn decision modeling with time-to-event data, there are a variety of parametric models that can be used to extrapolate the survival function. Each model implies a different hazard function, and in situations in which there is moderate censoring, this can result in quite different survival projections. External information such as expert opinion on long-term survival can more accurately characterize the uncertainty in these extrapolations.ObjectiveWe present a general and easily implementable approach to incorporate various types of expert opinions into parametric survival models, focusing on opinions about survival at various landmark time points.MethodsExpert opinion is incorporated into parametric survival models using Bayesian and frequentist approaches. In the Bayesian method, expert opinion is included through a loss function and in the frequentist approach by penalizing the likelihood function, although in both cases the core approach is the same. The issue of aggregating multiple expert opinions is also considered.ResultsWe apply this method to data from a leukemia trial and use previously elicited expert opinion on survival probabilities for that particular trial population at years 4 and 5 to inform our analysis. We take a robust approach to modeling expert opinion by using pooled distributions and fit a broad class of parametric models to the data. We also assess statistical goodness of fit of the models to both the observed data and expert opinion.ConclusionsExpert opinions can be implemented in a straightforward manner using this novel approach; however, more work is required on the correct elicitation of these quantities.HighlightsPresentation of a novel and open-source method to incorporate expert opinion into decision modeling.Extends upon earlier work in that expert opinion can be incorporated into a wide range of parametric models.Provides methodological guidance for directly including expert opinion in decision modeling, which is a research focus area in NICE TSD 21.1 }
}

  @Article{Baio.2020,
    title = {{survHE}: Survival Analysis for Health Economic Evaluation and Cost-Effectiveness Modeling},
    author = {Gianluca Baio},
    journal = {Journal of Statistical Software},
    year = {2020},
    volume = {95},
    number = {14},
    pages = {1--47},
    doi = {10.18637/jss.v095.i14},
  }
  
  
    @Manual{SHELF.2021,
    title = {SHELF: Tools to Support the Sheffield Elicitation Framework},
    author = {Jeremy Oakley},
    year = {2021},
    note = {R package version 1.8.0},
    url = {https://CRAN.R-project.org/package=SHELF},
  }
  
  @article{OHagan.2019,
author = {Anthony O’Hagan},
title = {Expert Knowledge Elicitation: Subjective but Scientific},
journal = {The American Statistician},
volume = {73},
number = {sup1},
pages = {69-81},
year  = {2019},
publisher = {Taylor & Francis},
doi = {10.1080/00031305.2018.1518265},

URL = { 
        https://doi.org/10.1080/00031305.2018.1518265
    
},
eprint = { 
        https://doi.org/10.1080/00031305.2018.1518265
    
}

}

 @Article{flexsurv,
    title = {{flexsurv}: A Platform for Parametric Survival Modeling in
      {R}},
    author = {Christopher Jackson},
    journal = {Journal of Statistical Software},
    year = {2016},
    volume = {70},
    number = {8},
    pages = {1--33},
    doi = {10.18637/jss.v070.i08},
  }