# Measuring Haplotype Rarity

## Deviation Index

We also considered an index based on standard deviations^{[33]} from the mode.
This metric was developed specifically to highlight uncommon and rare haplotypes.

We also considered an index based on standard deviations^{[33]} from the mode.
This metric was developed specifically to highlight uncommon and rare haplotypes.

- Determining a standard deviation for the frequency distribution of each marker; this will be less than 1, ranging from near zero to ~0.17. (To avoid division by zero errors, take the maximum of the standard deviation or 0.001, 10
^{-3}.) - Determining the absolute difference between the marker modal value and the subject value, resulting in numbers ≥0.
- We chose to compare to the modal value, rather then the mean (average), as it is not affected by extremes.

- Dividing difference (B) by standard deviation (A), again ≥0.
- Summing across all markers in the marker set.
- Dividing sums by nominal marker set size.

The rationale for the method is

Figure 8 displays the distribution graphs. See Appendix D for details. Note the additional peaks, at >=16, for the 37- and 67-marker scores; these were due to this methodâ€™s tendency to emphasize less-common values. 19% of 12-marker scores, 2% of 25-marker scores, 27% of 37-marker scores and 28% of 67 marker scores are greater than 16.

Resulting scores, however, do not directly relate to probabilities. They are simply indicators of how common or rare the haplotype. Lower scores are more common; higher scores more uncommon. If scores seem abnormally high, it is because each allele difference from a modal value represents many standard deviations.

Table 8 Deviation Index Summary Stistics |
||||
---|---|---|---|---|

Statistic | 12 mkr. | 25 mkr. | 37 mkr. | 67 mkr. |

Average )mean) | 10.31 | 7.27 | 16.57 | 9.52 |

Standard Deviation | 9.41 | 6.48 | 19.26 | 7.53 |

Minimum | 0.00 | 0.00 | 1.00 | 1.05 |

Maximum | 371.50 | 292.56 | 372.09 | 50.93 |

Median |
9.19 |
6.50 |
9.62 |
6.07 |

Mode | # N/A | # N/A | # N/A | # N/A |

n= | 4,940 | 4,203 | 3,824 | 1953 |

Comment: The deviation method highlights uncommon and rare haplotypes. It performs poorly at distinguishing common from average-rarity haplotypes.

Table 9 Deviation Index Interpretation |
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---|---|---|---|---|

Category | 12 markers | 25 markers | 37 markers | 67 markers |

Very common | =0 | 0-2 | 0-4 | 0-2 |

Common | >0, <4 | 2-4 | 4-6 | 2-4 |

Average | 4-14 | 4-10 | 6-16 | 4-10 |

Uncommon | 14-22 | 10-20 | 16-40 | 10-22 |

Rare | >22 | >20 | >40 | >22 |

- For example, men with the WAMH
^{[34]}score zero for 12 markers. However, for 67 markers these men average a score of 7.28 and none who tested to this level scored less than 5.46.

Disadvantages appear to outweigh the advantages.