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Cross-Population Haplotype Effect Concordance

Source: R/haplotype_association.R
compare_block_effects.Rd

Given two allele_tests data frames produced by test_block_haplotypes on two independent populations, computes per-block (and optionally per-trait) statistics that quantify how consistently haplotype allele effects replicate across populations.

Statistics computed per block:

Effect correlation (\(r\))

Pearson correlation of per-allele effect sizes between populations across all shared alleles. Requires at least 3 shared alleles; NA otherwise.

Direction agreement

Proportion of shared alleles where both populations assign the same sign to the effect. A value >= 0.75 (i.e. at least 3 out of 4 alleles agree in direction) is considered strong directional replication.

Inverse-variance weighted (IVW) meta-analytic effect

The weighted mean effect \(\hat\beta_{\mathrm{IVW}} = \sum w_i \beta_i / \sum w_i\) where \(w_i = 1/\mathrm{SE}_i^2\). Computed separately for each shared allele and summarised as the mean of per-allele IVW estimates. The IVW meta-analysis is the same framework used in two-sample Mendelian randomisation and cross-population GWAS meta-analysis (see Borenstein et al. 2009).

Cochran's Q heterogeneity statistic

Tests whether effect sizes differ significantly between the two populations: \(Q = \sum w_i (\beta_i - \hat\beta_{\mathrm{IVW}})^2\). Under the null of no heterogeneity, \(Q \sim \chi^2_{n-1}\). Significant Q (large \(Q_p\)) indicates that effect sizes differ between populations - a sign of GxE interaction, LD structure differences, or population-specific allelic action.

\(I^2\) inconsistency

\(I^2 = 100 \times \max(0,\, (Q - df)/Q)\). Values > 50% indicate substantial between-population heterogeneity.

Block boundary concordance

When blocks_pop1 and blocks_pop2 are both supplied, the bp overlap ratio of the two populations' block definitions is computed for each block. A ratio < 0.8 flags blocks where LD structure likely differs between populations and effect comparisons should be interpreted cautiously.

Addressing the two principal limitations of cross-population validation:

  1. Population structure confounding: The Q+K mixed model in test_block_haplotypes() already corrects for within-population structure via the haplotype GRM. Cross-population validation inherently controls between-population confounding by design: the same haplotype allele must associate with the phenotype in a genetically distinct background, making false-positive carry-over from Pop A's stratification implausible. The meta-analytic \(I^2\) statistic additionally flags cases where the effect sizes are so heterogeneous that a shared biological mechanism is unlikely.

  2. LD block boundary differences: Block boundaries can differ between populations due to different historical recombination rates and ancestral haplotype structure. The boundary_overlap_ratio column quantifies this directly for every block. Low overlap (< 0.8) means the two populations carve the same genomic region into blocks of different sizes; in that case a haplotype allele tested over a 50 kb window in Pop A is compared to an allele over a 30 kb window in Pop B and the strings will not match well. The n_shared_alleles column is the empirical consequence: very low shared-allele counts despite adequate allele frequencies in both populations are a direct symptom of block boundary mismatch. The recommended remedy - passing Pop A's block table as the blocks argument to test_block_haplotypes() in Pop B - eliminates this issue entirely by forcing both runs to use identical coordinates.

Usage

compare_block_effects(
  assoc_pop1,
  assoc_pop2,
  pop1_name = "pop1",
  pop2_name = "pop2",
  traits = NULL,
  min_shared_alleles = 2L,
  blocks_pop1 = NULL,
  blocks_pop2 = NULL,
  block_match = c("id", "position"),
  overlap_min = 0.5,
  direction_threshold = 0.75,
  boundary_overlap_warn = 0.8,
  verbose = TRUE
)

Arguments

assoc_pop1

Output of test_block_haplotypes for population 1 (discovery). Must contain an allele_tests data frame with columns block_id, CHR, start_bp, end_bp, trait, allele, effect, SE, p_wald.

assoc_pop2

Output of test_block_haplotypes for population 2 (validation). Same structure as assoc_pop1.

pop1_name

Character. Label for population 1 in the output. Default "pop1".

pop2_name

Character. Label for population 2 in the output. Default "pop2".

traits

Character vector or NULL. Traits to compare. If NULL (default), all traits present in both result objects are included.

min_shared_alleles

Integer. Minimum number of alleles shared between the two populations for a block to be included in the output. Blocks with fewer shared alleles are retained but marked with enough_shared = FALSE. Default 2L.

blocks_pop1

Optional data frame of LD blocks from population 1 (output of run_Big_LD_all_chr). When both blocks_pop1 and blocks_pop2 are supplied, a boundary_overlap_ratio column is computed for every block. Required columns: block_id (or constructible from CHR/start.bp/end.bp), start.bp, end.bp.

blocks_pop2

Optional data frame of LD blocks from population 2. Same structure as blocks_pop1.

block_match

Character. How to match blocks between populations.

