Linkage Detection Adaptive to Linkage Disequilibrium: The Disequilibrium Maximum-Likelihood–Binomial Test for Affected-Sibship Data

Abstract

It has been demonstrated in the literature that the transmission/disequilibrium test (TDT) has higher power than the affected-sib-pair (ASP) mean test when linkage disequilibrium (LD) is strong but that the mean test has higher power when LD is weak. Thus, for ASP data, it seems clear that the TDT should be used when LD is strong but that the mean test or other linkage tests should be used when LD is weak or absent. However, in practice, it may be difficult to follow such a guideline, because the extent of LD is often unknown. Even with a highly dense genetic-marker map, in which some markers should be located near the disease-predisposing mutation, strong LD is not inevitable. Besides the genetic distance, LD is also affected by many factors, such as the allelic heterogeneity at the disease locus, the initial LD, the allelic frequencies at both disease locus and marker locus, and the age of the mutation. Therefore, it is of interest to develop methods that are adaptive to the extent of LD. In this report, we propose a disequilibrium maximum-binomial-likelihood (DMLB) test that incorporates LD in the maximum-binomial-likelihood (MLB) test. Examination of the corresponding score statistics shows that this method adaptively combines two sources of information: (a) the identity-by-descent (IBD) sharing score, which is informative for linkage regardless of the existence of LD, and (b) the contrast between allele-specific IBD sharing score, which is informative for linkage only in the presence of LD. For ASP data, the proposed test has higher power than either the TDT or the mean test when the extent of LD ranges from moderate to strong. Only when LD is very weak or absent is the DMLB slightly less powerful than the mean test; in such cases, the TDT has essentially no power to detect linkage. Therefore, the DMLB test is an interesting approach to linkage detection when the extent of LD is unknown.

A Marginal Likelihood Model for Family‐Based Data

“…The proposed model, extending the maximumlikelihood-binomial (MLB) method and the disequilibrium maximum-likelihood-binomial (DMLB) method Abel & Müller-Myhsok, 1998;Huang & Jiang, 1999), is adaptive to linkage disequilibrium (LD) and linkage heterogeneity. Compared with other procedures, the likelihood ratio test (LRT) derived from the proposed model enjoys superior qualities.…”

Evaluating linkage and linkage disequilibrium: use of excess sharing and transmission disequilibrium methods in affected sib pairs

“…The overall linkage test, LR L (15), is the sum of a test of excess sharing, LR S (11), which is the familiar mean test, and a novel test of transmission disequilibrium for multi-allelic ASP data, LR T (13). Motivated by the transmission probability model given in the Appendix, the test of excess sharing employs a one-sided alternative hypothesis, as advocated by Holmans (1993) and more recently by Huang & Jiang (1999). The transmission probability model also provides an interpretation of the parameters that are estimated in the calculation of the transmission disequilibrium statistic.…”

“…For tests of no transmission disequilibrium, which are based on H T 0 , a similar one-sided restriction on the alternative hypothesis is possible if a particular marker allele is thought to be positively associated with disease, as pointed out by Huang & Jiang (1999). If no such prior information is available, then one is forced to use the general alternative hypothesis H T A : P 11 P 22 .…”

“…The statistic X 2 S is the one-sided mean sharing statistic obtained from restricting excess sharing to the 'possible triangle' of Holmans (1993). The use of one-sided alternative hypotheses was recently advocated by Huang & Jiang (1999). They derive a statistic for affected sibships which reduces to X 2 L when the data consist of ASPs.…”

“…Various aspects of the disease model affect the comparative power of the two tests; however the key factor is the extent of LD, which is usually unknown. Thus there has been recent interest in methods which use both kinds of approaches in an overall test of linkage (Huang & Jiang, 1999).…”