API Reference

This page provides detailed documentation for the core functions in the traceCB package.

• API Reference
• traceCB.gmm
  • GMM
  • GMMtissue
• traceCB.ldsc
  • Run_Single_LDSC
  • Run_Cross_LDSC

traceCB.gmm

Core functions for the Generalized Method of Moments (GMM) estimation.

GMM

Apply cross-population GMM (without tissue-specific information) to estimate effect sizes.

def GMM(
    Omega: np.ndarray,
    C: np.ndarray,
    beta1: float,
    se1: float,
    ld1: float,
    beta2: float,
    se2: float,
    ld2: float,
    ldx: float,
) -> tuple[float, float, float, float]

Parameters

• Omega (np.ndarray): A (2, 2) per-SNP covariance matrix.
• C (np.ndarray): A (2, 2) genetic drift matrix estimated from LDSC.
• beta1 (float): Effect size (beta) for the SNP in population 1.
• se1 (float): Standard error for the SNP in population 1.
• ld1 (float): LD score between the SNP and the rest of the SNPs in the target gene in population 1.
• beta2 (float): Effect size (beta) for the SNP in population 2.
• se2 (float): Standard error for the SNP in population 2.
• ld2 (float): LD score between the SNP and the rest of the SNPs in the target gene in population 2.
• ldx (float): Cross-population LD score for the SNP between population 1 and population 2.

Returns

• beta1_blue (float): GMM estimate (BLUE) for population 1.
• se1_blue (float): Standard error of the GMM estimate for population 1.
• beta2_blue (float): GMM estimate (BLUE) for population 2.
• se2_blue (float): Standard error of the GMM estimate for population 2.

---

GMMtissue

Apply cross-population GMM incorporating tissue-specific information (e.g., from scRNA-seq derived eQTLs).

def GMMtissue(
    Omega: np.ndarray,
    C: np.ndarray,
    beta1: float,
    se1: float,
    ld1: float,
    beta2: float,
    se2: float,
    ld2: float,
    ldx: float,
    beta_t: float,
    se_t: float,
    pi2_omega_o: float,
    propt: float,
) -> tuple[float, float, float, float]

Parameters

• Omega (np.ndarray): A (2, 2) per-SNP covariance matrix.
• C (np.ndarray): A (3, 3) genetic drift matrix estimated from LDSC.
• beta1 (float): Effect size (beta) for the SNP in population 1.
• se1 (float): Standard error for the SNP in population 1.
• ld1 (float): LD score for population 1.
• beta2 (float): Effect size (beta) for the SNP in population 2.
• se2 (float): Standard error for the SNP in population 2.
• ld2 (float): LD score for population 2.
• ldx (float): Cross-population LD score.
• beta_t (float): Effect size (beta) for the SNP in the specific tissue/cell-type.
• se_t (float): Standard error for the SNP in the specific tissue/cell-type.
• pi2_omega_o (float): Variance component of other cell types within the tissue.
• propt (float): Proportion of the specific cell type in the tissue.

Returns

• beta1_blue (float): GMM estimate for population 1.
• se1_blue (float): Standard error for population 1.
• beta2_blue (float): GMM estimate for population 2.
• se2_blue (float): Standard error for population 2.

---

traceCB.ldsc

Functions for running Single and Cross-Population LD Score Regression (LDSC).

Run_Single_LDSC

Run LDSC regression to estimate heritability ($h^2$) in a single population.

def Run_Single_LDSC(
    zscore: np.ndarray,
    n: np.ndarray,
    ldscore: np.ndarray,
    intercept: float = np.nan,
) -> tuple[float, float]

Parameters

• zscore (np.ndarray): Array of Z-scores for SNPs, shape (num_SNP,).
• n (np.ndarray): Array of sample sizes for each SNP, shape (num_SNP,).
• ldscore (np.ndarray): Array of LD scores, shape (num_SNP,).
• intercept (float, optional): Fixed intercept value. If np.nan (default), the intercept is estimated from the data.

Returns

• h2 (float): Estimated heritability. (Clipped to be $\ge$ MIN_HERITABILITY).
• h2_se (float): Standard error of the heritability estimate.

---

Run_Cross_LDSC

Run LDSC regression to estimate genetic covariance ($\Omega$) between two populations.

def Run_Cross_LDSC(
    zscore1: np.ndarray,
    n1: np.ndarray,
    ldscore1: np.ndarray,
    zscore2: np.ndarray,
    n2: np.ndarray,
    ldscore2: np.ndarray,
    crossld: np.ndarray,
    intercept: np.ndarray = np.array([np.nan, np.nan, np.nan]),
) -> tuple[np.ndarray, np.ndarray]

Parameters

• zscore1 (np.ndarray): Z-scores for population 1.
• n1 (np.ndarray): Sample sizes for population 1.
• ldscore1 (np.ndarray): LD scores for population 1.
• zscore2 (np.ndarray): Z-scores for population 2.
• n2 (np.ndarray): Sample sizes for population 2.
• ldscore2 (np.ndarray): LD scores for population 2.
• crossld (np.ndarray): Cross-population LD scores.
• intercept (np.ndarray, optional): Array of intercept values [h11, h22, h12]. Default is [nan, nan, nan], which estimates all intercepts.

Returns

• Omega (np.ndarray): Estimated genetic covariance matrix of shape (2, 2).
• Omega[0, 0]: Heritability pop 1
• Omega[1, 1]: Heritability pop 2
• Omega[0, 1] / Omega[1, 0]: Genetic covariance
• Omega_se (np.ndarray): Standard error matrix for Omega, shape (2, 2).