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Diffusion piecewise exponential models for survival extrapolation using Piecewise Deterministic Monte Carlo

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read The diffusion piecewise exponential model couples a discretised diffusion prior for the log-hazard with a Poisson-process prior for knots, so observed survival data and expert prior information jointly determine long-term extrapolations.

desk verdict Genuinely new combination of diffusion priors and random knots for survival extrapolation, with a clever PDMP sampler; needs a simulation study and an honest check of the splitting-scheme bias before I'd trust the numbers. read the letter →

arxiv 2505.05932 v1 pith:HZSHSAA7 submitted 2025-05-09 stat.ME stat.AP

Luke Hardcastle , Samuel Livingstone , Gianluca Baio This is my paper · ORCID
classification stat.MEstat.AP MSC 62F1562N0165C05
keywords survivalanalysispiecewiseexponentialmodeldiffusionpriorextrapolationPoissonprocessdeterministicMonteCarlostickyPDMPhealthtechnologyassessment
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper proposes a Bayesian model for survival data in which the log-hazard is piecewise constant, with local hazards following a discretised stochastic differential equation whose drift encodes prior belief about long-term mortality, and with knot locations drawn from a Poisson process. The goal is to make extrapolation beyond the end of a trial principled: during the observation period the data dominate, while in the extrapolation period the drift and the knot intensity control how quickly prior information takes over. This matters for health technology assessment, where mean survival beyond the trial horizon is a key input to cost-effectiveness decisions and data are often heavily administratively censored. The paper also contributes a sampling algorithm that extends sticky piecewise deterministic Monte Carlo dynamics to models with a random number of knots, so the model can be fitted without tuning between-model proposals.

What carries the argument

The key object is the drift function $\mu$ of the diffusion prior together with the Poisson-process intensity $\gamma$ for the knots. The drift can encode a stationary distribution for the hazard, an underlying Gompertz hazard, or a time-varying target such as a waning treatment effect; the discretisation uses a skew-symmetric innovation scheme that remains stable for non-Lipschitz drifts. The Poisson knot process acts as a random time change between the diffusion skeleton and calendar time, so the number of knots controls both flexibility and the speed at which the prior dominates in the extrapolation period. Transdimensional sampling is achieved by sticky piecewise deterministic dynamics: each candidate knot is a switchable variable, movement onto and off the 'on' state happens at hyperplane crossings without likelihood evaluations, and inactive knots are refreshed from the prior in a Gibbs step. A proposition shows the skew-symmetric parameterisation gives a smaller expected recurrence time to the null model than the Euler-Maruyama parameterisation, supporting faster mixing.

What would settle it

Fit the same survival model twice on the colon cancer data, once with the paper's approximate event-time generation and once with an exact event-time method known to be valid for this model, and compare the posterior hazard curves. A difference larger than Monte Carlo error would show the approximation error is material.

Watch

Extended reading notes

Core claim

The central claim is that prior beliefs about the long-term hazard can be encoded as the drift of a diffusion and combined with the observed-data likelihood through a piecewise exponential model, without forcing a parametric hazard shape. The log-hazard values are a discretisation of $\mathrm{d}\alpha = \mu(\alpha)\,\mathrm{d}y + \mathrm{d}W_y$, and the knots form a Poisson process that acts as a random time change; this makes the prior adaptive to volatility in the data and determines how fast the drift dominates beyond the end of observation. The authors show that the resulting posterior, which lives over models with different numbers of knots, can be sampled with sticky piecewise deterministic Monte Carlo by treating each candidate knot as a switchable variable, then refreshing inactive candidate knots from the prior in a Gibbs step. On colon cancer and leukaemia trial data, they demonstrate that observation-period inference is nearly unaffected by the drift, while extrapolated mean survival and its uncertainty respond strongly to the chosen drift, and that the sampler explores the posterior more fully than a reversible jump comparator.

Load-bearing premise

The load-bearing assumption is that the approximate method used to generate the sampler's event times biases the posterior only negligibly; the paper gives no bound or diagnostic for that error.

