Quasi-Monte Carlo Methods for Binary Event Models with Complex Family Data

References

• Bai, D., Yip, B. H. K., Windham, G. C., Sourander, A., Francis, R., Yoffe, R., Glasson, E., Mahjani, B., Suominen, A., Leonard, H., Gissler, M., Buxbaum, J. D., Wong, K., Schendel, D., Kodesh, A., Breshnahan, M., Levine, S. Z., Parner, E. T., Hansen, S. N., Hultman, C., Reichenberg, A., and Sandin, S. (2019), “Association of Genetic and Environmental Factors With Autism in a 5-Country Cohort,” JAMA Psychiatry, 76, 1035–1043. DOI: 10.1001/jamapsychiatry.2019.1411.
   PubMed Web of Science ®Google Scholar
• Botev, Z. I. (2017), “The Normal Law under Linear Restrictions: Simulation and Estimation via Minimax Tilting,” Journal of the Royal Statistical Society, Series B, 79, 125–148. DOI: 10.1111/rssb.12162.
   Google Scholar
• Breslow, N. E., and Clayton, D. G. (1993), “Approximate Inference in Generalized Linear Mixed Models,” Journal of the American Statistical Association, 88, 9–25.
   Web of Science ®Google Scholar
• Brown, H., and Prescott, R. (2014), Applied Mixed Models in Medicine, Chichester: Wiley.
   Google Scholar
• Buluç, A., Meyerhenke, H., Safro, I., Sanders, P., and Schulz, C. (2016), Recent Advances in Graph Partitioning, pp. 117–158, Cham: Springer.
   Google Scholar
• Caflisch, R. E. (1998), “Monte Carlo and quasi-Monte Carlo Methods,” Acta Numerica, 7, 1–49. DOI: 10.1017/S0962492900002804.
   Google Scholar
• Chlebíková, J. (1996), “Approximating the Maximally Balanced Connected Partition Problem in Graphs,” Information Processing Letters, 60, 225–230. DOI: 10.1016/S0020-0190(96)00175-5.
   Web of Science ®Google Scholar
• Christoffersen, B., Clements, M., Kjellström, H., and Humphreys, K. (2021), “Approximation Methods for Mixed Models with Probit Link Functions.” DOI: 10.48550/ARXIV.2110.14412.
   Google Scholar
• de Villemereuil, P., Schielzeth, H., Nakagawa, S., and Morrissey, M. (2016), “General Methods for Evolutionary Quantitative Genetic Inference from Generalized Mixed Models,” Genetics, 204, 1281–1294. DOI: 10.1534/genetics.115.186536.
   PubMed Web of Science ®Google Scholar
• Eddelbuettel, D., Emerson, J. W., and Kane, M. J. (2020), BH: Boost C++ Header Files. R package version 1.72.0-3.
   Google Scholar
• Ekbom, A. (2010), “The Swedish Multi-Generation Register,” in Methods in Molecular Biology, ed. J. Dillner, pp. 215–220, Totowa, NJ: Humana Press.
   Google Scholar
• Falchi, M., Forabosco, P., Mocci, E., Borlino, C. C., Picciau, A., Virdis, E., Persico, I., Parracciani, D., Angius, A., and Pirastu, M. (2004), “A Genomewide Search Using an Original Pairwise Sampling Approach for Large Genealogies Identifies a New Locus for Total and Low-Density Lipoprotein Cholesterol in Two Genetically Differentiated Isolates of Sardinia,” The American Journal of Human Genetics, 75, 1015–1031. DOI: 10.1086/426155.
   PubMed Web of Science ®Google Scholar
• Fiduccia, C., and Mattheyses, R. (1982), “A Linear-Time Heuristic for Improving Network Partitions,” in 19th Design Automation Conference, pp. 175–181.
   Google Scholar
• Genz, A. (1992), “Numerical Computation of Multivariate Normal Probabilities,” Journal of Computational and Graphical Statistics, 1, 141–149.
   Google Scholar
• Genz, A., and Bretz, F. (2002), “Comparison of Methods for the Computation of Multivariate t Probabilities,” Journal of Computational and Graphical Statistics, 11, 950–971. DOI: 10.1198/106186002394.
   Web of Science ®Google Scholar
• Genz, A., and Bretz, F. (2009), Computation of Multivariate Normal and t Probabilities, Lecture Notes in Statistics, Heidelberg: Springer-Verlag.
