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Bivariate Density for Split-Sample HR Threshold Detection

Source: R/truefind_asymptotic.R
density_threshold_both.Rd

Computes the joint density for the two-split detection criterion where both split-halves must exceed individual thresholds and their average must exceed a consistency threshold.

Usage

density_threshold_both(x, theta, prop_cens = 0.3, n_sg, k_avg, k_ind)

Arguments

x

Numeric vector of length 2. Log hazard ratio estimates from the two split-halves.

theta

Numeric. True hazard ratio in the subgroup.

prop_cens

Numeric. Proportion censored (0-1). Default: 0.3

n_sg

Integer. Subgroup sample size.

k_avg

Numeric. Threshold for average log(HR) across splits. Typically log(hr.threshold).

k_ind

Numeric. Threshold for individual split log(HR). Typically log(hr.consistency).

Value

Numeric. Joint density value at x, or 0 if thresholds not met.

Details

The detection criterion requires:

  • Average of two splits: (x1 + x2)/2 >= k_avg

  • Individual splits: x1 >= k_ind AND x2 >= k_ind

Under the asymptotic approximation, each split-half log(HR) estimator follows N(log(theta), 8/d) where d = n_sg * (1 - prop_cens) / 2 is the expected number of events per split.