Calculate the parameters of a parametric probability distribution from reported values of percentiles, or median and range

Summary data of distributions, as provided by reports and meta-analyses, can be used to extract the parameters of a chosen distribution. Currently available distributions are: lognormal, gamma, Weibull and normal. Extracting from a lognormal returns the meanlog and sdlog parameters, extracting from the gamma and Weibull returns the shape and scale parameters, and extracting from the normal returns the mean and sd parameters.

Usage

extract_param(
  type = c("percentiles", "range"),
  values,
  distribution = c("lnorm", "gamma", "weibull", "norm"),
  percentiles,
  samples,
  control = list(max_iter = 1000, tolerance = 1e-05)
)

Arguments

type: A character defining whether summary statistics based around percentiles (default) or range.
values: A vector. If type = percentiles: c(percentile_1, percentile_2); and if type = range: c(median, min, max).
distribution: A character specifying distribution to use. Default is lnorm; also takes gamma, weibull and norm.
percentiles: A vector with two elements specifying the percentiles defined in values if using type = "percentiles". Percentiles should be specified between 0 and 1. For example 2.5th and 97.5th percentile is given as c(0.025, 0.975).
samples: A numeric specifying the sample size if using type = "range".
control: A named list containing options for the optimisation. List element $max_iter is a numeric specifying the maximum number of times the parameter extraction will run optimisation before returning result early. This prevents overly long optimisation loops if optimisation is unstable and does not converge over multiple iterations. Default is 1000 iterations. List element $tolerance is passed to .check_optim_conv() for tolerance on parameter convergence over iterations of optimisation. Elements of in the control list are not passed to optim().

Value

A named numeric vector with the parameter values of the distribution. If the distribution = lnorm then the parameters returned are the meanlog and sdlog; if the distribution = gamma or distribution = weibull then the parameters returned are the shape and scale; if distribution = norm then the parameters returned are mean and sd.

Details

For gamma, lnorm and weibull, extract_param() works only for strictly positive values at the percentiles of a distribution or the median and range of data (numerics supplied to the values argument). This means that negative values at the lower percentile or lower range will not work with this function although they may present themselves in epidemiological data (e.g. negative serial interval). For the norm distribution negative values are allowed.

Author

Adam Kucharski, Joshua W. Lambert

Examples

# set seed to control for stochasticity
set.seed(1)

# extract parameters of a lognormal distribution from the 75 percentiles
extract_param(
  type = "percentiles",
  values = c(6, 13),
  distribution = "lnorm",
  percentiles = c(0.125, 0.875)
)
#> Stochastic numerical optimisation used. 
#> Rerun function multiple times to check global optimum is found
#>   meanlog     sdlog 
#> 2.1783557 0.3360688 

# extract parameters of a gamma distribution from median and range
extract_param(
  type = "range",
  values = c(10, 3, 18),
  distribution = "gamma",
  samples = 20
)
#> Stochastic numerical optimisation used. 
#> Rerun function multiple times to check global optimum is found
#>    shape    scale 
#> 5.342206 1.994304