dot_sst {dotgen}

Methods for combining decorrelated summary statistics

Description

Decorrelates and combines per-variant genetic association test statistics, Z, given the correlation matrix among them, C.

Usage

dot_chisq(Z, C, ...)

dot_fisher(Z, C, ...)

dot_art(Z, C, k = NULL, ...)

dot_arta(Z, C, k = NULL, w = NULL, ...)

dot_rtp(Z, C, k = NULL, ...)

dot_tpm(Z, C, tau = 0.05, ...)

Arguments

Z

vector of association test statistics (i.e., Z-scores).

C

matrix of correlation among the test statistics, as obtained by cst().

...

additional parameters

k

combine k smallest (decorrelated) P-values.

w

weight assigned to partial sums in ARTA implementation; default is 1.

tau

combine (decorrelated) P-values no large than tau; default is 0.05.

Details

These functions first call dot() to decorrelate the genetic association test statistics and then provide various options to combine independent statistics or corresponding P-values into the overall statistic and P-value.

The two rank truncated tests (i.e., dot_art(), dot_rtp()) require an additional parameter k that specifes the number of smallest (decorrelated) P-values to combine. By default, k equals half of the number of variants. The adaptive rank truncation method, dot_arta(), determines the optimal truncation value between 1 and k.

The truncated product method, dot_tpm(), combines P-values at least as small as tau (0.05 by default). If tau is equal to 1, then dot_tpm() provides the same result as dot_fisher() (i.e., Fisher's method for combining P-values). Similarly, if k is equal to the total number of tests, the results of dot_art() and dot_rtp() will be the same as that of dot_fisher().

Reference (a) below details how to combine decorrelated test statistics or P-values via dot_art(), dot_rtp() and dot_arta(); reference (b) details dot_tpm() method.

Value

a list of

• X: decorrelated association statistics.

• H: orthogonal transformation, such that X = H %*% Z.

• Y: the overall combined statistic.

• P: the P-value corresponding to Y.

for Augmented Rank Truncated Adaptive (ARTA) test,

• k: the number of decorrelated P-values that were adaptively picked.

for Truncated Product Method (TPM),

• k: the number of decorrelated P-values \le tau.

Functions

• dot_chisq: decorrelation followed by a Chi-square test.

• dot_fisher: decorrelated Fisher's combined P-value test.

• dot_art: decorrelated Augmented Rank Truncated (ART) test.

• dot_arta: decorrelated Augmented Rank Truncated Adaptive (ARTA) test.

• dot_rtp: decorrelated Rank Truncated Product (RTP) test.

• dot_tpm: decorrelated Truncated Product Method (TPM) test.

References

(a) Vsevolozhskaya, O. A., Hu, F., & Zaykin, D. V. (2019). Detecting weak signals by combining small P-values in genetic association studies. Frontiers in genetics, 10, 1051.

(b) Zaykin, D. V., Zhivotovsky, L. A., Westfall, P. H., & Weir, B. S. (2002). Truncated product method for combining P-values. Genetic Epidemiology, 22(2), 170-185.

See Also

dot()

Examples

## get the test statistics and pre-calculated LD matrix
stt <- readRDS(system.file("extdata", 'art_zsc.rds', package="dotgen"))
sgm <- readRDS(system.file("extdata", 'art_ldm.rds', package="dotgen"))


## decorrelated chi-square test
result <- dot_chisq(stt, sgm)
print(result$Y)  # 37.2854
print(result$P)  # 0.0003736988

## decorrelated Fisher's combined P-value chi-square test
result <- dot_fisher(stt, sgm)
print(result$Y)  # 58.44147
print(result$P)  # 0.0002706851

## decorrelated augmented rank truncated (ART) test.
result <- dot_art(stt, sgm, k=6)
print(result$Y)  # 22.50976
print(result$P)  # 0.0006704994

## decorrelated Augmented Rank Truncated Adaptive (ARTA) test
result <- dot_arta(stt, sgm, k=6)
print(result$Y)  # -1.738662
print(result$k)  #  5 smallest P-values are retained
print(result$P)  #  0.003165 (varies)

## decorrelated Rank Truncated Product (RTP)
result <- dot_rtp(stt, sgm, k=6)
print(result$Y)  # 22.6757
print(result$P)  # 0.0007275518

## decorrelated Truncated Product Method (TPM)
result <- dot_tpm(stt, sgm, tau=0.05)
print(result$Y)  #  1.510581e-08
print(result$k)  #  6 P-values <= tau
print(result$P)  #  0.0007954961