William Allan Award Address: On the Role and Soul of a Statistical Geneticist

Main Text

The Allan Award is truly the culmination of my long career in human genetics. I am grateful to the American Society of Human Genetics and to the award committee for bestowing this honor on me, with previous recipients including such well-known scientists as Newton Morton, Arno Motulsky, and Robert Elston. It also feels good to be among my many friends in human genetics and to celebrate this award with them.

In this brief outline of my career, I would like to begin with my student years and then highlight major results in my research (the “role” part), concluding with my current work in China and some thoughts on genetic versus environmental determinants of disease. In addition to discussing research work, I will point out the importance of good mentoring (the “soul” part). When I entered the University of Zürich at the age of 20, I was unsure what to study. I always liked mathematics but also many other things, including playing piano in a jazz band. Eventually, I decided on zoology as I wanted to know more about “life.” After several years of field work on the cytogenetics of the common shrew, finishing up with my PhD degree,¹ I entered the scientific computing center of a pharmaceutical company in Basel, J.R. Geigy, now Novartis. However, I was not satisfied with applying statistical tests like recipes from a cookbook and went to the University of Washington to embark on an MS program in biomathematics designed for graduates holding a higher degree. Upon completion of my MS degree with a thesis on classification procedures,² rather than returning to Basel as originally planned, I stayed on at the UW as a postdoc in Arno Motulsky's Division of Medical Genetics.

Linkage Analysis

My first task was to develop an approach for genetic linkage analysis in large family pedigrees. Researchers around Dr. Motulsky, including Dr. Joseph Goldstein, had collected a multigenerational kindred, the Alaska pedigree, segregating familial hypercholesterolemia and had shown convincing evidence for a monogenic mode of inheritance.³ However, despite various attempts, nobody had been able to find evidence for linkage to any of the several dozen markers then known. Fortunately, the Elston-Stewart algorithm had just been published showing how to calculate likelihoods for genetic loci in large pedigrees,⁴ and Dr. Joseph Felsenstein pointed out to me that this could be the basis for a linkage program. A year of planning and programming in Fortran IV later, the LIPED program was born.⁵ I am proud to say that it contained only one minor error, which was caught by Dr. Robert Elston: the denominator in the normal density for quantitative traits was off by a factor of two.

Application of the LIPED program to the Alaska pedigree demonstrated weak evidence for linkage to the C3 polymorphism,⁶ which was later confirmed independently.^7,8 The gene responsible for this form of hypercholesterolemia turned out to be the LDL receptor; in 1985 Drs. Joseph Goldstein and Michael Brown received the Nobel prize for their research on the LDL receptor.

The LIPED program proved to be an instant success because it was the only freely available software for linkage analysis in large pedigrees. LIPED formed the basis for many successful linkage analyses of well-known traits^9–12 and was used as late as 1995,¹³ 20 years after its publication.

I owe much of my early success to Joseph Felsenstein for the many discussions we had on the historical background of statistical genetics. Also, Arno Motulsky was an excellent mentor. Early on he sent me to meetings and gave me much freedom to pursue my interests. He also allowed me to hire a programmer, Bob Cottingham, who contributed much to our work in Seattle and later in Paris.¹⁴ It was partly because of my experience with Arno Motulsky that I have a strong desire to give to my own students what I had received so graciously myself. Much later, I was interviewed on my experiences with mentors and on my own role as a mentor. Several such interviews were incorporated in a book on mentoring,¹⁵ in which Arno Motulsky is broadly featured as a model mentor.

