evppi {BCEA}R Documentation

Expected Value of Perfect Partial Information (EVPPI) for Selected Parameters


Calculates the Expected Value of Perfect Partial Information (EVPPI) for subsets of parameters. Uses GAM non-parametric regression for single parameter EVPPI and the SPDE-INLA method for larger parameter subsets.


evppi(he, param_idx, input, N = NULL, plot = FALSE, residuals = TRUE, ...)

## S3 method for class 'bcea'
evppi(he, param_idx, input, N = NULL, plot = FALSE, residuals = TRUE, ...)

## Default S3 method:
evppi(he, ...)



A bcea object containing the results of the Bayesian modelling and the economic evaluation.


A vector of parameters for which the EVPPI should be calculated. This can be given as a string (or vector of strings) of names or a numeric vector, corresponding to the column numbers of important parameters.


A matrix containing the simulations for all the parameters monitored by the call to JAGS or BUGS. The matrix should have column names matching the names of the parameters and the values in the vector parameter should match at least one of those values.


The number of PSA simulations used to calculate the EVPPI. The default uses all the available samples.


A logical value indicating whether the triangular mesh for SPDE-INLA should be plotted. Default set to 'FALSE'.


A logical value indicating whether the fitted values for the SPDE-INLA method should be outputted. Default set to 'TRUE'.


Additional arguments. The default methods to compute the EVPPI are: - For single-parameter: GAM regression. - For multi-parameter: INLA/SPDE. However, it is possible (mainly for backward compatibility) to use different methods. For single-parameter, the user can specify the method of Sadatsafavi et al. or the method of Strong & Oakley. In order to do so, it is necessary to include the extra parameter method which takes as value a string "sad" in the former case and a string "so" in the latter. In case "sal" is selected, then it is possible to also specify the number of "separators" (e.g. n.seps=3). If none is specified, the default value n.seps=1 is used. If "so" is used as method for the calculation of the EVPPI, then the user *needs* to also specify the number of "blocks" (e.g. n.blocks=20).


The single parameter EVPPI has been calculated using the non-parametric GAM regression developed by Strong et al. (2014). The multi-parameter EVPPI is calculated using the SPDE-INLA regression method for Gaussian Process regression developed by Heath et al. (2015).

This function has been completely changed and restructured to make it possible to change regression method. The method argument can now be given as a list. The first element element in the list is a vector giving the regression method for the effects. The second gives the regression method for the costs. The ‘method’ argument can also be given as before which then uses the same regression method for all curves. All other 'extra_args' can be given as before. 'int.ord' can be updated using the list formulation above to give the interactions for each different curve. The formula argument for GAM can only be given once, either 'te()' or 's() + s()' as this is for computational reasons rather than to aid fit. You can still plot the INLA mesh elements but not output the meshes.


Object of class 'evppi':


The computed values of evppi for all values of the parameter of willingness to pay.


A numerical vector with the index associated with the parameters for which the EVPPI was calculated.


The vector of values for the willingness to pay.


The vector of values for the overall EVPPI.


The fitted values for the costs.


The fitted values for the effects.


A single string containing the names of the parameters for which the EVPPI was calculated, used for plotting the EVPPI.


Computational time (in seconds).


The object produced by the model fit for the costs.


The object produced by the model fit for the effects.


The formula used to fit the model.


A string indicating the method used to estimate the EVPPI.

GAM regression

For multi-parameter, the user can select 3 possible methods. If method = "GAM" (BCEA will accept also "gam", "G" or "g"), then the computations are based on GAM regression. The user can also specify the formula for the regression. The default option is to use a tensor product (e.g. if there are two main parameters, p1 and p2, this amounts to setting formula = "te(p1,p2)", which indicates that the two parameters interact). Alternatively, it is possible to specify a model in which the parameters are independent using the notation formula = "s(p1) + s(p2)". This may lead to worse accuracy in the estimates.

Strong et al. GP regression

This is used if method="GP" (BCEA will also accept the specification method="gp"). In this case, the user can also specify the number of PSA runs that should be used to estimate the hyperparameters of the model (e.g. n.sim=100). This value is set by default to 500.

