empirical_EVPI {decisionSupport}

Expected value of perfect information (EVPI) for a simple model with the predictor variable sampled from a normal distribution with.

Description

The Expected Value of Perfect Information is a concept in decision analysis. It measures the expected loss of gain (expected opportunity loss, EOL) that is incurred because the decision-maker does not have perfect information about a paricular variable. It is determined by examining the influence of that variable on the output value of a decision model. Its value is best illustrated by a plot of weighed decision outcomes as a function of the variable in question. If this curve intersects zero and the recommendation without perfect information is to go ahead with the project, the EVPI is the negative area under the curve, or the positive area if the recommendation is not to go ahead. If there is no intersection point, the EVPI is zero.

Usage

empirical_EVPI(mc, test_var_name, out_var_name)

## S3 method for class 'EVPI_res'
summary(object, ...)

## S3 method for class 'EVPI_res'
plot(x, res = TRUE, ...)

Arguments

mc

output table from a Monte Carlo simulation, e.g. as realized with the decisionSupport package

test_var_name

character; name of an independent variable in mc, sampled from a normal distribution

out_var_name

character; name of a dependent variable in mc

object

EVPI_res object (produced with empirical_EVPI) as input to the summary function.

...

Arguments to be passed to methods, such as graphical parameters (see par).

x

EVPI_res object (produced with empirical_EVPI) as input to the plotting function.

res

boolean parameter indicating whether the plot function should output a plot of opportunity losses and gains (res = TRUE) or a plot of the original data with the loess prediction (res = FALSE).

Details

The EVPI is often calculated by assuming that all variables except the one being tested take their best estimate. This makes it possible to calculate the EVPI very quickly, but at a high price: the assumption that many variables simply take their best value ignores uncertainties about all these variables. In the present implementation, this problem is addressed by using the outputs of a Monte Carlo simulation and assessing the EVPI empirically. In the first step, the output variable is smoothed using a loess regression with an automated optimization of the bandwidth parameter, based on a generalized cross validation procedure. Then the values are weighted according to the probability density function that has been used for Monte Carlo sampling (i.e. a normal distribution, with mean and standard deviation being estimated automatically) and the resulting positive and negative areas under the curve are calculated. After this, the expected gain (exptected mean value - EMV) without perfect information (PI) is calculated, the recommendation whether to go ahead with the project without PI determine and the EVPI returned by the function.

Value

list of 11 elements: (1) expected_gain: expected gain when project is implemented, without knowing the value of the test variable, equals NA when there is no variation in the output variable (2) recommendation: should project be implemented? Decision without knowing the value of the test variable (3) EVPI_do: the Expected Value of Perfect Information (EVPI) for this variable, if the recommended decision is to implement the project. (4) EVPI_dont: the Expected Value of Perfect Information (EVPI) for this variable, if the recommended decision is not to implement the project. (5) tests_var_data: values of the test variable (6) out_var_data: values of the outcome variable (7) out_var_sm: results of loess regression = smoothed outcome variable (8) weight: values by which smoothed outcome variable is weighted (9) out_var_weight: smoothed and weighted outcome variable (10) test_var_name: variable name of test data (11) out_var_name: variable name of outcome data

Author(s)

Eike Luedeling, Katja Schiffers

Examples

### In the following example, the sign of the calculation
### is entirely determined by the predictor variable
### 'indep1', so this should be expected to have a high
### EVPI.

montecarlo <- data.frame(indep1 = rnorm(1000), indep2 = rlnorm(1000))
montecarlo[, 'output1'] <- montecarlo[, 'indep1'] * montecarlo[, 'indep2']

evpi1 <- empirical_EVPI(mc = montecarlo, test_var_name = 'indep1', out_var_name = 'output1')
summary(evpi1)
plot(evpi1, res = FALSE)
plot(evpi1, res = TRUE)


### In this example, the sign of the output variable does not change depending on the
### predictor variable 'indep1' so the EVPI should be zero.
montecarlo[, 'output2'] <- (montecarlo[, 'indep1'] * (montecarlo[, 'indep2']) + 10)
evpi2 <- empirical_EVPI(mc = montecarlo, test_var_name = 'indep1', out_var_name = 'output2')
summary(evpi2)
plot(evpi2, res = FALSE)
plot(evpi2, res = TRUE)