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HEART test: adaptive transfer via null decomposition

Source: R/heart_test.R
heart_test.Rd

Step 2 of HEART. Given target-only p-values \(p_{tar,j}\) and decorrelated p-values \(p_{de,j}\) for \(J\) variants (typically genome-wide), this function

  1. estimates the four-group proportions (heart_pi_estimate()),

  2. estimates the tail parameters \((\alpha_1, C_1)\) from \(p_{tar}\) and \((\alpha_2, C_2)\) from \(p_{de}\) (heart_tail_estimate()),

  3. computes the HEART statistic \(T_j\) (heart_statistic()),

  4. estimates its composite null distribution (heart_null_cdf()), and

  5. returns HEART p-values, FDR q-values and FWER-adjusted p-values.

Usage

heart_test(
  p_tar,
  p_de,
  alpha = 0.05,
  snp = NULL,
  par = NULL,
  tail_k = 50,
  pi0_cap = 0.996,
  alpha_bounds = c(1e-05, 1 - 1e-05),
  C_bounds = c(0.1, 3),
  lambdas = c(0.5, 0.6, 0.7, 0.8),
  p_min = 1e-300,
  exact = FALSE,
  n_exact = 5000L,
  n_grid = 500L
)

Arguments

p_tar, p_de

Target-only and decorrelated p-values (same length).

alpha

Nominal FDR / FWER level used for the reject_* columns.

snp

Optional variant identifiers.

par

Optional list of model parameters (pi00, pi01, pi10, alpha1, alpha2, C1, C2, and optionally pi11) to bypass estimation.

tail_k, pi0_cap, alpha_bounds, C_bounds

Passed to heart_tail_estimate().

lambdas

Passed to heart_pi_estimate().

p_min

P-values are bounded below by p_min to avoid log(0).

exact, n_exact, n_grid

Passed to heart_null_cdf().

Value

An object of class "heart": a list with

results

data.frame with snp, p_tar, p_de, log_T, p_heart, q_heart, padj_fwer, reject_fdr, reject_fwer.

par

Estimated parameters.

alpha, n_tests

Level and number of valid tests.

Details

The FDR procedure rejects \(\{j: T_j \le \hat t_\alpha\}\) with \(\hat t_\alpha = \sup\{t: \hat N(t)/\bar F(t) \le \alpha\}\); equivalently q_heart <= alpha. The FWER procedure rejects \(\{j: \hat N(T_j) \le \alpha/J\}\); equivalently padj_fwer <= alpha. The per-variant HEART p-value is \(\hat F_0(T_j)\), the estimated composite-null CDF evaluated at the observed statistic, which can be used e.g. for Manhattan plots with a genome-wide threshold.

The parameters must be estimated from all variants jointly; when variants are analysed in chunks with heart_assoc(), combine the chunks before calling heart_test().

Examples

sim <- heart_simulate(n_tar = 1500, n_src = 6000, J = 1000, seed = 1)
fit <- heart_assoc(sim$Y, sim$G, sim$D, sim$X)
res <- heart_test(fit$p_tar, fit$p_de_pooled, snp = fit$snp)
res
#> HEART: Heterogeneity-aware Empowerment via Adaptive Robust Transfer
#>   tests: 1000
#>   four-group proportions: pi00 = 0.8100, pi01 = 0.0750, pi10 = 0.1150, pi11 = 0.0000
#>   tail parameters: alpha1 = 0.401, C1 = 1.014, alpha2 = 0.095, C2 = 1.020
#>   discoveries at level 0.05: FDR = 6, FWER = 2 (target-only BH = 2, Bonferroni = 0)