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

evppi(
  outputs,
  inputs,
  pars = NULL,
  method = NULL,
  se = FALSE,
  B = 500,
  nsim = NULL,
  verbose = FALSE,
  ...
)

Arguments

outputs

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.

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.

inputs

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.

pars

A character vector giving the parameters of interest, for which a single EVPPI calculation is required. If the vector has multiple element, then the joint expected value of perfect information on all these parameters together is calculated.

Alternatively, pars may be a list. Multiple EVPPI calculations are then performed, one for each component of pars 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, then pars is not required.

method

Character string indicating the calculation method. 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 (http://savi.shef.ac.uk/SAVI/).

"inla" for an INLA/SPDE Gaussian process regression method, from Heath et al. (2016). This is the default method for calculating the EVPPI of more than 4 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.

se

If possible, calculate a standard error for the EVPPI. Currently only supported for method="gam".

B

Number of parameter replicates for calculating the standard error.

nsim

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

verbose

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

...

Other arguments to control specific methods.

For method="gam":

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 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 (http://savi.shef.ac.uk/SAVI/).

For method="gp":

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", 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.

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.

For method="so":

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

For method="sal":

n.seps Number of separators (default 1).

Value

A data frame with a column evppi giving the 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 pars is a list, so that multiple EVPPI calculations are performed with different parameters, then another column pars identifies the parameters.

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

References

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. https://CRAN.R-project.org/package=earth.

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.