A quantitative trait rare variant nonparametric linkage method with application to age-at-onset of Alzheimer’s disease


To analyze pedigrees with quantitative trait (QT) and sequence data, we developed a rare variant (RV) quantitative nonparametric linkage (QNPL) method, which evaluates sharing of minor alleles. RV-QNPL has greater power than the traditional QNPL that tests for excess sharing of minor and major alleles. RV-QNPL is robust to population substructure and admixture, locus heterogeneity, and inclusion of nonpathogenic variants and can be readily applied outside of coding regions. When QNPL was used to analyze common variants, it often led to loci mapping to large intervals, e.g., >40 Mb. In contrast, when RVs are analyzed, regions are well defined, e.g., a gene. Using simulation studies, we demonstrate that RV-QNPL is substantially more powerful than applying traditional QNPL methods to analyze RVs. RV-QNPL was also applied to analyze age-at-onset (AAO) data for 107 late-onset Alzheimer’s disease (LOAD) pedigrees of Caribbean Hispanic and European ancestry with whole-genome sequence data. When AAO of AD was analyzed regardless of APOE ε4 status, suggestive linkage (LOD = 2.4) was observed with RVs in KNDC1 and nominally significant linkage (p < 0.05) was observed with RVs in LOAD genes ABCA7 and IQCK. When AAO of AD was analyzed for APOE ε4 positive family members, nominally significant linkage was observed with RVs in APOE, while when AAO of AD was analyzed for APOE ε4 negative family members, nominal significance was observed for IQCK and ADAMTS1. RV-QNPL provides a powerful resource to analyze QTs in families to elucidate their genetic etiology.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Pedigree structures used in simulation studies.
Fig. 2: Exome-wide power for RV-QNPL and CHP-QNPL in extended pedigrees.


  1. 1.

    Nicolae DL. Association tests for rare variants. Annu Rev Genomics Hum Genet. 2016;17:117–30.

    CAS  Article  Google Scholar 

  2. 2.

    He Z, Zhang D, Renton AE, Li B, Zhao L, Wang GT, et al. The rare-variant generalized disequilibrium test for association analysis of nuclear and extended pedigrees with application to Alzheimer disease WGS data. Am J Hum Genet. 2017;100:193–204.

    CAS  Article  Google Scholar 

  3. 3.

    Santorico SA, Hendricks AE. Progress in methods for rare variant association. BMC Genet. 2016;17:S6.

    Article  Google Scholar 

  4. 4.

    Chen H, Meigs JB, Dupuis J. Sequence kernel association test for quantitative traits in family samples. Genet Epidemiol. 2013;37:196–204.

    Article  Google Scholar 

  5. 5.

    MacCallum RC, Zhang S, Preacher KJ, Rucker DD. On the practice of dichotomization of quantitative variables. Psychol Methods. 2002;7:19–40.

    Article  Google Scholar 

  6. 6.

    Haseman JK, Elston RC. The investigation of linkage between a quantitative trait and a marker locus. Behav Genet. 1972;2:3–19.

    CAS  Article  Google Scholar 

  7. 7.

    Elston RC, Buxbaum S, Jacobs KB, Olson JM. Haseman and Elston revisited. Genet Epidemiol. 2000;19:1–17.

    CAS  Article  Google Scholar 

  8. 8.

    Sham PC, Purcell S. Equivalence between Haseman-Elston and variance-components linkage analyses for sib pairs. Am J Hum Genet. 2001;68:1527–32.

    CAS  Article  Google Scholar 

  9. 9.

    Sham PC, Purcell S, Cherny SS, Abecasis GR. Powerful regression-based quantitative-trait linkage analysis of general pedigrees. Am J Hum Genet. 2002;71:238–53.

    CAS  Article  Google Scholar 

  10. 10.

    Allison DB, Neale MC, Zannolli R, Schork NJ, Amos CI, Blangero J. Testing the robustness of the likelihood-ratio test in a variance-component quantitative-trait loci–mapping procedure. Am J Hum Genet. 1999;65:531–44.