   Google Scholar
• Genz, A., Bretz, F., Miwa, T., Mi, X., Leisch, F., Scheipl, F., and Hothorn, T. (2020), mvtnorm: Multivariate Normal and t Distributions. R package version 1.1-1.
   Google Scholar
• Hadfield, J. D. (2010), “MCMC Methods for Multi-Response Generalized Linear Mixed Models: The MCMCglmm R Package,” Journal of Statistical Software, 33, 1–22. DOI: 10.18637/jss.v033.i02.
   PubMed Web of Science ®Google Scholar
• Hajivassiliou, V., McFadden, D., and Ruud, P. (1996), “Simulation of Multivariate Normal Rectangle Probabilities and their Derivatives Theoretical and Computational Results,” Journal of Econometrics, 72, 85–134. DOI: 10.1016/0304-4076(94)01716-6.
   Web of Science ®Google Scholar
• Hickernell, F. J., Lemieux, C., and Owen, A. B. (2005), “Control Variates for Quasi-Monte Carlo,” Statistical Science, 20, 1–31. DOI: 10.1214/088342304000000468.
   Web of Science ®Google Scholar
• Holand, A. M., Steinsland, I., Martino, S., and Jensen, H. (2013), “Animal Models and Integrated Nested Laplace Approximations,” G3 Genes—Genomes—Genetics, 3, 1241–1251. DOI: 10.1534/g3.113.006700.
   Web of Science ®Google Scholar
• Hopcroft, J., and Tarjan, R. (1973), “Algorithm 447: Efficient Algorithms for Graph Manipulation,” Communications of the ACM, 16, 372–378. DOI: 10.1145/362248.362272.
   Web of Science ®Google Scholar
• Hothorn, T., Möst, L., and Bühlmann, P. (2018), “Most Likely Transformations,” Scandinavian Journal of Statistics, 45, 110–134. DOI: 10.1111/sjos.12291.
   Web of Science ®Google Scholar
• Joe, H. (2008), “Accuracy of Laplace Approximation for Discrete Response Mixed Models,” Computational Statistics & Data Analysis, 52, 5066–5074.
   Web of Science ®Google Scholar
• Joe, S., and Kuo, F. Y. (2003), “Remark on Algorithm 659: Implementing Sobol’s Quasirandom Sequence Generator,” ACM Transactions on Mathematical Software, 29, 49–57. DOI: 10.1145/641876.641879.
   Web of Science ®Google Scholar
• Kernighan, B. W., and Lin, S. (1970), “An Efficient Heuristic Procedure for Partitioning Graphs,” The Bell System Technical Journal, 49, 291–307. DOI: 10.1002/j.1538-7305.1970.tb01770.x.
   Google Scholar
• Kirichenko, A. V., Belonogova, N. M., Aulchenko, Y. S., and Axenovich, T. I. (2009), “Pedstr Software for Cutting Large Pedigrees for Haplotyping, IBD Computation and Multipoint Linkage Analysis,” Annals of Human Genetics, 73, 527–531. DOI: 10.1111/j.1469-1809.2009.00531.x.
   PubMed Web of Science ®Google Scholar
• Lichtenstein, P., Yip, B. H., Björk, C., Pawitan, Y., Cannon, T. D., Sullivan, P. F., and Hultman, C. M. (2009), “Common Genetic Determinants of Schizophrenia and Bipolar Disorder in Swedish Families: A Population-based Study,” The Lancet, 373, 234–239. DOI: 10.1016/S0140-6736(09)60072-6.
   PubMed Web of Science ®Google Scholar
• Liu, F., Kirichenko, A., Axenovich, T. I., van Duijn, C. M., and Aulchenko, Y. S. (2008), “An Approach for Cutting Large and Complex Pedigrees for Linkage Analysis,” European Journal of Human Genetics, 16, 854–860. DOI: 10.1038/ejhg.2008.24.
   PubMed Web of Science ®Google Scholar
• Liu, X.-R., Pawitan, Y., and Clements, M. S. (2017), “Generalized Survival Models for Correlated Time-to-Event Data,” Statistics in Medicine, 36, 4743–4762. DOI: 10.1002/sim.7451.
   PubMed Web of Science ®Google Scholar
• Mahjani, B., Klei, L., Hultman, C. M., Larsson, H., Devlin, B., Buxbaum, J. D., Sandin, S., and Grice, D. E. (2020), “Maternal Effects as Causes of Risk for Obsessive-Compulsive Disorder,” Biological Psychiatry, 87, 1045–1051. Obsessive-Compulsive Disorder and Developmental Disorders. DOI: 10.1016/j.biopsych.2020.01.006.