Zürich City Statistics Office

In the late 1970s, linkage analysis appeared to be losing some of its importance due to the upcoming methods of radiation hybrid mapping. For this and personal reasons, in 1979 I accepted a civil service position as the associate director of the Statistisches Amt der Stadt Zürich. Although this must have been a dream job for many people, I sorely missed science. Fortunately, I had enough free time to collaborate with science colleagues and to write the first edition of my textbook.¹⁶

A collaboration with colleagues at the University of Basel involved two sets of families, 194 families previously collected for screening for CF mutations and genetic counseling, and 1005 families with HLA typing for bone marrow transplantation. We used this dataset to estimate the rate of nonpaternity in these families, which posed interesting statistical problems.¹⁷ In the 1607 children investigated, the observed exclusion rate turned out to be 0.7%, considerably lower than in many other countries¹⁸ and evidently lower than in previous centuries.¹⁹ The underlying, true nonpaternity rate in Switzerland was estimated as 0.8%.

Colleagues urged me to extend the LIPED program to multi-point analysis, but I knew of such efforts being undertaken by Dr. Mark Lathrop, although he was at the time only planning to develop a program for marker loci without regard to disease traits. I convinced him to develop a general linkage program, and this resulted in the LINKAGE suite of programs^20,21 still in use today. I fondly remember many weekends in Paris collaborating and discussing with Drs. Lathrop, Jean-Marc Lalouel, Florence Demenais, and Jayanti Chotai.²²

Transition to Association Analysis

After I started working at Columbia University in 1986, Joseph Terwilliger became my first student. We carried out much fruitful work together. One of the highlights was the development of the haplotype-based haplotype relative risk (HRR) approach,²³ an extension of the HRR method that had introduced family-based controls as opposed to population controls.²⁴ Our extension was based on my theoretical analysis²⁵ showing that the HRR statistic is different from its null value only in the presence of linkage (recombination fraction less than 50%) and association (linkage disequilibrium different from zero). This analysis was also the basis for the TDT, introduced 1993 by Spielman, McGinnis, and Ewens.²⁶ While the TDT is a test for linkage in the presence of association, a more general approach is to combine linkage and association analysis for increased power; our analysis of intervertebral disc disease²⁷ may be viewed as a forerunner of more modern forms of combined linkage and association analysis.²⁸

In analyses involving relatives, stated relationships sometimes have to be taken with a grain of salt; for example, stated siblings may in reality be half-sibs. One of my Columbia students, Harald Goring, developed an approach to estimate relationships from genetic marker data²⁹ and implemented it in a computer program, RELATIVE.

Early on, I [was] interested in the question of how to handle genotyping errors. In my Columbia time, I proposed ways to incorporate error rates into linkage analysis by allowing for small probabilities that observed (apparent) genotypes are different from underlying (true) genotypes.³⁰ Several years later, regenotyping of a small number of marker loci allowed us to estimate error rates and to demonstrate dramatic effects of removing erroneous genotypes:³¹ LOD scores tend to increase, and map distances (recombination rates) between loci will become smaller.³²

After my move to Rockefeller University in 1996, I continued investigating effects of errors, now more with respect to association analysis and family-based association analysis. An important observation was that random errors inflate the type 1 error (rate of false positive results) of the TDT,³³ while as is well-known, errors in linkage analysis reduce power but do not increase the type 1 error. In the TDT, this bias is particularly disturbing because with SNP data, only roughly one-third of errors can be detected as Mendelian inconsistencies in trio families.³⁴ This work, spearheaded by Derek Gordon, culminated in the development of a very general kind of TDT, TDTae,³⁵ and in its implementation in a computer program. It estimates error probabilities based on one of several error models and treats these estimates as nuisance parameters in a likelihood ratio test.