Editorial extensions

If this is right

  • Analysts can encode beliefs about long-term mortality—stationary hazard levels, an external Gompertz curve, or a waning treatment effect—as a drift and obtain extrapolated mean survival with credible intervals that reflect both the data and that belief.
  • Because the drift and the knot intensity are separated, information criteria can pick the knot intensity without dictating the long-term hazard, breaking the usual trade-off between fit in the observation period and plausibility of the tail.
  • The sticky piecewise deterministic construction extends to any transdimensional posterior with a centring hyperplane where the two models' likelihoods agree, so similar transdimensional problems need no reversible-jump proposals.
  • Even with administrative censoring rates near 90 percent, posterior inference remains computationally feasible and the prior becomes influential exactly as the data thin out.
  • Reversible-jump comparisons in the paper suggest the sampler explores the posterior tails more completely for the same computational budget.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The authors do not explore it, but the same diffusion-prior idea could be applied to the cumulative hazard or survival function directly, letting blended-survival information enter as a time-varying drift rather than as synthetic data.
  • A quantitative consequence that is not tested in the paper: the rate at which $\gamma$ lets the prior overwhelm the data in the extrapolation period should be measurable in prior simulations, and could be used to calibrate $\gamma$ to a desired 'memory' of the data.
  • A practical sensitivity check implied by the construction is to increase the discretisation step $\sigma$ and re-run the colon cancer analysis; if extrapolated mean survival shifts substantially, the assumedly small discretisation bias is not small.
  • For health technology assessment reporting, the model suggests that extrapolated mean survival should be published together with the drift and knot intensity, since those encode the untestable assumptions that drive the decision-relevant estimate.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper introduces the diffusion piecewise exponential model, a Bayesian survival model in which the piecewise constant log-hazard is assigned a discretised diffusion prior and the knot locations are assigned a Poisson process prior. The drift of the diffusion is used to encode prior information about long-term hazard behaviour, with the aim of combining observation-period learning with expert opinion when extrapolating beyond administrative censoring. Posterior inference is performed with a Piecewise Deterministic Markov Process sampler: the authors extend sticky PDMP dynamics from spike-and-slab priors to general transdimensional posteriors, using a Gibbs step to resample inactive candidate knots. Extrapolations are generated by continuing the discretised diffusion from the last observation-period state, with a proposed rescaling of the discretisation parameters. The method is illustrated on colon cancer data and CLL-8 trial data, with mean survival estimates compared against parametric, independent piecewise exponential, and M-spline models.

Significance. If the claims hold, the paper makes a useful contribution to Bayesian survival extrapolation for health technology assessment. The prior framework is more flexible than fixed-knot spline or random-walk priors, and the explicit separation of observation-period flexibility from extrapolation-period prior information is a principled response to the administrative censoring problem. The technical contribution of extending sticky PDMP samplers to general transdimensional posteriors is also of independent interest, and Proposition 3.1 gives a clean, parameter-free comparison of expected recurrence times under two discretisations. The authors are transparent that the splitting scheme introduces an approximation error and that extrapolation is driven by the prior. The main weaknesses are the absence of any quantification of the sampler's approximation error and the lack of a simulation-based calibration check for the extrapolation procedure.

