Simulating ACE symptom counts

Simulating ACE symptom counts

An adverse-childhood-experience score is how many of a fixed list of items a person endorses. That makes it bounded (out of k), zero-heavy, and built from binary items that are correlated with each other. sim_symptoms() reproduces that shape by drawing correlated Bernoulli items through a Gaussian copula, so the realized distribution looks like real ACE data rather than an idealized one.

sim_symptoms()

sim_symptoms(n, effect = 0, k = 10, p_items = NULL, rho = 0.30)

Argument	What it is
n	Sample size per group.
effect	Group effect as a uniform shift in every item's log-odds. 0 is the null.
k	Number of items, the ceiling (10 for the modern instrument, 7 for the original).
p_items	Per-item endorsement probabilities. Defaults to default_ace_probs(k).
rho	Latent (Gaussian) inter-item correlation. This is the correlation of the underlying normals; the correlation among the observed 0/1 items is lower and varies by pair.

It returns a data frame with group, ace (the count), and k.

library(countkit)
set.seed(1)
d <- sim_symptoms(n = 1e5, effect = 0, k = 10, rho = 0.30)
c(mean = mean(d$ace), pct_zero = mean(d$ace == 0), max = max(d$ace))
#>  mean pct_zero      max
#>  1.49     0.35    10.00
c(p_ge1 = mean(d$ace >= 1), p_ge4 = mean(d$ace >= 4))
#> p_ge1 p_ge4
#> 0.650 0.121

That is the empirical ACE shape: a mean near 1.5, about a third of people at zero, a long right tail, and roughly the population benchmark of 65% with at least one adversity. It is bounded and correlated, which is exactly why a beta-binomial, not a Poisson, is the model that respects it.

default_ace_probs()

The per-item probabilities behind the default, descending from about .30 to .05. Ask for 7 items and you get the probabilities for the original instrument.

default_ace_probs(10)
#>  [1] 0.30 0.25 0.20 0.18 0.15 0.12 0.10 0.08 0.06 0.05
default_ace_probs(7)
#> [1] 0.30 0.25 0.20 0.18 0.15 0.12 0.10

Pass your own vector to sim_symptoms(p_items = ...) to calibrate to a different instrument.

true_diff_symptoms()

The true difference in expected count under a given log-odds shift, for scoring bias and coverage. The item correlation does not affect the mean, so this is just the difference of the summed marginals.

true_diff_symptoms(effect = 0.6, k = 10)
#> 0.864