# FLOSS: Frequently Asked Questions (FAQ)

Last updated 15 Dec 2005.

### How do I test the low-to-high covariate ordering of the families without also testing the high-to-low ordering?

FLOSS analyzes both ascending and descending orderings of the covariate because the analyst rarely knows a "correct" direction of the covariate ordering a priori. Automatically testing both ascending and descending orderings in the same analysis simplifies the ordered subset analysis. In the rare cases where one desires to test a specific direction of covariate ordering (for example in a replication analysis), the specific range of the covariate will often be known as well, so that restricting the linkage analysis to the families in the target covariate range would be a better analysis choice (in our opinion).

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`.
Note that you are interested in estimating the probability of event A, `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)`.

### How can I reduce the FLOSS running time?

If you have a large data set and need to decrease the running time of FLOSS, consider the following strategies
• 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.
1. For the initial analysis set `-maxperms` to a small numbers (say 100, 200, or 400).
2. 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.
3. 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)`.
• .
• 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.

### What does FLOSS do with individuals or families that have missing covariate values?

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.

### What does FLOSS do with families that have tied covariate scores?

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`.