major comments (3)
  1. [Section 3.2 and Sections 4.1-4.2] The sampler generates PDMP event times with a splitting scheme, and the paper states that this introduces a small approximation error that was found unnecessary to correct. No bound, diagnostic, or comparison against the exact line-search scheme is provided for the settings of Sections 4.1 and 4.2. This is load-bearing because the splitting scheme replaces the continuous-time PDMP with a discrete-time approximation; if the stationary distribution is biased, every posterior hazard estimate, credible interval, and extrapolated mean survival estimate in Tables 1-3 is potentially biased. Since the exact scheme is available for the random walk, Gaussian Langevin, and Gompertz drifts (Section 3.2), I ask the authors to compare posterior summaries from both schemes for at least one of the data analyses, and to report a calibration check on synthetic data with a known hazard.
  2. [Section 3.6] The extrapolation period is sampled by continuing the discretised skew-symmetric diffusion from the last observation-period value, with a rescaling of (γ, σ) intended to reduce first-order discretisation bias. The rescaling is described only in the supplement, and no sensitivity analysis is reported in the main text. Because extrapolated mean survival is the primary output of the method, the reader cannot determine whether the rescaling is a principled correction or an ad hoc adjustment; please present the derivation and report extrapolations with and without the rescaling for the two data examples.
  3. [Section 4] The two case studies are informative but do not validate the extrapolation claim, because no simulation experiment with a known hazard is reported. Comparisons against M-spline and parametric models in Tables 1-3 place the method in context, but they cannot show that the model and sampler recover calibrated posterior statements for extrapolation. A simulation study with data generated from the model and from misspecified hazards, reporting coverage of the true mean survival over (0, y∞), would substantially strengthen the paper.
minor comments (5)
  1. [Section 2.2] The relation α_j := ˇα_{jσ²} uses the random step size σ as a time index; please define explicitly how σ, the knots s_j, and the diffusion time scale are linked, since this mapping is used later in the extrapolation procedure.
  2. [Section 3.4] The reparameterisation γ = ωΓ is clear, but it would help to state the implied joint prior on the candidate, active, and inactive knot sets as an explicit equation, since the thinning construction is central to the Gibbs update.
  3. [Section 4.1] The statement that the leave-one-out criterion 'does not always sufficiently penalise overly complex models' is non-standard for a predictive criterion; please report the PSIS diagnostics (e.g., k-hat values) and the full comparison underlying this conclusion.
  4. [Section 4] Please state the time horizon y∞ used for the colon cancer and CLL-8 analyses; the M-spline comparisons depend on the final knot locations (5, 10, 15), but the corresponding horizon is not given in the main text.
  5. [Table 3] The estimate of E[Y_t] − E[Y_c] and its credible interval should be accompanied by a note on whether the two arms are analysed jointly or independently and how the posterior difference is computed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the prior-driven extrapolation is an openly stated modelling commitment, not a hidden fit or relabelled prediction.

full rationale

The paper's central claim is that the diffusion piecewise exponential model combines observation-period inference with explicit prior information for extrapolation. This is a design statement, not a derivation that secretly assumes its conclusion: the drift function mu is chosen by the analyst to encode long-term hazard behaviour, and the paper repeatedly and openly states that extrapolation is prior-driven, e.g. 'inferences during the latter, however, will inherently be driven by model and prior specification.' No fitted parameter is relabelled as a prediction: gamma is selected via information criteria or given a hyperprior, the drift mu is elicited from external/expert information, and these choices are acknowledged as model specifications rather than validated predictions. The sticky-PDMP transdimensional sampler is an extension of published spike-and-slab PDMP constructions; the paper supplies its own Proposition 3.1 and sampler comparisons rather than importing a uniqueness theorem from the authors' earlier work. The skew-symmetric discretisation scheme is adopted from a co-authored paper, but it is used as a computational tool and its approximation error is disclosed, making this a correctness/robustness risk rather than a circular step. The unvalidated splitting-scheme bias and the heuristic rescaling in Section 3.6 are concerns about bias and external validation, not about the derivation reducing to its inputs. There are no self-definitional constructions, no fitted inputs called predictions, and no renaming of a known result as a new derivation.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The model introduces no new physical or qualitative entities. It does depend on several hand-set hyperparameters (γ, drift parameters, ω, a) and on unverified approximation assumptions for both the PDMP sampler and the extrapolation step. These are the main sources of uncertainty beyond the prior itself.

