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Calculate the expected value of partial perfect information from a decision-analytic model


  pars = NULL,
  method = NULL,
  se = FALSE,
  B = 1000,
  nsim = NULL,
  verbose = FALSE,
  check = FALSE,



This could take one of two forms

"net benefit" form: a matrix or data frame of samples from the uncertainty distribution of the expected net benefit. The number of rows should equal the number of samples, and the number of columns should equal the number of decision options.

"cost-effectiveness analysis" form: a list with the following named components:

"c": a matrix or data frame of samples from the distribution of costs. There should be one column for each decision option.

"e": a matrix or data frame of samples from the distribution of effects, likewise.

"k": a vector of willingness-to-pay values.

Objects of class "bcea", as created by the BCEA package, are in this "cost-effectiveness analysis" format, therefore they may be supplied as the outputs argument.

Users of heemod can create an object of this form, given an object produced by run_psa (obj, say), with import_heemod_outputs.

If outputs is a matrix or data frame, it is assumed to be of "net benefit" form. Otherwise if it is a list, it is assumed to be of "cost effectiveness analysis" form.


Matrix or data frame of samples from the uncertainty distribution of the input parameters of the decision model. The number of columns should equal the number of parameters, and the columns should be named. This should have the same number of rows as there are samples in outputs, and each row of the samples in outputs should give the model output evaluated at the corresponding parameters.

Users of heemod can create an object of this form, given an object produced by run_psa (obj, say), with import_heemod_inputs.


Either a character vector, or a list of character vectors.

If a character vector is supplied, then a single, joint EVPPI calculation is done with for the parameters named in this vector.

If a list of character vectors is supplied, then multiple EVPPI calculations are performed, one for each list component defined in the above vector form.

pars must be specified if inputs is a matrix or data frame. This should then correspond to particular columns of inputs. If inputs is a vector, this is assumed to define the single parameter of interest, and then pars is not required.


Character string indicating the calculation method. If one string is supplied, this is used for all calculations. A vector of different strings can be supplied if a different method is desired for different list components of pars.

The default methods are based on nonparametric regression:

"gam" for a generalized additive model implemented in the gam function from the mgcv package. This is the default method for calculating the EVPPI of 4 or fewer parameters.

"gp" for a Gaussian process regression, as described by Strong et al. (2014) and implemented in the SAVI package ( This is the default method for calculating the EVPPI of more than 4 parameters.

"inla" for an INLA/SPDE Gaussian process regression method, from Heath et al. (2016).

"bart" for Bayesian additive regression trees, using the dbarts package. Particularly suited for joint EVPPI of many parameters.

"earth" for a multivariate adaptive regression spline with the earth package (Milborrow, 2019).

"so" for the method of Strong and Oakley (2013). Only supported for single parameter EVPPI.

"sal" for the method of Sadatsafavi et al. (2013). Only supported for single parameter EVPPI.


If this is TRUE, calculate a standard error for the EVPPI if possible. Currently only supported for methods "gam", "earth" and method="bart". (In the latter method it is more correctly called a posterior standard deviation). These represent uncertainty about the parameters of the fitted regression model, and will naturally be lower when more simulations from the decision model are used to fit it. They do not represent uncertainty about the structure of the regression model, and are also typically small in the context of uncertainties arising from converting individual-level to population VoI.


Number of parameter replicates for calculating the standard error. Only applicable to method="gam". For method="bart" the analogous quantity is the number of MCMC samples, which is controlled by the ndpost argument to bart, which can be passed as an argument to evppi.


Number of simulations from the decision model to use for calculating EVPPI. The first nsim rows of the objects in inputs and outputs are used.


If TRUE, then messages are printed describing each step of the calculation, if the method supplies these. Can be useful to see the progress of slow calculations.


If TRUE, then extra information about the estimation is saved inside the object that this function returns. This currently only applies to the regression-based methods "gam" and "earth" where the fitted regression model objects are saved. This allows use of the check_regression function, which produces some diagnostic checks of the regression models.


Other arguments to control specific methods.

For method="gam", the following arguments can be supplied:

  • gam_formula: a character string giving the right hand side of the formula supplied to the gam() function. By default, this is a tensor product of all the parameters of interest, e.g. if pars = c("pi","rho"), then gam_formula defaults to t(pi, rho, bs="cr"). The option bs="cr" indicates a cubic spline regression basis, which is more computationally efficient than the default "thin plate" basis. If there are four or more parameters of interest, then the additional argument k=4 is supplied to te(), specifying a four-dimensional basis, which is currently the default in the SAVI package.

