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Compute Detection Probability for GLM Outcomes

Source: R/truefind_asymptotic_glm.R
compute_detection_probability_glm.Rd

Extends the Section 2.1 approximation (Leon et al., 2024, eq. 3) to arbitrary GLM outcomes via the effective information \(d_{\text{eff}}\). This is the GLM generalization of compute_detection_probability.

Usage

compute_detection_probability_glm(
  theta,
  d_eff,
  c1 = 1.25,
  c2 = 1,
  effect_scale = c("ratio", "difference"),
  method = c("cubature", "monte_carlo"),
  n_mc = 500000L,
  seed = 42L,
  verbose = FALSE
)

Arguments

theta

Numeric (scalar or vector). True treatment effect in the subgroup on the natural scale:

Ratio measures (HR, OR, IRR)

The ratio itself, e.g., 2.0 for doubling.

Difference measures (MD)

The mean difference, e.g., 0.5.

d_eff

Numeric. Effective information in the subgroup. Use the d_eff_* helpers: d_eff_survival, d_eff_binary, d_eff_count, d_eff_continuous.

c1

Numeric. Screening threshold on the natural scale. For ratio measures: the ratio (e.g., 1.25). For difference measures: the difference (e.g., 0.2).

c2

Numeric. Consistency threshold on the natural scale. Default: 1.0 for ratio, 0.0 for difference.

effect_scale

Character. "ratio" (default) for log-scale effects (HR, OR, IRR); "difference" for identity-scale (MD).

method

Character. "cubature" or "monte_carlo".

n_mc

Integer. Monte Carlo samples if method = "monte_carlo".

seed

Integer. RNG seed for Monte Carlo.

verbose

Logical. Progress messages for vector theta.

Value

If theta is scalar, a single probability. If vector, a data.frame with columns theta, probability.

Details

The detection criterion (Leon et al., 2024, Section 2.1):

  1. Screening: \(W_1 + W_2 \ge 2k_1\)

  2. Consistency: \(\min(W_1, W_2) \ge k_2\)

with \(W_1, W_2 \sim N(\beta, 8/d_{\text{eff}})\) independently.

For ratio-scale effects, \(\beta = \log(\theta)\), \(k_j = \log(c_j)\). For difference-scale effects, \(\beta = \theta\), \(k_j = c_j\).

See also

compute_detection_probability for the survival-specific version.

Examples

# \donttest{
# Survival: reproduce Figure 2
d <- d_eff_survival(n_sg = 60, prop_cens = 0.45)
compute_detection_probability_glm(theta = 2.0, d_eff = d)
#> [1] 0.8282823

# Binary: OR = 2.0, event rate 30%
d <- d_eff_binary(n_sg = 100, p_event = 0.30)
compute_detection_probability_glm(theta = 2.0, d_eff = d)
#> [1] 0.7368968

# Count: IRR = 2.0, 80 total events
d <- d_eff_count(total_events = 80)
compute_detection_probability_glm(theta = 2.0, d_eff = d)
#> [1] 0.9634817

# Continuous: mean difference = 0.5, sigma = 1.5
d <- d_eff_continuous(n_sg = 100, sigma_y = 1.5)
compute_detection_probability_glm(
  theta = 0.5, d_eff = d,
  c1 = 0.2, c2 = 0.0,
  effect_scale = "difference"
)
#> [1] 0.7432167

# Power curve
d <- d_eff_binary(100, 0.30)
result <- compute_detection_probability_glm(
  theta = seq(0.5, 3.0, by = 0.1), d_eff = d
)
plot(result$theta, result$probability, type = "l")

# }