free parameters (4)
  • γ (Poisson process knot intensity) = γ = 7 for colon cancer data (selected by LOOCV); Gamma(7,1) hyperprior also considered
    Controls the number of knots and the rate at which the prior drift dominates during extrapolation. The value 7 is selected on the same colon dataset used for reporting results.
  • Drift hyperparameters μ = Normal(log(0.29), 0.4) and log-Gamma(2,7) for colon; Gamma(10,10) and tapering Gamma for CLL-8; Gompertz ψ=0.3…
    Hand-set parameters that encode expert opinion about long-term hazard behaviour and largely determine extrapolation results. They are not estimated from the relevant data.
  • ω (spike-and-slab weight) = 0.5
    Set to 0.5 in all examples; defines the prior probability that a candidate knot is active, interacting with γ via γ = ωΓ.
  • a (exponential prior rate on σ) = 2
    Set once for all examples; the authors claim inferences are generally unaffected for sensible choices, but no sensitivity analysis is shown.
assumptions (5)
  • standard math Sticky PDMP samplers for spike-and-slab priors have the stationary distribution and recurrence-time properties stated in Bierkens et al. (2023) and Chevallier et al. (2023).
    Invoked in Sections 3.3 and 3.4 to derive the unsticking rate (10) and the recurrence-time relation (12) used in Proposition 3.1.
  • domain assumption The skew-symmetric discretisation (7) is an adequate approximation to the SDE (3) for the chosen step size σ, with bias small enough to ignore in posterior inference.
    The authors note the approximation error vanishes as σ → 0 but do not quantify the bias for finite σ or check its impact on the reported posteriors (Sections 3.2 and 3.6).
  • domain assumption Censoring is non-informative and administrative at y+, with all observations censored after y+.
    Standard setup in HTA survival extrapolation, stated at the start of Section 2 and used in the likelihood and in defining the extrapolation task.
  • ad hoc to paper The extrapolation period can be sampled by continuing the skew-symmetric scheme from the last observation-period value, possibly after rescaling (γ, σ).
    Section 3.6 states this without a derivation in the main text; the details are deferred to the supplement.
  • domain assumption The piecewise exponential form (2) is flexible enough to capture the hazard during the observation period.
    Working assumption of all piecewise exponential models; not tested in the paper.

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Cite this review

Pith. "Pith review of Diffusion piecewise exponential models for survival extrapolation using Piecewise Deterministic Monte Carlo." pith.science (2026). https://pith.science/paper/HZSHSAA7

@misc{pith2026250505932,
  author       = {Pith},
  title        = {Pith review of: Diffusion piecewise exponential models for survival extrapolation using Piecewise Deterministic Monte Carlo},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HZSHSAA7}},
  note         = {Machine review of arXiv:2505.05932}
}
read the original abstract

The piecewise exponential model is a flexible non-parametric approach for time-to-event data, but extrapolation beyond final observation times typically relies on random walk priors and deterministic knot locations, resulting in unrealistic long-term hazards. We introduce the diffusion piecewise exponential model, a prior framework consisting of a discretised diffusion for the hazard, that can encode a wide variety of information about the long-term behaviour of the hazard, time changed by a Poisson process prior for knot locations. This allows the behaviour of the hazard in the observation period to be combined with prior information to inform extrapolations. Efficient posterior sampling is achieved using Piecewise Deterministic Markov Processes, whereby we extend existing approaches using sticky dynamics from sampling spike-and-slab distributions to more general transdimensional posteriors. We focus on applications in Health Technology Assessment, where the need to compute mean survival requires hazard functions to be extrapolated beyond the observation period, showcasing performance on datasets for Colon cancer and Leukaemia patients.

Figures

Figures reproduced from arXiv: 2505.05932 by the authors.

