- Institute for Medical Informatics and Statistics - = IMIS =

---

An entropy-based multilocus measure for linkage disequilibrium

Normalized Entropy Difference ε

---

Go to Web Calculator

Download calculator program

---

M. Nothnagel, R. Fürst, K. Rohde (2002).
Entropy as a Measure for Linkage Disequilibrium over Multilocus Haplotype Blocks.
Hum Hered 2002; 54(4):186-198.
NCBI PubMed Human Heredity

Request for Reprints: nothnagel medinfo.uni-kiel.de

Idea

We developed the Normalized Entropy Difference, ε, as a measure to describe linkage disequilibrium (LD) of multilocus sequences. It is based on the concept of entropy and applies it to SNP sequences. The basic idea is to consider haplotypes as possible states of a multi-marker system and use entropy to describe the system's state. We normalize the entropy difference between the observed state (i.e. the haplotype sample estimates) and the expected one under linkage equilibrium (i.e. the sum of the single SNP's entropy values).

Features

The measure's main features are:

• Consideration of sequences of (theoretically) arbitrary lengths
  (in practice limited by the need to estimate haplotype frequencies from genotypes with sufficient samples sizes)
• Assessment of LD with regard to the sequence, not a particular haplotype; a single quantity summarizing the LD status of the sequence
• Sensitivity to both the number of haplotypes present at the sequence and their frequency pattern; no emphasis on a particular source of LD such as absent recombination as seen for the pairwise measure D'
• An approximate chi-squared test of the significance of the deviation from linkage equilibrium by an related quantity
• ε can be regarded as a multilocus extension of the commonly used pairwise LD measure r² (Δ²).

Simulation studies and application to real-world data have supported a reasonable behaviour of ε for the description and detection of regions in elevated LD.

Extensions

ε values range between 0 (linkage equilibirum) and (m-1)/m (perfect LD - exactly two haplotypes in the sample), where m is the number of markers considered. Thus, the measure can be further normalized to assume values in the standard interval [0,1] by multiplying ε by m/(m-1), yielding ε' (see Ph.D. thesis). We recently extended this idea to two multi-allelic markers, yielding the measure φ'.

For additional information, please contact Michael Nothnagel (nothnagel medinfo.uni-kiel.de).

Last modified: 06/29/2006