Effective Information for Count Outcomes (Poisson)

Computes \(d_{\text{eff}} = D / \phi\) where \(D\) is the total expected events and \(\phi\) is the dispersion parameter.

Usage

d_eff_count(
  n_sg = NULL,
  event_rate = NULL,
  total_events = NULL,
  dispersion = 1
)

Arguments

n_sg

Integer. Subgroup sample size. Required if total_events is not provided.

event_rate

Numeric. Mean events per patient. Required if total_events is not provided.

total_events

Numeric. Total observed events \(D\). Overrides n_sg * event_rate if provided.

dispersion

Numeric. Overdispersion parameter (1.0 for Poisson, greater than 1 for quasi-Poisson). Default: 1.0.

Value

Numeric. Effective information.

Details

For Poisson regression with log-offset: $$\text{Var}(\hat\beta) = \phi \left(\frac{1}{D_0} + \frac{1}{D_1}\right) \approx \frac{4\phi}{D}$$ Under proportional hazards, \(D = d\) (Cox events), so \(d_{\text{eff}}^{\text{Poisson}} = d_{\text{eff}}^{\text{Cox}}\) (Laird and Olivier, 1981).

Examples

# From total events
d_eff_count(total_events = 55)
#> [1] 55

# From sample size and rate
d_eff_count(n_sg = 100, event_rate = 0.8)
#> [1] 80

# Quasi-Poisson with overdispersion
d_eff_count(total_events = 55, dispersion = 1.5)
#> [1] 36.66667