Figure 1
Figure 1. Prior simulations for h(y) under different specifications for µ(ˇαyˇ). (Left) Ran￾dom Walk prior µ(ˇαyˇ) = 0. (Centre) Gaussian Langevin prior (4). (Right) Gompertz prior dynamics (log-linear drift) (5). for example, by the log-Gamma Langevin drift (4). More broadly, it is unrealistic to ask practitioners without a mathematical background to carefully check whether the drifts they elicit meet this condition before i… view at source ↗
Figure 2
Figure 2. Density functions for the innovations θ under the Euler-Maruyama (dashed) and skew-symmetric (solid) schemes for increasing values of µ(ˇαyˇ) = 1, 2, 3, 4 and fixed σ 2 . To complete the specification of the above process, we place an exponential prior on σ, σ ∼ Exponential(a), corresponding to a penalised-complexity prior (Simpson et al., 2017). This prior shrinks the innovation standard deviation towards 0, thus s… view at source ↗
Figure 3
Figure 3. Trajectories for the PDMP sampler for knot selection viewed on [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Comparison of efficiency of the PDMP sampler under the skew-symmetric [PITH_FULL_IMAGE:figures/full_fig_p016_4.png]
Figure 5
Figure 5. Figure 5: (Left) Inferred hazards under the reversible jump sampler (Orange) and the [PITH_FULL_IMAGE:figures/full_fig_p017_5.png]
Figure 6
Figure 6. Figure 6: Hazard functions for the colon cancer data for observation period (top) and [PITH_FULL_IMAGE:figures/full_fig_p020_6.png]
Figure 7
Figure 7. Figure 7: Survival curves for the diffusion piecewise exponential model for varying spec [PITH_FULL_IMAGE:figures/full_fig_p022_7.png]
Figure 8
Figure 8. Figure 8: (Left) Hazard functions for the control and treatment arms with correspond [PITH_FULL_IMAGE:figures/full_fig_p024_8.png]

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Reference graph

Works this paper leans on

56 extracted references · 50 canonical work pages

  1. [1]

    , " * write output.state after.block = add.period write newline

    ENTRY address author booktitle chapter edition editor howpublished institution journal key month note number organization pages publisher school series title type url volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1 'mid.sentence := ...

  2. [2]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in capitalize " " * FUNCT...

  3. [3]

    Aalen, O. O. and Gjessing, H. K. (2004). Survival models based on the Ornstein-Uhlenbeck process. Lifetime data analysis\/ , 10: 407--423

    work page 2004

  4. [4]

    and Kamatani, K

    Andral, C. and Kamatani, K. (2024). Automated Techniques for Efficient Sampling of Piecewise-Deterministic Markov Processes. arXiv preprint arXiv:2408.03682\/

    arXiv 2024

  5. [5]

    and Livingstone, S

    Andrieu, C. and Livingstone, S. (2021). Peskun--Tierney ordering for Markovian Monte Carlo: beyond the reversible scenario. The Annals of Statistics\/ , 49(4): 1958--1981

    work page 2021

  6. [6]

    and Beale, S

    Bagust, A. and Beale, S. (2014). Survival Analysis and Extrapolation Modeling of Time-to-Event Clinical Trial Data for Economic Evaluation: An Alternative Approach. Medical Decision Making\/ , 34(3): 343--351. PMID: 23901052

    work page 2014

  7. [7]

    Baio, G. (2020). survHE: survival analysis for health economic evaluation and cost-effectiveness modeling. Journal of Statistical Software\/ , 95: 1--47

    work page 2020

  8. [8]

    and Bierkens, J

    Bertazzi, A. and Bierkens, J. (2022). Adaptive schemes for piecewise deterministic Monte Carlo algorithms. Bernoulli\/ , 28(4): 2404--2430

    work page 2022

Show all 56 references
  1. [9]

    Bertazzi, A., Dobson, P., and Monmarch \'e , P. (2023). Piecewise deterministic sampling with splitting schemes. arXiv preprint arXiv:2301.02537\/

    2023

  2. [10]

    and Girolami, M

    Betancourt, M. and Girolami, M. (2015). Hamiltonian Monte Carlo for hierarchical models. Current trends in Bayesian methodology with applications\/ , 79(30): 2--4

    2015

  3. [11]

    Bierkens, J., Grazzi, S., Meulen, F. v. d., and Schauer, M. (2023). Sticky PDMP samplers for sparse and local inference problems. Statistics and Computing\/ , 33(1): 8

    2023

  4. [12]

