evppi {BCEA}  R Documentation 
Expected Value of Perfect Partial Information (EVPPI) for Selected Parameters
Description
Calculates the Expected Value of Perfect Partial Information (EVPPI) for subsets of parameters. Uses GAM nonparametric regression for single parameter EVPPI and the SPDEINLA method for larger parameter subsets.
Usage
evppi(he, param_idx, input, N = NULL, plot = FALSE, residuals = TRUE, ...)
## Default S3 method:
evppi(he, ...)
## S3 method for class 'bcea'
evppi(
he,
param_idx = NULL,
input,
N = NULL,
plot = FALSE,
residuals = TRUE,
method = NULL,
...
)
Arguments
he 
A 
param_idx 
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. 
input 
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. 
N 
The number of PSA simulations used to calculate the EVPPI. The default uses all the available samples. 
plot 
A logical value indicating whether the triangular mesh for
SPDEINLA should be plotted. Default set to 
residuals 
A logical value indicating whether the fitted values for
the SPDEINLA method should be outputted. Default set to 
... 
Additional arguments. Details of the methods to compute the EVPPI and their additional arguments are:

method 
Character string to select which method to use. The default methods are recommended. However, it is possible (mainly for backward compatibility) to use different methods. 
Details
The single parameter EVPPI has been calculated using the nonparametric GAM regression developed by Strong et al. (2014). The multiparameter EVPPI is calculated using the SPDEINLA 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_argscan be given as before.
int.ordcan 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.
Value
Object of class evppi
:
evppi 
The computed values of evppi for all values of the parameter of willingness to pay. 
index 
A numerical vector with the index associated with the parameters for which the EVPPI was calculated. 
k 
The vector of values for the willingness to pay. 
evi 
The vector of values for the overall EVPPI. 
fitted.costs 
The fitted values for the costs. 
fitted.effects 
The fitted values for the effects. 
parameters 
A single string containing the names of the parameters for which the EVPPI was calculated, used for plotting the EVPPI. 
time 
Computational time (in seconds). 
fit.c 
The object produced by the model fit for the costs. 
fit.e 
The object produced by the model fit for the effects. 
formula 
The formula used to fit the model. 
method 
A string indicating the method used to estimate the EVPPI. 
GAM regression
For multiparameter, 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.
INLArelated 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 kway interactions will be used for the
effects and all hway 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 gridsearch 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.
Author(s)
Anna Heath, Gianluca Baio
References
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 singleparameter 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 CostEffectiveness Analysis with the R package BCEA. Springer International Publishing. https://link.springer.com/book/10.1007/9783319557182.
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 02776715, doi:10.1002/sim.6983, 1504.05436, https://pubmed.ncbi.nlm.nih.gov/27189534/.
See Also
Examples
# See Baio G., Dawid A.P. (2011) for a detailed description of the
# Bayesian model and economic problem
## Not run:
# Load the postprocessed 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$mat)
plot(EVPPI)
# deprecated (single parameter) methods
EVPPI.so < evppi(m, c("beta.1.", "beta.2."), inp$mat, method = "so", n.blocks = 50)
EVPPI.sad < evppi(m, c("beta.1.", "beta.2."), inp$mat, method = "sad", n.seps = 1)
plot(EVPPI.so)
plot(EVPPI.sad)
# Compute the EVPPI using INLA/SPDE
if (require("INLA"))
x_inla < evppi(he = m, 39:40, input = inp$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")
}
data(Smoking)
treats < c("No intervention", "Selfhelp",
"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$mat, h.value = 0.0000005)
plot(EVPPI)
## End(Not run)
data(Vaccine, package = "BCEA")
treats < c("Status quo", "Vaccination")
bcea_vacc < bcea(e.pts, c.pts, ref = 2, interventions = treats)
inp < createInputs(vaccine_mat)
evppi(bcea_vacc, c("beta.1.", "beta.2."), inp$mat)