healthiar (version 0.2.1)

summarize_uncertainty: Get Monte Carlo confidence intervals

Description

This function determines summary uncertainty (based on central, lower and upper estimates of at least one input variable) using attribute() or compare() function output by 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)

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.

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. Based on it, each geographic unit is assigned a different. If empty, 123 is used as the base seed per default. The function preserves and restores the user's original random seed (if set prior to calling the function) upon function completion.

Author

Alberto Castro & Axel Luyten

Details

Method

For each processed input variable with a provided 95% confidence interval value, a distribution is fitted (see below). From these, n_sim input value sets are sampled to compute n_sim attributable impacts. The median value of these attributable impacts is reported as the central estimate, and the 2.5th and 97.5th percentiles define the lower and upper bounds of the 95% summary uncertainty confidence interval, respectively. Aggregated central, lower and upper estimates are obtained by summing the corresponding values of each lower level unit.

Distributions used for simulation

Relative risk values are simulated based on an optimized gamma distribution, which fits well as relative risks are positive and its distributions usually right-skewed. The gamma distribution best fitting the inputted central relative risk estimate and corresponding lower and upper 95% confidence interval values is fitted using stats::qgamma() (with rate = shape / rr_central) and then stats::optimize is used to optimize the distribution parameters. Finally, n_sim relative risk values are simulated using stats::rgamma().

Exposure values are simulated based on a normal distribution using stats::rnorm() with mean = exp_central and a standard deviation based on corresponding lower and upper 95% exposure confidence interval values.

Cutoff values are simulated based on a normal distribution using stats::rnorm() with mean = cutoff_central and a standard deviation based on corresponding lower and upper 95% cutoff confidence interval values.

Baseline health data values are simulated based on a normal distribution using stats::rnorm() with mean = bhd_central and a standard deviation based on corresponding lower and upper 95% exposure confidence interval values.

Disability weights values of the morbidity health outcome of interest are simulated based on a beta distribution, as both the disability weights and the beta distribution are bounded by 0 and 1. The beta distribution best fitting the inputted central disability weight estimate and corresponding lower and upper 95% confidence interval values is fitted using stats::qgamma() (the best fitting distribution parameters shape1 and shape2 are determined using stats::optimize()). Finally, n_sim disability weight values are simulated using stats::rbeta().

Duration values of the morbidity health outcome of interest are simulated based on a normal distribution using stats::rnorm() with mean = duration_central and a standard deviation based on corresponding lower and upper 95% exposure confidence interval values.

Function arguments

seed

If the seed argument is specified then 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 and scenarios.

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