    If there are spaces in the variable names in inputs, then these should be converted to underscores before forming an explicit gam_formula.

For method="gp", the following arguments can be supplied:

  • gp_hyper_n: number of samples to use to estimate the hyperparameters in the Gaussian process regression method. By default, this is the minimum of the following three quantities: 30 times the number of parameters of interest, 250, and the number of simulations being used for calculating EVPPI.

  • maxSample: Maximum sample size to employ for method="gp". Only increase this from the default 5000 if your computer has sufficent memory to invert square matrices with this dimension.

For method="inla", the following arguments can be supplied, as described in detail in Baio, Berardi and Heath (2017):

  • int.ord (integer) maximum order of interaction terms to include in the regression predictor, e.g. if int.ord=k then all k-way interactions are used. Currently this applies to both effects and costs.

  • cutoff (default 0.3) controls the density of the points inside the mesh in the spatial part of the mode. Acceptable values are typically in the interval (0.1,0.5), with lower values implying more points (and thus better approximation and greatercomputational time).

  • convex.inner (default = -0.4) and convex.outer (default = -0.7) control the boundaries for the mesh. These should be negative values and can be decreased (say to -0.7 and -1, respectively) to increase the distance between the points and the outer boundary, which also increases precision and computational time.

  • robust. if TRUE then INLA will use a t prior distribution for the coefficients of the linear predictor, rather than the default normal distribution.

  • h.value (default=0.00005) controls the accuracy of the INLA grid-search for the estimation of the hyperparameters. Lower values imply a more refined search (and hence better accuracy), at the expense of computational speed.

  • plot_inla_mesh (default FALSE) Produce a plot of the mesh.

  • max.edge Largest allowed triangle edge length when constructing the mesh, passed to inla.mesh.2d.

  • pfc_struc Variance structure to pass to pfc in the ldr package for principal fitted components. The default "AIC" selects the one that fits best given two basis terms. Change this to, e.g. "iso", "aniso" or "unstr" if an "Error in eigen..." is obtained.

For any of the nonparametric regression methods:

  • ref The reference decision option used to define the incremental net benefit, cost or effects before performing nonparametric regression. Either an integer column number, or the name of the column from outputs.

For method="so":

  • n.blocks Number of blocks to split the sample into. Required.

For method="sal":

  • n.seps Number of separators (default 1).


A data frame with a column pars, indicating the parameter(s), and a column evppi, giving the corresponding EVPPI.

If outputs is of "cost-effectiveness analysis" form, so that there is one EVPPI per willingness-to-pay value, then a column k identifies the willingness-to-pay.

If standard errors are requested, then the standard errors are returned in the column se.


Heath, A., Kunst, N., & Jackson, C. (eds.). (2024). Value of Information for Healthcare Decision-Making. CRC Press.

Strong, M., Oakley, J. E., & Brennan, A. (2014). Estimating multiparameter partial expected value of perfect information from a probabilistic sensitivity analysis sample: a nonparametric regression approach. Medical Decision Making, 34(3), 311-326.

Heath, A., Manolopoulou, I., & Baio, G. (2016). Estimating the expected value of partial perfect information in health economic evaluations using integrated nested Laplace approximation. Statistics in Medicine, 35(23), 4264-4280.

Baio, G., Berardi, A., & Heath, A. (2017). Bayesian cost-effectiveness analysis with the R package BCEA. New York: Springer.

Milborrow, S. (2019) earth: Multivariate Adaptive Regression Splines. R package version 5.1.2. Derived from mda:mars by Trevor Hastie and Rob Tibshirani. Uses Alan Miller's Fortran utilities with Thomas Lumley's leaps wrapper.

Strong, M., & Oakley, J. E. (2013). An efficient method for computing single-parameter partial expected value of perfect information. Medical Decision Making, 33(6), 755-766. Chicago

Sadatsafavi, M., Bansback, N., Zafari, Z., Najafzadeh, M., & Marra, C. (2013). Need for speed: an efficient algorithm for calculation of single-parameter expected value of partial perfect information. Value in Health, 16(2), 438-448.