73 1 1 1 1

74 1 1 1 1

75 1 2 1 1

77 1 2 1 2

64 1 1 2 2

74 1 2 1 2

67 2 2 1 1

68 2 2 1 1

70 2 2 1 2

68 2 2 2 2

64 2 2 2 2

? 2 2 2 2

In this example, there are 12 patients which have been genotyped at two linked markers, thought to be linked to a qtl responsible for differences in blood pressure. This data can be cut and paste into the box on the previous page.

In the box labelled, "Enter number of markers:" on the previous page,

the number "2" should be given, as in this example we have 2 markers.

The option, "Columns are separated by a tab, space, comma or any whitespace."

can be left as whitespace (either tabs or spaces), since the columns in the data set are separated by spaces.

If you now click on the button marker run, you should get the page:

If you scroll down the page...

you will see the question "Enter the number of alleles at..."

This will need a "2" in both boxes, since there are 2 alleles (labelled 1 and 2) for both markers. The smallest allele is 1 at both markers. The program will assume that the allele labels are in ascending order, starting with the smallest allele. If there are gaps, the program should still work (although it may take a bit longer to realise the frequency of the missing alleles is zero).

The default values of this form are correct for the example data set and you won't need actually need to change anything, unless you wont to carry out a hypothesis test.

The program then used an EM algorithm to estimate the influence of a haplotype on the phenotype. It is assumed that the influence of each haplotype is additive. This means that the expected phenotype of an individual given its haplotypes is the sum of the influence from the two haplotypes. The expected phenotypic value is then modelled with a normal mixture model with parameters

The

Haplotype | Frequency | µ _{hap} |
---|---|---|

1-1 | 0.273 | 38.373 |

1-2 | 0.102 | 32.001 |

2-1 | 0.268 | 34.214 |

2-2 | 0.357 | 34.484 |

In this example, an individual with haplotypes 1-1 and 1-2 has an expected phenotypic value of

Similarly, the expected phenotype can be found for an individual with any of the 16 possible pairs of haplotypes here.

The hypothesis test is designed to see if the phenotype is influenced by the genetic information at the linked markers. If the phenotype is independent of the haplotypes an individual has at the linked markers (

In the example,

The permutation test will permute the phenotypic values with respect to the genotype information. Each permutation represents an example data set under the null hypothesis. The log likelihood is calculated for each permutation and the p-value is given by the proportion of permutations where the log likelihood value is greater than that of the original data set.

There is an option to give a graph of the distribution function of the log likelihood under H

where D = p(1-1) × p(2-2) - p(1-2) × p(2-1)

D

D

p(1-1) is the frequency of haplotype 1-1 (and similarly for 1-2 , 2-1 , 2-2 )

p

p

Russell Thomson