    CAS  Article  Google Scholar 

  11. 11.

    Mackay TF, Stone EA, Ayroles JF. The genetics of quantitative traits: challenges and prospects. Nat Rev Genet. 2009;10:565.

    CAS  Article  Google Scholar 

  12. 12.

    Drinkwater NR, Gould MN. The long path from QTL to gene. PLoS Genet. 2012;8:e1002975.

    CAS  Article  Google Scholar 

  13. 13.

    Greenberg DA, Abreu PC. Determining trait locus position from multipoint analysis: accuracy and power of three different statistics. Genet Epidemiol. 2001;21:299–314.

    CAS  Article  Google Scholar 

  14. 14.

    Zhao L, He Z, Zhang D, Wang GT, Renton AE, Vardarajan BN, et al. A rare variant nonparametric linkage method for nuclear and extended pedigrees with application to late-onset Alzheimer disease via WGS data. Am J Hum Genet. 2019;105:822–35.

    CAS  Article  Google Scholar 

  15. 15.

    Wang GT, Zhang D, Li B, Dai H, Leal SM. Collapsed haplotype pattern method for linkage analysis of next-generation sequence data. Eur J Hum Genet EJHG. 2015;23:1739–43.

    CAS  Article  Google Scholar 

  16. 16.

    Van Cauwenberghe C, Van Broeckhoven C, Sleegers K. The genetic landscape of Alzheimer disease: clinical implications and perspectives. Genet Med. 2016;18:421.

    Article  Google Scholar 

  17. 17.

    Lee JH, Cheng R, Vardarajan B, Lantigua R. Genetic modifiers of age at onset in carriers of the G206A mutation in PSEN1 with familial Alzheimer disease among Caribbean hispanics. JAMA Neurol. 2015;72:1043–51.

    Article  Google Scholar 

  18. 18.

    Hayashi K, Furuya A, Sakamaki Y, Akagi T, Shinoda Y, Sadakata T, et al. The brain-specific RasGEF very-KIND is required for normal dendritic growth in cerebellar granule cells and proper motor coordination. PLoS ONE. 2017;12:e0173175.

    Article  Google Scholar 

  19. 19.

    Cacace R, Sleegers K, Van Broeckhoven C. Molecular genetics of early-onset Alzheimer’s disease revisited. Alzheimers Dement. 2016;12:733–48.

    Article  Google Scholar 

  20. 20.

    Aikawa T, Holm M-L, Kanekiyo T. ABCA7 and pathogenic pathways of Alzheimer’s disease. Brain Sci. 2018;8:27.

    Article  Google Scholar 

  21. 21.

    Kunkle BW, Grenier-Boley B, Sims R, Bis JC, Damotte V, Naj AC, et al. Genetic meta-analysis of diagnosed Alzheimer’s disease identifies new risk loci and implicates Aβ, tau, immunity and lipid processing. Nat Genet. 2019;51:414.

    CAS  Article  Google Scholar 

  22. 22.

    Abecasis GR, Cherny SS, Cookson WO, Cardon LR. Merlin–rapid analysis of dense genetic maps using sparse gene flow trees. Nat Genet. 2002;30:97–101.

    CAS  Article  Google Scholar 

  23. 23.

    Karczewski KJ, Francioli LC, Tiao G, Cummings BB, Alföldi J, Wang Q, et al. Variation across 141,456 human exomes and genomes reveals the spectrum of loss-of-function intolerance across human protein-coding genes. bioRxiv. 2019;30:531210.

    Google Scholar 

  24. 24.

    Lek M, Karczewski KJ, Minikel EV, Samocha KE, Banks E, Fennell T, et al. Analysis of protein-coding genetic variation in 60,706 humans. Nature. 2016;536:285–91.

    CAS  Article  Google Scholar 

  25. 25.

    Matise TC, Chen F, Chen W, Francisco M, Hansen M, He C, et al. A second-generation combined linkage–physical map of the human genome. Genome Res. 2007;17:1783–6.