  • "id" (default) - match by exact block_id string. Fast and backward-compatible. Use when both populations were analysed with the same block table (recommended workflow: run test_block_haplotypes() on both populations using Pop A's block boundaries for Pop B as well).

  • "position" - match by genomic interval overlap (Intersection-over-Union, IoU, in base pairs). For each Pop1 block, the best-matching Pop2 block on the same chromosome is found. Blocks with IoU \(\geq\) overlap_min are matched; those below are labelled "pop1_only". Use when block boundaries genuinely differ between populations (different ancestral LD structures, different CLQcut used, or independent block detection runs).

overlap_min

Numeric in (0, 1]. Minimum Intersection-over-Union (IoU) in base pairs for two blocks to be considered the same region when block_match = "position". Default 0.50. Blocks below this threshold are assigned match_type = "pop1_only" and not compared. Lower values (e.g. 0.30) tolerate more boundary discordance; higher values (e.g. 0.80) require tighter boundary agreement. Ignored when block_match = "id".

direction_threshold

Numeric in (0.5, 1]. Minimum direction-agreement proportion to consider a block directionally concordant. Default 0.75.

boundary_overlap_warn

Numeric in (0, 1). Threshold used to raise a warning flag in the output. When the automatically computed boundary_overlap_ratio (an output column, not a user-set value) is below this threshold, the corresponding boundary_warning output column is set to TRUE. Default 0.80. Raise this value (e.g. 0.90) to flag more conservatively, or lower it (e.g. 0.60) to flag only severely mismatched blocks.

verbose

Logical. Print progress. Default TRUE.

Value

A named list of class c("LDxBlocks_effect_concordance", "list"):

concordance

Data frame with one row per block per trait. Columns:

  • block_id, CHR, start_bp, end_bp, trait - block coordinates and trait name.

  • n_alleles_pop1, n_alleles_pop2 - alleles tested in each population (before intersection).

  • n_shared_alleles - alleles present in both populations.

  • enough_shared - logical; TRUE when n_shared_alleles >= min_shared_alleles.

  • effect_correlation - Pearson r of per-allele effects across populations (NA when n_shared < 3).

  • direction_agreement - proportion of shared alleles with concordant effect signs.

  • directionally_concordant - logical; direction_agreement >= direction_threshold.

  • meta_effect - IVW meta-analytic effect (mean over shared alleles, each weighted by combined inverse-variance).

  • meta_SE - SE of the IVW estimate.

  • meta_z - meta-analytic z-score.

  • meta_p - two-sided p-value of meta-analytic effect.

  • Q_stat - Cochran Q heterogeneity statistic.

  • Q_df - degrees of freedom of Q (n_shared - 1).

  • Q_p - p-value of Q under chi-squared distribution.

  • I2 - \(I^2\) inconsistency (0-100%).

  • replicated - logical; TRUE when directionally_concordant AND Q_p > 0.05 AND enough_shared.

  • boundary_overlap_ratio - bp intersection / bp union of the two populations' block boundaries. NA when block tables not supplied.

  • boundary_warning - logical; TRUE when boundary_overlap_ratio < boundary_overlap_warn. These blocks should be interpreted cautiously because different LD structures likely produce non-comparable haplotype strings.

  • match_type - character; how the block was matched between populations: "exact" (same block_id string), "position" (matched by genomic IoU \(\geq\) overlap_min when block_match = "position"), "pop1_only" (no Pop2 block overlapped at the threshold), or NA when no block tables were supplied.

Sorted by CHR, start_bp, meta_p (ascending).

shared_alleles

Data frame. One row per shared allele per block per trait. Contains effect_pop1, SE_pop1, p_wald_pop1, effect_pop2, SE_pop2, p_wald_pop2, direction_agree, ivw_effect, ivw_SE, for detailed per-allele inspection.

pop1_name, pop2_name

Character. Population labels.

block_match

Character. Matching strategy used.

overlap_min

Numeric. IoU threshold used (relevant when block_match = "position").

traits

Character vector of traits compared.

direction_threshold

Numeric. Threshold used.

boundary_overlap_warn

Numeric. Boundary warning threshold.

References

Borenstein M, Hedges LV, Higgins JPT, Rothstein HR (2009). Introduction to Meta-Analysis. Wiley.

