Heterogeneity-Aware Empowerment via Adaptive Robust Transfer • HEART

Heterogeneity-aware Empowerment via Adaptive Robust Transfer for target-population inference.

HEART tests variant–trait associations in a small target population (for example, an under-represented ancestry in a biobank) and borrows strength from a larger source population. It does not assume that genetic effects are shared between the two populations. Source-specific signals do not inflate the error rate, and HEART is asymptotically no less powerful than a target-only analysis.

Installation

# install.packages("remotes")
remotes::install_github("haoyu-yang001/HEART", build_vignettes = TRUE)

Documentation: https://haoyu-yang001.github.io/HEART/

Method in brief

For each variant j:

Estimation and decorrelation (heart_assoc()). HEART computes the target-only estimator β̂^tar and an auxiliary estimator β̂^aux. The auxiliary estimator is pooled, doubly robust (DR, using surrogate-based synthetic outcomes), or source-only. It is then decorrelated from the target-only estimator using their joint sandwich covariance:

β̂^de = β̂^aux − ρ̂ β̂^tar, with ρ̂ = Ĉov(β̂^aux, β̂^tar) / V̂ar(β̂^tar).

This step gives asymptotically independent p-values (p_tar, p_de).
Adaptive transfer via null decomposition (heart_test()). The target null H₀: β^tar = 0 is split into H₀₀ ∪ H₀₁. A four-group mixture model on (p_tar, p_de) gives the HEART statistic

T = π̂₀₀/(Ĉ₁Ĉ₂α̂₁α̂₂) · p_tar^1−α̂₁ p_de^1−α̂₂ + π̂₀₁/(Ĉ₁α̂₁) · p_tar^1−α̂₁.

HEART estimates the composite null distribution of T from the data. This gives per-variant HEART p-values, FDR q-values and FWER-adjusted p-values.

Quick start

library(HEART)
sim <- heart_simulate(n_tar = 2000, n_src = 20000, J = 2000, seed = 1)

res <- heart(Y = sim$Y, G = sim$G, D = sim$D, X = sim$X, aux = "pooled", alpha = 0.05)
res                       # summary of estimated parameters and discoveries
head(res$results)         # p_tar, p_de, log_T, p_heart, q_heart, padj_fwer, reject_*

Genome-wide analysis in chunks

heart_test() must see all variants, because the four-group parameters are estimated genome-wide. Step 1 can be split across jobs:

library(BEDMatrix)
G <- BEDMatrix("chr22.bed", simple_names = TRUE)        # rows must align with Y, D, X
idx <- match(sample_ids, rownames(G))

# --- one array job: a chunk of variants ---
fit_chunk <- heart_assoc(Y, G[idx, chunk_cols], D, X, aux = "pooled")
saveRDS(fit_chunk, sprintf("assoc_chunk%03d.rds", chunk_id))

# --- after all jobs finish ---
fit <- do.call(rbind, lapply(list.files(pattern = "^assoc_chunk"), readRDS))
res <- heart_test(fit$p_tar, fit$p_de_pooled, snp = fit$snp, alpha = 0.05)

For the Gaussian family the per-variant cost is linear in the number of covariates. The computation uses the Frisch–Waugh–Lovell representation of the sandwich (co)variances and is vectorised over blocks of variants.

Doubly robust auxiliary estimator with surrogates

# 1. Train a prediction model for Y from surrogates S on a held-out split,
#    then predict Y_hat on the analysis sample (e.g. ranger::ranger).
# 2. Density ratio c_i = P(D = 1 | S) / P(D = 1):
c_i <- heart_density_ratio(D, W = S)
# 3. Use aux = "dr":
fit <- heart_assoc(Y, G, D, X, aux = "dr", Y_hat = Y_hat, c_i = c_i)
res <- heart_test(fit$p_tar, fit$p_de_dr)

Summary statistics only

When the target and source studies are independent, heart_meta() builds the decorrelated inverse-variance meta-analytic estimator from (β̂, SE) of each study:

m   <- heart_meta(beta_tar, se_tar, beta_src, se_src, snp = snp_ids)
res <- heart_test(m$p_tar, m$p_de_meta, snp = m$snp)

Main functions

Function	Purpose
`heart()`	End-to-end analysis (Step 1 + Step 2)
`heart_assoc()`	Target-only, auxiliary (`pooled` / `dr` / `source`) and decorrelated estimators; Gaussian or binomial
`heart_density_ratio()`	Density ratio for the DR estimator
`heart_meta()`	Decorrelated meta-analysis from summary statistics
`heart_test()`	HEART statistic, composite null distribution, FDR / FWER control
`heart_pi_estimate()`, `heart_tail_estimate()`	Four-group proportions and tail parameters
`heart_statistic()`, `heart_null_cdf()`	Statistic and null CDF (F₀₀, Q̂, F̂₀₁, N̂, F̂₀)
`heart_simulate()`	Toy data under the four-group model

Citation

Yang H, Wang R, Lin X. Heterogeneity-aware Empowerment via Adaptive Robust Transfer for target-population inference. (manuscript)

License

MIT