Unifying ideas for non-parametric linkage analysis

Abstract

Objectives: Non-parametric linkage analysis (NPL) exploits marker allele sharing among affected relatives to map genes influencing complex traits. Computational barriers force approximate analysis on large pedigrees and the adoption of a questionable perfect data assumption (PDA) in assigning p values. To improve NPL significance testing on large pedigrees, we examine the adverse consequences of missing data and PDA. We also introduce a novel statistic, Q-NPL, appropriate for NPL analysis of quantitative traits.

Methods: Using simulated and real data sets with qualitative traits, we compare NPL analysis results for four testing procedures and various degrees of missing data. The simulated data sets vary from all nuclear families, to all large pedigrees, to a mix of pedigrees of different sizes. We implemented the Kong and Cox linear adjustment of p values in the software packages Mendel and SimWalk. We perform similar analysis with Q-NPL on quantitative traits of various heritabilities.

Results: The Kong and Cox extension for significance testing is robust to realistic missing data patterns, greatly improves p values in approximate analyses, and works equally well for qualitative and quantitative traits and small and large pedigrees. The Q-NPL statistic is robust to missing data and shows good power to detect linkage for quantitative traits with a wide spectrum of heritabilities.

Conclusions: The Kong and Cox extension should be a standard tool for calculating NPL p values. It allows the combination of exact and estimated analyses into a single significance score. Q-NPL should be a standard statistic for NPL analysis of quantitative traits. The new statistics are implemented in Mendel and SimWalk.

Fig. 1

Data set 3 (large pedigrees): NPL results. a 0%, b 20%, c 30%, d 40% missing genotypes.

Fig. 2

Data set 4 (mixed pedigrees): NPL results. a 0%, b 20%, c 30%, d 40% missing genotypes.

Fig. 3

Re-analysis of Pajukanta et al.'s data [18].

Fig. 4

Q-NPL p value distribution using data set 1 (small pedigrees), Marker5, and 50% heritability. a Distribution between 0 and 1, b distribution between 0 and 0.1.

Fig. 5

Data set 1 (nuclear families): Q-NPL results using 25% heritability. a 0%, b 20%, c 30%, d 40% missing genotypes.

Fig. 6

Data set 1 (nuclear families): Q-NPL results using 50% heritability. a 0%, b 20%, c 30%, d 40% missing genotypes.

Fig. 7

Data set 4 (mixed pedigrees): Q-NPL results using 25% heritability. a 0%, b 20%, c 30%, d 40% missing genotypes.

Fig. 8

Data set 4 (mixed pedigrees): Q-NPL results using 50% heritability. a 0%, b 20%, c 30%, d 40% missing genotypes.

Fig. 9

QTL and Q-NPL analysis of a real data set.

Fig. 10

QTL and Q-NPL analysis of a real data set with SNP data.