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The goal of psm3mkv is to evaluate the efficiency and fit of certain three state model structures to data typical from an oncology clinical trial, as described in an accompanying article (Muston 2024). The package evaluates the following structures:

  • Partitioned Survival Model/analysis (PSM),

  • Clock-forward State Transition Model (STM-CF), and

  • Clock-reset State Transition Model (STM-CR).

The state transition models differ from each other in that the transition from progressive disease to death is a function of time from baseline in the STM-CF and time from progression in the STM-CR (Jackson 2016; Woods et al. 2020).

The package requires a patient-level dataset of time to progression (TTP), progression-free survival (PFS) and overall survival (OS).

Given this, the package enables:

  • Fitting a range of models to endpoints relevant each model type:

    • One piece parametric (distributions according to flexsurv).

    • Royston-Parmar splines (1-3 internal knots, hazard/odds/normal scales, again as per flexsurv) (Royston and Parmar 2002).

    • Two piece parametric (given a time cutoff).

  • Selecting the “best fit” survival models for each endpoint (using the Akaike Information Criterion, Bayesian Information Criterion or other user preference).

  • Deriving and presenting likelihoods for the 3 structures so as to evaluate fit.

  • Presenting the total number of parameters used for each structure, to additionally evaluate efficiency.

  • Deriving and presenting restricted mean durations by health state and for each of the 3 model structures (given a time horizon), to evaluate plausibility and structural sensitivity. Additional functionality:

    • Constraining the estimates to ensure that survival is no greater than survival in a background lifetable.

    • Applying discounting to obtained discounted restricted means.

    • Bootstrap standard errors can be derived.

  • Graphically illustrate observed and fitted membership probabilities, to allow visual inspection of fit of the 3 model structures.

Where two piece modeling is used, modelers should be advised to take care of interpretation and validity in case different cutoff points are selected for different endpoints.

Additionally, for parametric modeling of STM structures, the model for survival in the progressive disease state (post progression survival, PPS) may be a function of an additional arbitrary explanatory variable. This is intended to enable the exploration of TTP (or some transformation) as a predictor for PPS.


The accompanying vignette("example") illustrates how the package can be used for the one-piece parametric and spline modeling.

A second vignette, vignette("background-mortality") illustrates how, after fitting models, estimates of restricted mean durations in health states can be calculated after constraining for background mortality from a given life table. Survival is assumed to be no greater than in a background lifetable.


The package requires version R >= 4.1.0 due to use of the native pipe. Please ensure R is updated first.

Latest stable release

Install the latest stable release from CRAN:


Development version

Install the latest development version from GitHub (this may not be as stable):

# install.packages("pak")

Note that pak::pak() does not build the vignettes by default when installing a package from GitHub, which is ideal because the vignettes can take a long time to generate. You can conveniently view them on the package documentation website.

Additional dependencies

Running the vignettes requires additional dependencies, which are all either imported by or suggested by psm3mkv. Thus you can ensure they are all installed by specifying dependencies = TRUE.

pak::pak("Merck/psm3mkv@*release", dependencies = TRUE)


If you use this software, please cite it as below.

Muston, D. 2024. “Informing Structural Assumptions for Three State Oncology Cost-Effectiveness Models through Model Efficiency and Fit.” Applied Health Economics and Health Policy. DOI: 10.1007/s40258-024-00884-2

A BibTeX entry for LaTeX users is

  author  = {Dominic Muston},
  title   = {Informing structural assumptions for three state oncology cost-effectiveness models through model efficiency and fit},
  journal = {Applied Health Economics and Health Policy},
  year    = {2024},
  doi     = {10.1007/s40258-024-00884-2}


Jackson, Christopher. 2016. “flexsurv: A Platform for Parametric Survival Modeling in R.” Journal of Statistical Software 70 (8): 1–33.

Woods, Beth S, Eleftherios Sideris, Stephen Palmer, Nick Latimer, and Marta Soares. 2020. “Partitioned Survival and State Transition Models for Healthcare Decision Making in Oncology: Where Are We Now?” Value in Health 23 (12): 1613–1621.

Royston, Patrick, and Mahesh KB Parmar. 2002. “Flexible Parametric Proportional-Hazards and Proportional-Odds Models for Censored Survival Data, with Application to Prognostic Modelling and Estimation of Treatment Effects.” Statistics in Medicine 21 (15): 2175–2197.