    J., and Doucet, A

    Bouchard-C \^o t \'e , A., Vollmer, S. J., and Doucet, A. (2018). The bouncy particle sampler: A nonreversible rejection-free Markov chain Monte Carlo method. Journal of the American Statistical Association\/ , 113(522): 855--867

    2018

  5. [13]

    P., Giudici, P., and Roberts, G

    Brooks, S. P., Giudici, P., and Roberts, G. O. (2003). Efficient construction of reversible jump Markov chain Monte Carlo proposal distributions. Journal of the Royal Statistical Society Series B: Statistical Methodology\/ , 65(1): 3--39

    2003

  6. [14]

    G., Peak, T., and Hemal, A

    Chapple, A. G., Peak, T., and Hemal, A. (2020). A novel Bayesian continuous piecewise linear log-hazard model, with estimation and inference via reversible jump Markov chain Monte Carlo. Statistics in medicine\/ , 39(12): 1766--1780

    2020

  7. [15]

    Che, Z., Green, N., and Baio, G. (2023). Blended survival curves: a new approach to extrapolation for time-to-event outcomes from clinical trials in health technology assessment. Medical Decision Making\/ , 43(3): 299--310

    2023

  8. [16]

    Chevallier, A., Fearnhead, P., and Sutton, M. (2023). Reversible jump PDMP samplers for variable selection. Journal of the American Statistical Association\/ , 118(544): 2915--2927

    2023

  9. [17]

    and White, A

    Cooney, P. and White, A. (2023). Extending Beyond Bagust and Beale: Fully Parametric Piecewise Exponential Models for Extrapolation of Survival Outcomes in Health Technology Assessment. Value in Health\/ , 26(10): 1510--1517

    2023

  10. [18]

    E., and Roberts, G

    Corbella, A., Spencer, S. E., and Roberts, G. O. (2022). Automatic Zig-Zag sampling in practice. Statistics and Computing\/ , 32(6): 107

    2022

  11. [19]

    N., Loschi, R

    Demarqui, F. N., Loschi, R. H., Dey, D. K., and Colosimo, E. A. (2012). A class of dynamic piecewise exponential models with random time grid. Journal of Statistical Planning and Inference\/ , 142(3): 728--742

    2012

  12. [20]

    Demiris, N., Lunn, D., and Sharples, L. D. (2015). Survival extrapolation using the poly-Weibull model. Statistical Methods in Medical Research\/ , 24(2): 287--301

    2015

  13. [21]

    and Lang, S

    Fahrmeir, L. and Lang, S. (2001). Bayesian inference for generalized additive mixed models based on Markov random field priors. Journal of the Royal Statistical Society Series C: Applied Statistics\/ , 50(2): 201--220

    2001

  14. [22]

    J., and Sherlock, C

    Fearnhead, P., Nemeth, C., Oates, C. J., and Sherlock, C. (2024). Scalable Monte Carlo for Bayesian Learning. arXiv preprint arXiv:2407.12751\/

    2024 arXiv

  15. [23]

    and Zelen, M

    Feigl, P. and Zelen, M. (1965). Estimation of exponential survival probabilities with concomitant information. Biometrics\/ , 826--838

    1965

  16. [24]

    Gibbons, C. L. and Latimer, N. R. (2024). Prevalence of Immature Survival Data for Anti-Cancer Drugs Presented to the National Institute for Health and Care Excellence between 2018-2022. Value in Health\/

    2024

  17. [25]

    Green, P. J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika\/ , 82(4): 711--732

    1995

  18. [26]

    (2024 a )

    Hardcastle, L., Livingstone, S., and Baio, G. (2024 a ). Averaging polyhazard models using Piecewise deterministic Monte Carlo with applications to data with long-term survivors. arXiv preprint arXiv:2406.14182\/

    2024 arXiv

  19. [27]

    Supplement to ``Diffusion piecewise exponential models for survival extrapolation using Piecewise Deterministic Monte Carlo"

    --- (2024 b ). Supplement to ``Diffusion piecewise exponential models for survival extrapolation using Piecewise Deterministic Monte Carlo"

    2024

  20. [28]

