Estimate the four-group proportions from a pair of p-value sequences
Source:R/heart_test.R
heart_pi_estimate.RdEstimates \(\pi_{00}, \pi_{01}, \pi_{10}, \pi_{11}\) of the four-group
model for \((p_{tar,j}, p_{de,j})\), where the first index refers to
\(\beta^{tar}_j\) and the second to \(\beta^{de}_j\)
(0 = null, 1 = non-null). The marginal and joint null proportions are
estimated by Storey-type ratios
$$\hat\pi_{0\cdot}(\lambda) = \frac{\#\{p_{tar,j} > \lambda\}}{J(1-\lambda)},\quad
\hat\pi_{\cdot0}(\lambda) = \frac{\#\{p_{de,j} > \lambda\}}{J(1-\lambda)},\quad
\hat\pi_{00}(\lambda) = \frac{\#\{p_{tar,j} > \lambda, p_{de,j} > \lambda\}}{J(1-\lambda)^2},$$
with \(\hat\pi_{01} = (\hat\pi_{0\cdot} - \hat\pi_{00}) \vee 0\) and
\(\hat\pi_{10} = (\hat\pi_{\cdot0} - \hat\pi_{00}) \vee 0\). A marginal
proportion is set to one when a one-sided Kolmogorov-Smirnov test does not
reject uniformity. The tuning parameter \(\lambda\) is chosen among
lambdas by the QQ-slope criterion for the maximum p-value (as in the
HDMT procedure of Dai, Stanford and LeBlanc, 2022).
Usage
heart_pi_estimate(
p_tar,
p_de,
lambdas = c(0.5, 0.6, 0.7, 0.8),
ks_level = 0.05
)