    CAS  Article  Google Scholar 

  26. 26.

    Li B, Wang GT, Leal SM. Generation of sequence-based data for pedigree-segregating Mendelian or Complex traits. Bioinformatics. 2015;14:btv412.

    Google Scholar 

  27. 27.

    Lander E, Kruglyak L. Genetic dissection of complex traits: guidelines for interpreting and reporting linkage results. Nat Genet. 1995;11:241–7.

    CAS  Article  Google Scholar 

  28. 28.

    Mandal DM, Wilson AF, Elston RC, Weissbecker K, Keats BJ, Bailey-Wilson JE. Effects of misspecification of allele frequencies on the Type I error rate of model-free linkage analysis. Hum Hered. 2000;50:126–32.

    CAS  Article  Google Scholar 

  29. 29.

    Risch NJ, Zhang H. Mapping quantitative trait loci with extreme discordant sib pairs: sampling considerations. Am J Hum Genet. 1996;58:836–43.

    CAS  PubMed  PubMed Central  Google Scholar 

  30. 30.

    Allison DB. The use of discordant sibling pairs for finding genetic loci linked to obesity: practical considerations. Int J Obes Relat Metab Disord J Int Assoc Study Obes. 1996;20:553–60.

    CAS  Google Scholar 

  31. 31.

    Allison DB, Heo M, Schork NJ, Wong S-L, Elston RC. Extreme selection strategies in gene mapping studies of oligogenic quantitative traits do not always increase power. Hum Hered. 1998;48:97–107.

    CAS  Article  Google Scholar 

  32. 32.

    Mandal DM, Sorant AJ, Atwood LD, Wilson AF, Bailey-Wilson JE. Allele frequency misspecification: effect on power and Type I error of model-dependent linkage analysis of quantitative traits under random ascertainment. BMC Genet. 2006;7:21.

    Article  Google Scholar 

  33. 33.

    He Z, O’Roak BJ, Smith JD, Wang G, Hooker S, Santos-Cortez RLP, et al. Rare-variant extensions of the transmission disequilibrium test: application to autism exome sequence data. Am J Hum Genet. 2014;94:33–46.

    CAS  Article  Google Scholar 

  34. 34.

    Vardarajan BN, Ghani M, Kahn A, Sheikh S, Sato C, Barral S, et al. Rare coding mutations identified by sequencing of Alzheimer disease genome-wide association studies loci. Ann Neurol. 2015;78:487–98.

    CAS  Article  Google Scholar 

Download references


We wish to thank the family members who participated in the Alzheimer Disease Sequencing Project and made this research possible. We also thank Katherine Montague for proof-reading this manuscript. The datasets used for the analyses in this manuscript were obtained from the database of Genotypes and Phenotypes (dbGaP) through dbGaP accession study number phs000572.v7.p4. We would like to thank dbGaP for distributing the data used in this study. We thank contributors, including the Alzheimer’s disease Centers who collected samples used in the NIA-LOAD study, as well as patients and their families, whose help and participation made this work possible. We also acknowledge the Genetic Studies of Alzheimer’s disease in Caribbean Hispanics (EFIGA) study participants and the EFIGA research and support staff for their contributions to this study. Complete acknowledgments can be found in the Supplemental Acknowledgments.


The National Institute on Aging (NIA)-LOAD supported the collection of samples used in this study through NIA grants U24AG026395, R01AG041797, 5R37AG015473, RF1AG015473, and R56AG051876. This work was also supported by grants from the National Human Genome Research Institute R01 HG008972 and NIA RF1 AG058131.

Author information



Corresponding author

Correspondence to Suzanne M. Leal.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zhao, L., Zhang, Z., Rodriguez, S.M.B. et al. A quantitative trait rare variant nonparametric linkage method with application to age-at-onset of Alzheimer’s disease. Eur J Hum Genet (2020). https://doi.org/10.1038/s41431-020-0703-z

Download citation