    Hird, M., Livingstone, S., and Zanella, G. (2020). A fresh take on ‘Barker dynamics’ for MCMC. In International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing\/ , 169--184. Springer

    2020

  21. [29]

    G., Chen, M.-H., Sinha, D., Ibrahim, J., and Chen, M

    Ibrahim, J. G., Chen, M.-H., Sinha, D., Ibrahim, J., and Chen, M. (2001). Bayesian survival analysis\/ , volume 2. Springer

    2001

  22. [30]

    Jackson, C., Stevens, J., Ren, S., Latimer, N., Bojke, L., Manca, A., and Sharples, L. (2017). Extrapolating Survival from Randomized Trials Using External Data: A Review of Methods. Medical Decision Making\/ , 37(4): 377--390. PMID: 27005519

    2017

  23. [31]

    Jackson, C. H. (2023). survextrap: a package for flexible and transparent survival extrapolation. BMC Medical Research Methodology\/ , 23(1): 282

    2023

  24. [32]

    D., Triantafyllopoulos, K., and Manca, A

    Kearns, B., Stevenson, M. D., Triantafyllopoulos, K., and Manca, A. (2019). Generalized linear models for flexible parametric modeling of the hazard function. Medical Decision Making\/ , 39(7): 867--878

    2019

  25. [33]

    Dynamic and Flexible Survival Models for Extrapolation of Relative Survival: A Case Study and Simulation Study

    --- (2022). Dynamic and Flexible Survival Models for Extrapolation of Relative Survival: A Case Study and Simulation Study. Medical Decision Making\/ , 42(7): 945--955

    2022

  26. [34]

    Latimer, N. (2011). NICE DSU technical support document 14: survival analysis for economic evaluations alongside clinical trials-extrapolation with patient-level data. Report by the Decision Support Unit\/

    2011

  27. [35]

    survival analysis and extrapolation modeling of time-to-event clinical trial data for economic evaluation: an alternative approach

    Latimer, N. R. (2014). Response to “survival analysis and extrapolation modeling of time-to-event clinical trial data for economic evaluation: an alternative approach” by Bagust and Beale. Medical Decision Making\/ , 34(3): 279--282

    2014

  28. [36]

    F., and Yuan, Y

    Lin, R., Thall, P. F., and Yuan, Y. (2021). Bags: A Bayesian adaptive group sequential trial design with subgroup-specific survival comparisons. Journal of the American Statistical Association\/ , 116(533): 322--334

    2021

  29. [37]

    F., and Roberts, G

    Livingstone, S., Faulkner, M. F., and Roberts, G. O. (2019). Kinetic energy choice in Hamiltonian/hybrid Monte Carlo. Biometrika\/ , 106(2): 303--319

    2019

  30. [38]

    Livingstone, S., N \"u sken, N., Vasdekis, G., and Zhang, R.-Y. (2024). Skew-symmetric schemes for stochastic differential equations with non-Lipschitz drift: an unadjusted Barker algorithm. arXiv preprint arXiv:2405.14373\/

    2024 arXiv

  31. [39]

    and Zanella, G

    Livingstone, S. and Zanella, G. (2022). The Barker proposal: combining robustness and efficiency in gradient-based MCMC. Journal of the Royal Statistical Society Series B: Statistical Methodology\/ , 84(2): 496--523

    2022

  32. [40]

    Michel, M., Durmus, A., and S \'e n \'e cal, S. (2020). Forward event-chain Monte Carlo: Fast sampling by randomness control in irreversible Markov chains. Journal of Computational and Graphical Statistics\/ , 29(4): 689--702

    2020

  33. [41]

    A., Chandramouli, S., Hartmann, M., Pla, O

    Mikkola, P., Martin, O. A., Chandramouli, S., Hartmann, M., Pla, O. A., Thomas, O., Pesonen, H., Corander, J., Vehtari, A., Kaski, S., et al. (2023). Prior Knowledge Elicitation: The Past, Present, and Future. Bayesian Analysis\/ , 1(1): 1--33