Another focal point of our work has been to investigate methods assessing the simultaneous disease association of multiple SNPs. There are two aspects to this task: (1) to select a set of SNPs and then (2) to assess their association with disease. One of the first papers to propose a two-stage procedure incorporating these two steps³⁶ used a computer-based nested bootstrap technique.^37,38 Unfortunately, it did not receive the attention it deserved. Our development of sum statistics, however, proved to be very fruitful. Briefly, we select a number m of SNPs (for example, m = 20) based on a given single-locus test statistic like the chi-square allele test with 1 df. Then, SNPs are ordered based on the sizes of their test statistics, and successive sums of the SNP-based test statistics are formed; for example, the third sum refers to the sum of the three largest test statistics for three SNPs wherever they occur in the genome. The significance level associated with each sum is assessed in randomization samples (labels case and control are randomly permuted); such a sum is an approximation to a multivariate test statistic.³⁹ The smallest among all m p values is then taken as our genome-wide test statistic, whose significance level is estimated based on the randomization samples already generated.⁴⁰ This approach has independently been shown to be more powerful than SNP-by-SNP analysis^41–44 and has been used successfully in various investigations.^45–50 Requiring that SNPs be contiguous, sum statistics leads to what is known as scan statistics, which may be viewed as genotype-based analogs to haplotype analysis.⁵¹ Scan statistics are ideally suited to investigate, for example, long stretches of homozygosity in an unbiased manner.⁵²

Last, but not least, I should mention Josephine Hoh's investigation of age-related macular degeneration (AMD), the first chip-based genome-wide association analysis. Against all odds, it resulted in a spectacular success.^53,54

Working in China

In a book recently published on the internet (see Web Resources), one of the chapters is highly critical of Chinese universities and other institutions of higher learning and points out that they “are in dire need of fundamental reform, a fact that has been emphasized by China's political and cultural leaders, from Premier Wen Jiabao to the nationally-revered and recently deceased scientist Qian Xuesen, both of whom have been sharply critical of the system's emphasis on rote learning and intellectual uniformity, at the expense of creativity, innovation, and discovery.” Similar views have recently been expressed by two leading researchers in Beijing who wrote that “to obtain major grants in China, it is an open secret that doing good research is not as important as schmoozing with powerful beaurocrats and their favorite reviewers”⁵⁵. The most satisfying and fruitful aspect of my work in Beijing has been working with my graduate students and undergraduate summer interns. We have carried out several interesting pieces of research, for example, estimating whether genotype pattern (diplotype) frequencies are different in cases and controls,⁵⁶ and other methods developments^57,58 and data analyses.^50,59,60 To support a healthy development of science research in China, it seems most promising to pin our hopes on current and upcoming students and to be good role models for them.

Genetics and Environment

There are well-known examples of traits that are almost entirely due to environment and others that are mostly genetically determined. For common complex traits, environmental effects are often much stronger than genetic effects. For example, an “important [genetic] determinant of obesity” has a pooled odds ratio of 1.2,⁶¹ while low education as a risk factor has an odds ratio of 3.8.⁶² Also, the strong association between the APOE gene and Alzheimer Disease (AD) is well known, but individuals who eat fish at least once a week have a 60% lower risk for developing AD.⁶³ It has been noted that approximately 80% of coronary heart disease and 90% of type 2 diabetes are potentially preventable by life-style modifications.⁶⁴ One might say that genetic research is likely to uncover additional genetic risk factors that are not yet known. However, in a large international study with approximately 15,000 cases and controls each, potentially preventable risk factors for heart disease were evaluated.⁶⁵ It was estimated that 90% of all heart disease cases (population attributable risk) are due to one or more of the risk factors listed in Table 1; clearly, there is not much room for genetic effects, although some of the risk factors in Table 1 have a genetic component. It must have been for these and similar reasons that a proposal was made to base funding of genetics research on its potential impact on public health.⁶⁶ While I cherish genetic research and would not want to miss it, we should not forget that to really have an impact on public health, one needs to preferentially act on nongenetic determinants of disease.

Table 1.

Potentially Modifiable Risk Factors for Myocardial Infarction

Risk Factor	Odds ratio
Smoking	2.59
Diabetes	3.08
Hypertension	2.48
Abdominal obesity	1.75
Psychosocial	2.51
Exercise	0.72
Alcohol intake	0.79
ApoB/ApoA1	2.36

Based on Yusuf et al.⁶⁵ but modified and simplified.

Web Resources

The URL for data presented herein is as follow:

• China The Way Forward, http://www.hkbu.edu.hk/∼iibd/WTCABook/