Estimation of Bias in Nongenetic Observational Studies Using ‘‘Mendelian Triangulation’’ LEONELO E. BAUTISTA, MD, MPH, DRPH, LIAM SMEETH, MRCGP, MSC,PHD, AROON D. HINGORANI, FRCP, PHD, AND JUAN P. CASAS, MD PURPOSE: Phenotype–disease odds ratios calculated from the effect of a genotype on its phenotype and on disease risk (‘‘Mendelian triangulation’’) can be used as a standard to assess bias on the corresponding odds ratio from nongenetic studies. Statistical tests are commonly used to compare these odds ratios. We propose a method to estimate the magnitude of the bias and judge the validity of the phenotype–disease association. METHODS: For four published examples, we obtained 10,000 random values from distributions of the odds ratios from both genetic and nongenetic studies. A range of values compatible with an unbiased odds ratio was then calculated from the empirical distribution of the differences between both odds ratios. RESULTS: We show that estimating a range of likely values for an unbiased odds ratio is useful to judge the effect of the phenotype and identify cases for which information from genetic studies adds little to the evaluation of the phenotype–disease association. Conversely, statistical tests could be misleading. CONCLUSIONS: Estimating a range of values for an unbiased odds ratio is more informative and appro- priate than statistical tests when using the Mendelian triangulation approach for assessment of bias in phenotype–disease association studies. Ann Epidemiol 2006;16:675–680. Ó 2006 Elsevier Inc. All rights reserved. KEY WORDS: Mendelian Randomization, Genetics, Observational Epidemiology. INTRODUCTION Observational epidemiologic studies are a useful tool to es- tablish causal associations and have had a considerable im- pact on public health and clinical practice. However, recent discrepancies with results from randomized clinical trials have brought to focus the need for careful design to control bias in observational studies (1). Spurious associations in these studies are frequently the result of uncontrolled con- founders and reverse-causality bias. Assessing the likelihood and magnitude of such biases is complicated because some confounding factors may be unknown or difficult to measure, and ascertaining the starting time for exposure and disease may not be possible. Assuming that the effect of a gene variant on disease is mediated exclusively through its influence on the interme- diate phenotype (IP) of interest, the odds ratio from studies of the effect of the genotype on disease risk (ORgd) and the between-genotype difference in IP (DIP) can be used to cal- culate an unconfounded odds ratio (ORgpd Z ORgd (k/DIP) ) for the effect of k units of the IP on the risk of disease (Fig. 1) (2). The fundamental concept behind this approach is that the inheritance of genetic variants is subject to the random assortment of maternal and paternal alleles at the time of gamete formation, according to Mendel’s second law (3). Because the presence of the genotype is unlikely to be re- lated to other risk factors for the disease, genotype–disease and genotype–IP studies should be largely free of confound- ing. They also should be free of reverse-causality bias be- cause genotype is a hereditary fixed characteristic (2, 4). Therefore, the ORgpd also should be unbiased and could be used as a standard to assess whether odds ratios from non- genetic observational studies of the association between an IP and a disease (ORpd) are biased. If ORgpd and ORpd are of a similar magnitude, this offers support for the validity of results from nongenetic observational studies. However, if ORgpd and ORpd differ to a substantial degree, this suggests that results from nongenetic observational studies may be biased. Although the ORgpd is supposedly unbiased, in some cases, it would not provide a conclusive picture of the phenotype–disease association. This would happen mostly when genetic studies are not large enough to produce a pre- cise estimate of ORgpd. In those cases, the ORgpd still could be used to assess the validity of ORpd and improve our esti- mates of the strength of the phenotype–disease association. From the Department of Population Health Sciences, Medical School, University of Wisconsin, Madison, WI (L.E.B.); Department of Epidemiol- ogy and Population Health, London School of Hygiene and Tropical Med- icine (L.S., J.P.C.); and Centre for Clinical Pharmacology, Department of Medicine, BHF Laboratories at University College London, UK (A.D.H.). Address correspondence to: Leonelo E. Bautista, MD, MPH, DrPH, Uni- versity of Wisconsin, Medical School, Department of Population Health Sciences, 610 Walnut Street, 703 WARF, Madison, WI 53726-2397. Tel.: (608) 265-6176; fax: (608) 263-2820. E-mail: lebautista@wisc.edu. Received September 8, 2005; accepted February 13, 2006. Ó 2006 Elsevier Inc. All rights reserved. 1047-2797/06/$–see front matter 360 Park Avenue South, New York, NY 10010 doi:10.1016/j.annepidem.2006.02.001