- How do I test the low-to-high direction of the covariate ordering of the families without also testing the high-to-low direction of the ordering?
- How can I reduce the FLOSS running time?
- What does FLOSS do with individuals or families that have missing covariate values?
- What does FLOSS do with families that have tied covariate scores?

However, if the user wants to test one direction only, this can still
be done with FLOSS. First, verify that the best ordered subset reported by
FLOSS is from the same direction you are testing (if it is from the opposite
direction, then accept the Null hypothesis of independent family linkage and covariate
scores). One-half the p-value reported by FLOSS will generally be an excellent
estimate for the Monte Carlo p-value provided the FLOSS p-value is not
too large (say p < 0.10). To see why this is true, assume
the maximal ordered subset linkage score for the ascending direction of a
covariate is `c`

. Given a random ordering, let

- event
`A`

be the event that the maximal ordered subset linkage score for the ascending direction is greater than`c`

- event
`D`

be the event that the maximal ordered subset linkage score for the descending direction is greater than`c`

. - event
`A union D`

be the event that the maximal ordered subset linkage score for the ascending*or*descending direction is greater than`c`

.

`P(A)`

,
under the Null hypothesis, but FLOSS estimates probability of events A or D occuring, `P(A union D)`

, under the Null hypothesis.
Then
`P(A union D) = P(A) + P(D) + P(A intersection D) = 2P(A) + P(A intersection D)`

since `P(A) = P(D)`

. If `P(A)`

is small then it is
unlikely for the smaller and larger linkage scores to segregate sufficiently to have
the maximal ordered subset linkage score from a single direction of a random ordering
be greater than `c`

. So it will be much more unlikely for
the smaller and larger linkage to segregate sufficiently to have the maximal ordered
subset linkage score from both directions of a random ordering
be greater than `c`

. Thus when `P(A)`

is small then
`P(A intersection D)`

is small compared to `P(A)`

and
`(0.5)* P(A union B)`

is approximately equal to `P(A)`

.

- Use the
`--npl`

option. The analysis time for FLOSS is much quicker when using nonparametric linkage analysis z-scores. Using the`--npl`

option is particularly attractive when the linkage analysis used a dense marker panel (say 4000 SNPs or 800 microsatellites with reasonable heterozygosities) since nonparametric linkage analysis z-scores become increasingly accurate as the information content increases. See Kruglyak L, et al (1996) Parametric and nonparametric linkage analysis: a unified multipoint approach. Am J Hum Genet 58:1347-1363. - Use the
`-maxperms`

and`-seed`

parameters to divide the analysis between multiple processors. Most of the running time is consumed with the permutation test, so under the default parameter settings the running time for an analysis can vary by a factor of 100 (100 permutations versus 10000 permutations). Here is a strategy for breaking up the analysis when the analysis may be too long for a single analysis run.- For the initial analysis set
`-maxperms`

to a small numbers (say 100, 200, or 400). - For the covariates which reached the maximum number of permutations,
run additional analyses, each on a separate computer or processor,
with the running time for each analysis controlled by setting the
number of permutations using the
`-minperms`

and`-maxperms`

option. It is important to use a different random seed (set with the`-seed`

parameter) for each separate analysis so that the permutations are independent. - Add up the total number of successes,
`s`

, and total number of permutations,`n`

, for the covariates reported in the "Permutation Test Summary" of the FLOSS`.out`

file. For a fixed number of permutations, the permutation p-value is`(s + 1)/(n + 1)`

.

.
- For the initial analysis set
- Make sure the linkage analysis software is reporting linkage scores at an appropriate density for the marker set density. Since the running FLOSS running time is linear in the number of loci, the running time is approximately 20 times faster when linkage scores are given every 2 cM than when linkage scores are given every 0.1 cM.

The ordered subset analysis is performed using only the families with covariate scores. Families with missing covariate scores are not used for the permutation test. This is why the original maximum linkage score and the total number of families can vary from covarite to covariate. in the "Old Max" and "#Families" columns of the "Brief Summary" of the FLOSS summary (.out) file.

When families share the same
covariate value for a specific covariate, this is taken into account
in the permutation test. Specifically, if `N`

families
are assigned `N-k`

distinct covariate values, then
the permuted order of the families assigns the `N`

families to `N-k`

distinct covariate values. This is
accomplished by randomly ordering the `N`

families
and assigning the `j`

-th family to have rank `j`

for families `1 ≤ j ≤ N-k`

, and assigning
families `(N-k+1) ≤ j ≤ N`

to have a random
rank in the range `1 ≤ rank ≤ N-k`

.

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