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Parameter Calculation Comparison Summary

parameter_summary.Rd

Implements several approaches to computing partition-aggregated parameters, then tables them up for convenient plotting.

Usage

parameter_summary(
  f_param,
  f_dense,
  model_partition,
  resolution = diff(range(model_partition)) + 1L
)

Arguments

f_param

a function, f(x) which transforms the feature (e.g. age), and yields the parameter value. Alternatively, a data.frame where the first column is the feature (x) and the second is the parameter (y); see xy.coords() for details. If the latter, combined with pars_interp_opts, and defaulting to spline interpolation.

f_dense

like f_param, either a density function (though it does not have to integrate to 1 like a pdf) or a data.frame of values. If the latter, combined with dens_interp_opts and defaulting to constant density from each x to the next.

model_partition

a numeric vector of cut points, which define the partitioning that will be used in the model

resolution

the number of points to calculate for the underlying f_param function.

Value

a data.table, columns:

  • model_category, a integer corresponding to which of the intervals of model_partition the x value is in

  • x, a numeric series from the first to last elements of model_partition with length resolution

  • method, a factor with levels:

    • f_val: f_param(x)

    • f_mid: f_param(x_mid), where x_mid is the midpoint x of the model_category

    • f_mean: f_param(weighted.mean(x, w)), where w defined by densities and model_category

    • mean_f: weighted.mean(f_param(x), w), same as previous

    • wm_f: the result as if having used paramix::blend(); this should be very similar to mean_f, though will be slightly different since blend uses integrate()

Examples

# COVID IFR from Levin et al 2020 https://doi.org/10.1007/s10654-020-00698-1
f_param <- function(age_in_years) {
  (10^(-3.27 + 0.0524 * age_in_years))/100
}

densities <- data.frame(
  from = 0:100,
  weight = c(rep(1, 66), exp(-0.075 * 1:35))
)

model_partition <- c(0, 5, 20, 65, 101)

ps_dt <- parameter_summary(f_param, densities, model_partition)
ps_dt
#>      model_category     x method        value
#>               <int> <num> <fctr>        <num>
#>   1:              1     0  f_val 5.370318e-06
#>   2:              1     1  f_val 6.058987e-06
#>   3:              1     2  f_val 6.835968e-06
#>   4:              1     3  f_val 7.712586e-06
#>   5:              1     4  f_val 8.701618e-06
#>  ---                                         
#> 501:              4    96   wm_f 9.557924e-02
#> 502:              4    97   wm_f 9.557924e-02
#> 503:              4    98   wm_f 9.557924e-02
#> 504:              4    99   wm_f 9.557924e-02
#> 505:              4   100   wm_f 9.557924e-02

ggplot(ps_dt) + aes(x, y = value, color = method) +
  geom_line(data = \(dt) subset(dt, method == "f_val")) +
  geom_step(data = \(dt) subset(dt, method != "f_val")) +
  theme_bw() + theme(
    legend.position = "inside", legend.position.inside = c(0.05, 0.95),
    legend.justification = c(0, 1)
  ) + scale_color_discrete(
    "Method", labels = c(
      f_val = "f(x)", f_mid = "f(mid(x))", f_mean = "f(E[x])",
      mean_f = "discrete E[f(x)]", wm_f = "integrated E[f(x)]"
    )
  ) +
  scale_x_continuous("Age", breaks = seq(0, 100, by = 10)) +
  scale_y_log10("IFR", breaks = 10^c(-6, -4, -2, 0), limits = 10^c(-6, 0))