Acceptable Z-scores file format

The Z score file should satisfy the following requirements:

1. It is a comma- or tab-separated text file (.gz compressed is acceptable)
2. The first row should be a header line, and every row after the first will be treated as a different SNP.
3. By default GhostKnockoffGWAS will search for column names CHR, POS, REF, ALT, and Z. Alternatively, you can specify which column should be used for each of these fields by providing the corresponding optional inputs, e.g. --CHR 6 tells GhostKnockoffGWAS to use column 6 as CHR. The ALT allele will be treated as the effect allele and REF be treated as non-effect allele. The POS (position) field of each variant must be from HG19 or HG38, which must be specified by the --genome-build argument.

Here is a minimal example with 10 Z scores

CHR	POS	REF	ALT	Z
17	150509	T	TA	1.08773561923134
17	151035	T	C	0.703898767202681
17	151041	G	A	NaN
17	151872	T	C	-0.299877259561085
17	152087	C	T	-0.371627135786605
17	152104	G	A	-0.28387322965385
17	152248	G	A	0.901618600934489
17	152427	G	A	1.10987516000804
17	152771	A	G	0.708492545266136

A toy example is example_zfile.txt (17MB).

Requirements on the input Z-scores

In our papers, Z-scores are defined by $z = \frac{1}{\sqrt{N}}X^ty$ where $X$ is the $N \times P$ standardized genotype matrix with $N$ samples and $P$ SNPs, $y$ is the normalized $n \times 1$ phenotype vector, and these Z-scores have $N(0, 1)$ distribution under the null.

In practice, this paper shows that other association test statistics that are $N(0, 1)$ under the null also result in FDR control. This includes commonly used tests in genetic association studies such as:

• generalized linear mixed effect model to account for sample relatedness
• saddle point approximation for extreme case-control imbalance
• meta-analysis that aggregates multiple studies.

If you have p-values, effect sizes, odds ratios,...etc, converting them into Z score might be possible, for example by following the Notes on computing Z-scores of this blog post.