Higgins JPT, Thompson SG (2002). Quantifying heterogeneity in a meta-analysis. Statistics in Medicine 21(11):1539-1558. doi:10.1002/sim.1186

See also

test_block_haplotypes, harmonize_haplotypes, score_favorable_haplotypes

Examples

# \donttest{
data(ldx_geno, ldx_snp_info, ldx_blocks, ldx_blues, package = "LDxBlocks")

# Simulate two populations by splitting the example dataset
set.seed(1L)
n     <- nrow(ldx_geno)
idx_1 <- sample(n, round(n * 0.6))
idx_2 <- setdiff(seq_len(n), idx_1)

haps_1 <- extract_haplotypes(ldx_geno[idx_1, ], ldx_snp_info, ldx_blocks)
haps_2 <- extract_haplotypes(ldx_geno[idx_2, ], ldx_snp_info, ldx_blocks)

blues_1 <- setNames(ldx_blues$YLD[idx_1], ldx_blues$id[idx_1])
blues_2 <- setNames(ldx_blues$YLD[idx_2], ldx_blues$id[idx_2])

res_1 <- test_block_haplotypes(haps_1, blues = blues_1,
                               blocks = ldx_blocks, verbose = FALSE)
res_2 <- test_block_haplotypes(haps_2, blues = blues_2,
                               blocks = ldx_blocks, verbose = FALSE)

conc <- compare_block_effects(res_1, res_2,
                              pop1_name = "pop1", pop2_name = "pop2",
                              blocks_pop1 = ldx_blocks,
                              blocks_pop2 = ldx_blocks)
#> [compare_block_effects] Comparing traits: trait
#> [compare_block_effects] Done. Blocks compared: 9 | Replicated (concordant, Q_p > 0.05): 1

# Replicated blocks
conc$concordance[conc$concordance$replicated, ]
#>               block_id CHR start_bp end_bp trait n_alleles_pop1 n_alleles_pop2
#> 5 block_2_86236_105290   2    86236 105290 trait              8              5
#>   n_shared_alleles enough_shared effect_correlation direction_agreement
#> 5                5          TRUE             0.6684                 0.8
#>   directionally_concordant meta_effect  meta_SE  meta_z    meta_p Q_stat Q_df
#> 5                     TRUE   -0.054497 0.102792 -0.5302 0.5959947 1.4741    4
#>         Q_p I2 replicated boundary_overlap_ratio boundary_warning match_type
#> 5 0.8312194  0       TRUE                      1            FALSE      exact

# Full per-allele details
head(conc$shared_alleles)
#>             block_id CHR start_bp end_bp trait                  allele
#> 1 block_1_1000_25027   1     1000  25027 trait block_1_1000_25027_hap1
#> 2 block_1_1000_25027   1     1000  25027 trait block_1_1000_25027_hap2
#> 3 block_1_1000_25027   1     1000  25027 trait block_1_1000_25027_hap3
#> 4 block_1_1000_25027   1     1000  25027 trait block_1_1000_25027_hap5
#> 5 block_1_1000_25027   1     1000  25027 trait block_1_1000_25027_hap4
#> 6 block_1_1000_25027   1     1000  25027 trait block_1_1000_25027_hap6
#>   effect_pop1  SE_pop1 p_wald_pop1 effect_pop2  SE_pop2 p_wald_pop2
#> 1   -0.397472 0.251976   0.1192082    0.211897 0.347946   0.5455243
#> 2   -0.310596 0.273817   0.2605300   -0.174085 0.401162   0.6663514
#> 3    0.237420 0.302744   0.4355541    0.757311 0.501033   0.1375008
#> 4    0.226424 0.321419   0.4834891   -0.729625 0.501925   0.1528313
#> 5    0.143343 0.303588   0.6382789   -0.338970 0.510885   0.5103244
#> 6   -0.181619 0.416618   0.6642237    0.562911 0.506570   0.2722476
#>   direction_agree ivw_effect   ivw_SE
#> 1           FALSE  -0.187836 0.204082
#> 2            TRUE  -0.267210 0.226157
#> 3            TRUE   0.376468 0.259115
#> 4           FALSE  -0.051613 0.270676
#> 5           FALSE   0.017475 0.260985
#> 6           FALSE   0.118784 0.321774

# Summary
print(conc)
#> LDxBlocks Cross-Population Effect Concordance
#>   Populations: pop1 vs pop2
#>   Traits:       trait 
#>   Blocks compared:           9 
#>   With enough shared alleles: 9 
#>   Directionally concordant:   1 
#>   Replicated (dir + Q_p>0.05): 1 
#>   Boundary warnings:          0 (overlap ratio < 0.8 )
#>   Median I2 (heterogeneity):  14.1 %
#>   Shared allele comparisons:  61 
# }