   PubMed Web of Science ®Google Scholar
• Misztal, I., Tsuruta, S., Lourenco, D., Masuda, Y., Aguilar, I., Legarra, A., and Vitezica, Z. (2018), Manual for BLUPF90 Family Programs, Athens, GA: University of Georgia.
   Google Scholar
• Owen, A. B. (1998), “Scrambling Sobol’ and Niederreiter–Xing Points,” Journal of Complexity, 14, 466–489. DOI: 10.1006/jcom.1998.0487.
   Web of Science ®Google Scholar
• Pawitan, Y., Reilly, M., Nilsson, E., Cnattingius, S., and Lichtenstein, P. (2004), “Estimation of Genetic and Environmental Factors for Binary Traits Using Family Data,” Statistics in Medicine, 23, 449–465. DOI: 10.1002/sim.1603.
   PubMed Web of Science ®Google Scholar
• Pinheiro, J. C., and Bates, D. M. (1995), “Approximations to the Log-Likelihood Function in the Nonlinear Mixed-Effects Model,” Journal of Computational and Graphical Statistics, 4, 12–35.
   Google Scholar
• Pinheiro, J. C., and Chao, E. C. (2006), “Efficient Laplacian and Adaptive Gaussian Quadrature Algorithms for Multilevel Generalized Linear Mixed Models,” Journal of Computational and Graphical Statistics, 15, 58–81. DOI: 10.1198/106186006X96962.
   Web of Science ®Google Scholar
• R Core Team (2020), R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing.
   Google Scholar
• Rodríguez, G., and N. Goldman (2001), “Improved Estimation Procedures for Multilevel Models with Binary Response: A Case-Study,” Journal of the Royal Statistical Society, Series A, 164, 339–355. DOI: 10.1111/1467-985X.00206.
   Web of Science ®Google Scholar
• Sandin, S., Lichtenstein, P., Kuja-Halkola, R., Hultman, C., Larsson, H., and Reichenberg, A. (2017), “The Heritability of Autism Spectrum Disorder,” JAMA, 318, 1182–1184. DOI: 10.1001/jama.2017.12141.
   PubMed Web of Science ®Google Scholar
• Scurrah, K. J., Palmer, L. J., and Burton, P. R. (2000), “Variance Components Analysis for Pedigree-based Censored Survival Data using Generalized Linear Mixed Models (GLMMs) and Gibbs Sampling in BUGS,” Genetic Epidemiology, 19, 127–148. DOI: 10.1002/1098-2272(200009)19:2<127::AID-GEPI2>3.0.CO;2-S.
   PubMed Web of Science ®Google Scholar
• Simon, H. D., and Teng, S.-H. (1997), “How Good is Recursive Bisection?” SIAM Journal on Scientific Computing, 18, 1436–1445. DOI: 10.1137/S1064827593255135.
   Web of Science ®Google Scholar
• Tenesa, A., and Haley, C. S. (2013), “The Heritability of Human Disease: Estimation, Uses and Abuses,” Nature Reviews Genetics, 14, 139–149. DOI: 10.1038/nrg3377.
   PubMed Web of Science ®Google Scholar
• Thompson, R. (1990), Generalized Linear Models and Applications to Animal Breeding, pp. 312–328, Berlin, Heidelberg: Springer.
   Google Scholar
• Varin, C., Reid, N., and Firth, D. (2011), “An Overview of Composite Likelihood Methods,” Statistica Sinica, 21, 5–42.
   Web of Science ®Google Scholar
• Villemereuil, P., Gimenez, O., and Doligez, B. (2013), “Comparing Parent–Offspring Regression with Frequentist and Bayesian Animal Models to Estimate Heritability in Wild Populations: A Simulation Study for Gaussian and Binary Traits,” Methods in Ecology and Evolution, 4, 260–275. DOI: 10.1111/2041-210X.12011.
   Web of Science ®Google Scholar
• Wichura, M. J. (1988), “The Percentage Points of the Normal Distribution,” Journal of the Royal Statistical Society, Series C, 37, 477–484.
   Web of Science ®Google Scholar
• Wilhelm, S., and de Matos, M. G. (2013), “Estimating Spatial Probit Models in R,” The R Journal, 5, 130–143. DOI: 10.32614/RJ-2013-013.
   Google Scholar