INLA-related options

These are all rather technical and are described in detail in Baio et al. (2017). The optional parameter vector int.ord can take integer values (c(1,1) is default) and will force the predictor to include interactions: if int.ord = c(k, h), then all k-way interactions will be used for the effects and all h-way interactions will be used for the costs. Also, the user can specify the feature of the mesh for the "spatial" part of the model. The optional parameter cutoff (default 0.3) controls the density of the points inside the mesh. Acceptable values are typically in the interval (0.1, 0.5), with lower values implying more points (and thus better approximation and greater computational time). The construction of the boundaries for the mesh can be controlled by the optional inputs convex.inner (default = -0.4) and convex.outer (default = -0.7). 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. The optional argumentrobust can be set to TRUE, in which case INLA will use a t prior distribution for the coefficients of the linear predictor. Finally, the user can control the accuracy of the INLA grid-search for the estimation of the hyperparameters. This is done by setting a value h.value (default = 0.00005). Lower values imply a more refined search (and hence better accuracy), at the expense of computational speed. The method argument can also be given as a list allowing different regression methods for the effects and costs, and the different incremental decisions. The first list element should contain a vector of methods for the incremental effects and the second for the costs, for example method = list(c("GAM"), c("INLA")). The int.ord argument can also be given as a list to give different interaction levels for each regression curve.

By default, when no method is specified by the user, evppi will use GAM if the number of parameters is <5 and INLA otherwise.


Anna Heath, Gianluca Baio


Strong M, Oakley JE, Brennan A (2014). “Estimating Multiparameter Partial Expected Value of Perfect Information from a Probabilistic Sensitivity Analysis Sample : A Nonparametric Regression Approach.” Medical Decision Making, 311–326. doi:10.1177/0272989X13505910.

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 Heal., 16(2), 438–448. ISSN 10983015, doi:10.1016/j.jval.2012.10.018, http://dx.doi.org/10.1016/j.jval.2012.10.018.

Baio G (2013). Bayesian Methods in Health Economics. CRC.

Baio, Gianluca, Berardi, Andrea, Heath A (2017). Bayesian Cost-Effectiveness Analysis with the R package BCEA. Springer International Publishing. https://link.springer.com/book/10.1007/978-3-319-55718-2.

Heath A, Manolopoulou I, Baio G (2016). “Estimating the expected value of partial perfect information in health economic evaluations using integrated nested Laplace approximation.” Stat. Med., 35(23), 4264–4280. ISSN 0277-6715, doi:10.1002/sim.6983, 1504.05436, https://pubmed.ncbi.nlm.nih.gov/27189534/.

See Also

bcea, plot.evppi


# See Baio G., Dawid A.P. (2011) for a detailed description of the 
# Bayesian model and economic problem

## Not run: 
# Load the post-processed results of the MCMC simulation model
# original JAGS output is can be downloaded from here
# https://gianluca.statistica.it/book/bcea/code/vaccine.RData

data(Vaccine, package = "BCEA")
treats <- c("Status quo", "Vaccination")

# Run the health economic evaluation using BCEA
m <- bcea(e.pts, c.pts, ref = 2, interventions = treats)

# Compute the EVPPI for a bunch of parameters
inp <- createInputs(vaccine_mat)

EVPPI <- evppi(m, c("beta.1." , "beta.2."), inp$mat)


# deprecated (single parameter) methods
EVPPI.so <- evppi(m, c("beta.1.", "beta.2."), inp$mat, method = "so", n.blocks = 50)
EVPPI.sad <- evppi(m, c("beta.1.", "beta.2."), inp$mat, method = "sad", n.seps = 1)

# Compute the EVPPI using INLA/SPDE
if (require("INLA"))
  x_inla <- evppi(he = m, 39:40, input = inp$mat)

# using GAM regression
x_gam <- evppi(he = m, 39:40, input = inp$mat, method = "GAM")

# using Strong et al GP regression
x_gp <- evppi(he = m, 39:40, input = inp$mat, method = "GP")

# plot results
if (require("INLA")) plot(x_inla)
points(x_inla$k, x_inla$evppi, type = "l", lwd = 2, lty = 2)
points(x_gam$k, x_gam$evppi, type = "l", col = "red")
points(x_gp$k, x_gp$evppi, type = "l", col = "blue")

if (require("INLA")) {
  plot(x_inla$k, x_inla$evppi, type = "l", lwd = 2, lty = 2)
  points(x_gam$k, x_gam$evppi, type = "l", col = "red")
  points(x_gp$k, x_gp$evppi, type = "l", col = "blue")

treats <- c("No intervention", "Self-help",
"Individual counselling", "Group counselling")
m <- bcea(eff, cost, ref = 4, interventions = treats, Kmax = 500)
inp <- createInputs(smoking_output)
EVPPI <- evppi(m, c(2,3), inp$mat, h.value = 0.0000005)

## End(Not run)

[Package BCEA version 2.4.4 Index]