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Get Monte Carlo confidence intervals

Source: R/summarize_uncertainty.R
summarize_uncertainty.Rd

This function obtains a summary of uncertainty (based on central, lower and upper estimates of at least one input variable) using a Monte Carlo simulation.

Input variables that will be processed are:

  • relative_risk (rr_...)

  • exposure (exp_...)

  • cutoff (cutoff_...)

  • baseline health data (bhd_...)

  • disability weight (dw_...)

  • duration (duration_...)

Usage

summarize_uncertainty(output_attribute, n_sim, seed = NULL)

Arguments

output_attribute

variable in which the output of a healthiar::attribute_...() function call are stored.

n_sim

numeric value indicating the number of simulations to be performed.

seed

numeric value for fixing the randomization, so that the same call always returns the same results. If empty (default), the base seed is drawn from the random number generator currently in use, i.e. the results differ across calls unless the user calls set.seed() beforehand. The function preserves and restores the user's original random seed (if set prior to calling the function) upon function completion.

Value

This function returns a list containing:

1) uncertainty_main (tibble) containing the numeric summary uncertainty central estimate and corresponding lower and upper confidence intervals for the attributable health impacts obtained through Monte Carlo simulation;

2) uncertainty_detailed (list) containing detailed (and interim) results.

  • impact_by_sim (tibble) containing the results for each simulation

  • uncertainty_by_geo_id_micro (tibble) containing results for each geographic unit under analysis (specified in geo_id_micro argument in the preceding attribute_health call)

The two results elements are added to the existing output.

Details

Function arguments seed The parallel package is used to generate independent L’Ecuyer random number streams. One stream is allocated per variable (or per variable–geography combination, as needed), ensuring reproducible and independent random draws across variables. The streams are shared by both scenarios of a comparison (see compare), so that the variables that are common to both scenarios (e.g. rr_...) take the same simulated value in each simulation of both scenarios. This is the case whether or not seed is entered by the user.

Methodology

This function summarizes the uncertainty of the attributable health impacts (i.e. a single confidence interval instead of many combinations). For this purpose, it employs a Monte Carlo simulation methodology (Robert and Casella 2004) and framework application (Rubinstein and Kroese 2016) .

The variables that cannot be negative and are simulated with a normal distribution (exp_..., cutoff_..., bhd_... and duration_...) are drawn from that distribution truncated at zero. As the normal distribution is symmetric, the simulated values reproduce the entered confidence interval only if ..._lower and ..._upper are symmetric around ..._central. The more asymmetric the entered confidence interval, the more the simulated values depart from it.

If the assessment covers several geographic units, the uncertainty of the aggregated unit (geo_id_macro) is obtained by first summing the impacts of all geo_id_micro within each simulation and only then taking the quantiles of those sums.

Detailed information about the methodology (including equations) is available in the package vignette. More specifically, see chapters:

References

Robert CP, Casella G (2004). Monte Carlo Statistical Methods, Springer Texts in Statistics. Springer Science and Business Media. doi:10.1007/978-1-4757-4145-2 .

Rubinstein RY, Kroese DP (2016). Simulation and the Monte Carlo Method. John Wiley and Sons. doi:10.1002/9781118631980 .

See also

Author

Alberto Castro & Axel Luyten

Examples

# Goal: obtain summary uncertainty for an existing attribute_health() output
# First create an assessment
attribute_health_output <- attribute_health(
  erf_shape = "log_linear",
  rr_central = 1.369,
  rr_lower = 1.124,
  rr_upper = 1.664,
  rr_increment = 10,
  exp_central = 8.85,
  exp_lower = 8,
  exp_upper = 10,
  cutoff_central = 5,
  bhd_central = 30747,
  bhd_lower = 28000,
  bhd_upper = 32000
)
# Then run Monte Carlo simulation
results <- summarize_uncertainty(
  output_attribute = attribute_health_output,
  n_sim = 100
)
results$uncertainty_main$impact # Central, lower and upper estimates
#> [1] 3531.129 1506.471 5365.979