The Annals of Applied Statistics

Adjustment of nonconfounding covariates in case-control genetic association studies

Hong Zhang, Nilanjan Chatterjee, Daniel Rader, and Jinbo Chen

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It has recently been reported that adjustment of nonconfounding covariates in case-control genetic association analyses may lead to decreased power when the phenotype is rare. This observation contrasts a well-known result for clinical trials where adjustment of baseline variables always leads to increased power for testing randomized treatment effects. In this paper, we propose a unified solution that guarantees increased power through covariate adjustment regardless of whether the phenotype is rare or common. Our method exploits external phenotype prevalence data through a profile likelihood function, and can be applied to fit any commonly used penetrance models including the logistic and probit regression models. Through extensive simulation studies, we showed empirically that the power of our method was indeed higher than available analysis strategies with or without covariate adjustment, and can be considerably higher when the phenotype was common and the covariate effect was strong. We applied the proposed method to analyze a case-control genetic association study on human high density lipoprotein cholesterol level.

Article information

Ann. Appl. Stat. Volume 12, Number 1 (2018), 200-221.

Received: May 2016
Revised: January 2017
First available in Project Euclid: 9 March 2018

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Case-control studies Hardy–Weinberg equilibrium nonconfounding covariates profile likelihood


Zhang, Hong; Chatterjee, Nilanjan; Rader, Daniel; Chen, Jinbo. Adjustment of nonconfounding covariates in case-control genetic association studies. Ann. Appl. Stat. 12 (2018), no. 1, 200--221. doi:10.1214/17-AOAS1065.

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  • Benjamin, M. N., Manuel, A. R., Benjamin, F. V., David, A., Bernie, D., Marju, O., Sekar, K., Shaun, M. P., Kathryn, R. and Mark, J. D. (2011). Testing for an unusual distribution of rare variants. PLoS Genet. 7 e1001322.
  • Chatterjee, N. and Carroll, R. J. (2005). Semiparametric maximum likelihood estimation exploiting gene-environment independence in case-control studies. Biometrika 92 399–418.
  • Edmondson, A. C., Braund, P. S., Stylianou, I. M., Khera, A. V., Nelson, C. P., Wolfe, M. L., DerOhannessian, S. L., Keating, B. J., Qu, L., He, J., Tobin, M. D., Tomaszewski, M., Baumert, J., Klopp, N., Döring, A., Thorand, B., Li, M., Reilly, M. P., Koenig, W., Samani, N. J. and Rader, D. J. (2011). Dense genotyping of candidate gene loci identifies variants associated with high-density lipoprotein cholesterol. Circ. Cardiovasc. Genet. 4 145–155.
  • Kuo, C.-L. and Feingold, E. (2010). What’s the best statistic for a simple test of genetic association in a case-control study? Genet. Epidemiol. 34 246–253.
  • Lee, S., Emond, M. J., Bamshad, M. J., Barnes, K. C., Rieder, M. J., Nickerson, D. A., NHLBI GO Exome Sequencing Project—ESP Lung Project Team, Christiani, D. C., Wurfel, M. M. and Lin, X. (2012). Optimal unified approach for rare-variant association testing with application to small-sample case-control whole-exome sequencing studies. Am. J. Hum. Genet. 91 224–237.
  • Li, B. and Leal, S. M. (2008). Methods for detecting associations with rare variants for common diseases: Application to analysis of sequence data. Am. J. Hum. Genet. 83 311–321.
  • Neuhaus, J. M. (1998). Estimation efficiency with omitted covariates in generalized linear models. J. Amer. Statist. Assoc. 93 1124–1129.
  • Neuhaus, J. M. and Jewell, N. P. (1993). A geometric approach to assess bias due to omitted covariates in generalized linear models. Biometrika 80 807–815.
  • Owen, A. B. (1988). Empirical likelihood ratio confidence intervals for a single functional. Biometrika 75 237–249.
  • Owen, A. (1990). Empirical likelihood ratio confidence regions. Ann. Statist. 18 90–120.
  • Pirinen, M., Donnelly, P. and Spencer, C. C. (2012). Including known covariates can reduce power to detect genetic effects in case-control studies. Nat. Genet. 44 848–851.
  • Qin, J. and Lawless, J. (1994). Empirical likelihood and general estimating equations. Ann. Statist. 22 300–325.
  • Qin, J., Zhang, H., Li, P., Albanes, D. and Yu, K. (2015). Using covariate-specific disease prevalence information to increase the power of case-control studies. Biometrika 102 169–180.
  • Stringer, S., Wray, N. R., Kahn, R. S. and Derks, E. M. (2011). Underestimated effect sizes in GWAS: Fundamental limitations of single SNP analysis for dichotomous phenotypes. PLoS ONE 6 e27964.
  • Sun, J., Zheng, Y. and Hsu, L. (2013). A unified mixed-effects model for rare-variant association in sequencing studies. Genet. Epidemiol. 37 334–344.
  • Wu, M. C., Lee, S., Cai, T., Li, Y., Boehnke, M. et al. (2001). Rare variant association testing for sequencing data using the sequence kernel association test (SKAT). Am. J. Hum. Genet. 891 82–93.
  • Zaitlen, N., Paşaniuc, B., Patterson, N., Pollack, S., Voight, B., Groop, L., Altshuler, D., Henderson, B. E., Kolonel, L. N., Le Marchand, L., Waters, K., Haiman, C. A., Stranger, B. E., Dermitzakis, E. T., Kraft, P. and Price, A. L. (2012a). Analysis of case-control association studies with known risk variants. Bioinformatics 28 1729–1737.
  • Zaitlen, N., Lindström, S., Pasaniuc, B., Cornelis, M., Genovese, G., Pollack, S., Barton, A., Bickeböller, H., Bowden, D. W., Eyre, S., Freedman, B. I., Friedman, D. J., Field, J. K., Groop, L., Haugen, A., Heinrich, J., Henderson, B. E., Hicks, P. J., Hocking, L. J., Kolonel, L. N., Landi, M. T., Langefeld, C. D., Le Marchand, L., Meister, M., Morgan, A. W., Raji, O. Y., Risch, A., Rosenberger, A., Scherf, D., Steer, S., Walshaw, M., Waters, K. M., Wilson, A. G., Wordsworth, P., Zienolddiny, S., Tchetgen, E. T., Haiman, C., Hunter, D. J., Plenge, R. M., Worthington, J., Christiani, D. C., Schaumberg, D. A., Chasman, D. I., Altshuler, D., Voight, B., Kraft, P., Patterson, N. and Price, A. L. (2012b). Informed conditioning on clinical covariates increases power in case-control association studies. PLoS Genet. 8 e1003032.
  • Zhang, M., Tsiatis, A. A. and Davidian, M. (2008). Improving efficiency of inferences in randomized clinical trials using auxiliary covariates. Biometrics 64 707–715.
  • Zhang, H., Chatterjee, N., Rader, D. and Chen, J. (2018). Supplement to “Adjustment of nonconfounding covariates in case-control genetic association studies.” DOI:10.1214/17-AOAS1065SUPP.

Supplemental materials

  • Appendix. Proof of Theorems 1–2 and equations (2.13) and (2.14), Figures S1–S7, and Tables S1–S10.