    2023

  34. [42]

    A., Hobbs, B

    Murray, T. A., Hobbs, B. P., Sargent, D. J., and Carlin, B. P. (2016). Flexible Bayesian survival modeling with semiparametric time-dependent and shape-restricted covariate effects. Bayesian analysis (Online)\/ , 11(2): 381

    2016

  35. [43]

    E., Ren, S., Forsyth, J

    Oakley, J. E., Ren, S., Forsyth, J. E., Gosling, J. P., Wilson, K., Latimer, N., Rutherford, M. J., Uttley, L., and Fotheringham, J. (2025). NICE DSU Technical Support Document 26: Expert elicitation for long-term survival outcomes. Technical Support Document 26, Decision Supp...

    2025

  36. [44]

    Oksendal, B. (2013). Stochastic differential equations: an introduction with applications\/ . Springer Science & Business Media

    2013

  37. [45]

    G., Jagannath, S., Jakubowiak, A., Usmani, S

    Palmer, S., Lin, Y., Martin, T. G., Jagannath, S., Jakubowiak, A., Usmani, S. Z., Buyukkaramikli, N., Phelps, H., Slowik, R., Pan, F., et al. (2023). Extrapolation of survival data using a Bayesian approach: a case study leveraging external data from Cilta-Cel therapy in multi...

    2023

  38. [46]

    and Bruti-Liberati, N

    Platen, E. and Bruti-Liberati, N. (2010). Numerical solution of stochastic differential equations with jumps in finance\/ , volume 64. Springer Science & Business Media

    2010

  39. [47]

    Roberts, G. O. and Sangalli, L. M. (2010). Latent diffusion models for survival analysis . Bernoulli\/ , 16(2): 435 -- 458

    2010

  40. [48]

    Roberts, G. O. and Tweedie, R. L. (1996). Exponential convergence of Langevin distributions and their discrete approximations. Bernoulli\/ , 2(3): 341--363

    1996

  41. [49]

    J., Lambert, P

    Rutherford, M. J., Lambert, P. C., Sweeting, M. J., Pennington, R., Crowther, M. J., Abrams, K. R., et al. (2020). NICE DSU technical support document 21: flexible methods for survival analysis. Decision Support Unit, ScHARR, University of Sheffield\/

    2020

  42. [50]

    Sachs, M., Sen, D., Lu, J., and Dunson, D. (2023). Posterior computation with the Gibbs zig-zag sampler. Bayesian Analysis\/ , 18(3): 909--927

    2023

  43. [51]

    L., Ruppert, D., Cowen, M., and Halasyamani, L

    Sharef, E., Strawderman, R. L., Ruppert, D., Cowen, M., and Halasyamani, L. (2010). Bayesian adaptive B-spline estimation in proportional hazards frailty models. Electronic Journal of Statistics\/ , 4: 606--642

    2010

  44. [52]

    G., and S rbye, S

    Simpson, D., Rue, H., Riebler, A., Martins, T. G., and S rbye, S. H. (2017). Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors . Statistical Science\/ , 32(1): 1 -- 28

    2017

  45. [53]

    and Fearnhead, P

    Sutton, M. and Fearnhead, P. (2023). Concave-convex PDMP-based sampling. Journal of Computational and Graphical Statistics\/ , 32(4): 1425--1435

    2023

  46. [54]

    Thatcher, A. R. (1999). The long-term pattern of adult mortality and the highest attained age. Journal of the Royal Statistical Society: Series A (Statistics in Society)\/ , 162(1): 5--43

    1999

  47. [55]

    Vehtari, A., Gelman, A., and Gabry, J. (2017). Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Statistics and computing\/ , 27: 1413--1432

    2017

  48. [56]

    D., Mackay, D

    Williams, C., Lewsey, J. D., Mackay, D. F., and Briggs, A. H. (2017). Estimation of survival probabilities for use in cost-effectiveness analyses: a comparison of a multi-state modeling survival analysis approach with partitioned survival and Markov decision-analytic modeling....

    2017

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.