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bgen / How much accuracy do I need

How much accuracy do you get?

Probability values in BGEN are stored to at least 4 decimal places in BGEN v1.1, or to within 1/(pow(2,b)-1), where b is the number of bits used, in BGEN v1.2. This gives the following table

Number of bits Probabilities accurate to within Decimal places of accuracy
1 1 0
2 1/3 0
3 1/7 0
4 1/15 0
5 1/31 1
6 1/63 1
7 1/127 1
8 1/255 2
9 1/511 2
10 1/1023 2
11 1/2047 3
12 1/4095 3
13 1/4095 3
14 1/4095 3
16 1/65535 4

How much accuracy do you need?

The following graphs depict a comparison of -log10 P-values for an association test conducted using an imputed GEN file (probabilities stored to about 3 decimal places of accuracy) versus the same data converted to BGEN v1.2 at different precisions. At 8 bits there's a maximum discrepancy of around 0.03 in the -log10( pvalues ). (The data here represents imputed genotypes at 48,000 and a simulated case/control trait. Only SNPs with a minor allele count of 100, i.e. MAF > 0.1% were tested; no IMPUTE info threshhold was applied.

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