Table 1 Comparison of complexity and speed between the HASE framework and a classical workflow.

From: HASE: Framework for efficient high-dimensional association analyses

Stage

Complexityc

Timea,b (hours)

Classical workflow

HASE

np = 1

np = 106

Classical workflow

HASE

Classical workflow

HASE

Single site analysis

O(ninpnt)

max (O(ninp), O(nint))

2.46

0.63

2.46 × 106

0.70

Data transfer

O(npnt)

O(ninp + nint)

0.04

0.07*

4 × 104

11.6

Meta-Analysis

O(npnt)

O(ninpnt)

0.06

0.03

6 × 104

1.7 × 103

  1. aBased on a model with three covariates and 9 million genetic variants, for a total of 4034 participants from three sites. For the classical workflow we used the PLINK software for single site analysis and METAL for the meta-analysis.
  2. bFor single site analysis and meta-analysis the time is given in CPU hours; for the data transfer stage this is in hours using an average network speed of 10 Mbps.
  3. cComplexity for CPU hours is given in terms of classical computation time complexity; complexity for data transfer is shown in terms of how the size of the to be transferred data depends on the size of the input data.
  4. *This time is derived from the transfer of partial derivatives only, because for an association analysis with relatively few phenotypes it is not necessary to transfer encoded data.
  5. ni - number of individuals in the study; np - number of phenotypes of interest; nt - number of tests (genetic variants); Ns - number of sites in the meta-analysis. In standard analysis ni ≪ np and ni ≪ nt.
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