The Impact of Nathan Mantel's “The Detection of Disease Clustering and a Generalized Regression Approach”
Authors: Michelle Wynn, Kelley M. Kidwell, Sofia D. Merajver
Journal: Cancer Research (2016)

Visit the Cancer Research 75th Anniversary timeline.See related article by Mantel, Cancer Res 1967;27:209–20.World War II was raging in Europe and it would be 11 months until the United States entered the war, when Cancer Research published its first issue in January 1941. As we celebrate the 75th Anniversary of Cancer Research, we pause to admire the authors of those volume issues who were conducting their research amidst one the of the most devastating armed and genocidal conflicts in human history; we are also gratified to contemplate the enduring role of science in human development, persevering in the face of profound aggression and impending tragedy. The author of the paper we honor in this article, Nathan Mantel, served in the U.S. Army between 1942 and 46 before he was recruited to the NCI as a biostatistician.Our task is to evaluate a landmark article by Nathan Mantel (1) published in 1967 that outlined a methodologic breakthrough to evaluate whether disease occurrences were related to exposures by their spatiotemporal pattern of clusters. During the previous three decades, there had been keen interest in discerning which environmental exposures might be responsible for the increasing incidence of cancers such as hematologic cancers, hepatocellular carcinoma, bladder, and breast cancer. This is a problem that captured the attention of the world following the Chernobyl nuclear accident and domestically in the United States through the popular accounts of famous cancer clusters associated with industrial waste in Woburn, MA and Toms River, NJ, both told in depth of detail and insight in two nonfiction books (2, 3). The methodology employed to discern whether these well-known cases and many other instances of suspected environmental contamination are true clusters, is based largely on Mantel's 1967 Cancer Research article.The standard methodology to evaluate spatial and temporal clusters prior to Mantel's article consisted mainly of measuring the distances between all possible pairs of observations, a method termed the permutational approach. A major advantage of this method was that it did not require any specific knowledge of the natural history of the disease or the geographical area characteristics. Furthermore, this methodology was easy to apply to a delineated spatial region over a well-defined time period, such as 2 years, as was typically done for cases of cancer. Because of the large variability of disease and populations, Mantel posed that the statistical power of cluster analyses would be improved by imposing a reciprocal transform to the distances between cases, without imposing any specific underlying relationship, such as linearity. That was the methodologic context in which the article we are considering here was published.In the original article, Mantel used leukemia as an example of a disease with an unknown etiology for which a statistical test for determining whether the disease was occurring in temporal-spatial clusters was needed. In the article, Mantel produced a Z statistic from the product of two difference matrices, where one matrix represented the spatial differences between measurements and the other matrix represented the differences in some other variable of interest (such as time in the case of disease epidemiology or plant size in ecology). Today, the Mantel test is most commonly used in a standard normal form to produce an r statistic (4). The simple Mantel test can also be used to check the goodness-of-fit of data to a model, a test that is only valid if the data in each computed difference matrix are obtained independently from one another. The partial Mantel test is an extension of the original test to include a third variable.To understand the broad applicability of the method as well as its limitations, it is relevant to summarize the main assumptions and characteristics of Mantel method in the 1967 Cancer Research article. Mantel's method for detecting the clustering of disease in time and space has been used in diverse scientific disciplines, such as evolutionary biology, epidemiology of infections and neoplasms, population and landscape genetics, due to its simplicity and lack of reliance on the type of data analyzed (e.g., continuous, categorical, rank) and parametric assumptions. Beyond the vast application of his methods, Mantel and his predecessors who described similar methods: Fraumeni and Ederer (5), Myers, and Knox (6), together sparked the creation of statistical theories that extend and tackle shortcomings of his simple test. The simple Mantel test has been extended to address the often violated assumptions of linearity and homoscedasticity between matrixes, which have led to many commentaries on the method's potential for low power and high type I error, particularly in spatial analysis in biology, outside of its original application in epidemiologic studies (7, 8). The limitations notwithstanding, the Mantel method of 1967 has been widely used in multiple disciplines, as exemplified below.Hutchinson and Templeton described a model for studying the influence of gene flow and drift on the distribution of genetic variability (9). They pointed out that many attempts to link the fixation index (FST), which is a fundamental statistic used in population genetics, to gene flow and drift were flawed because natural sets of populations will not necessarily be at equilibrium. Scatterplots of FST versus geographic distances of data collected from eastern collard lizards were generated and a Mantel test was used to test the null hypothesis that the degree of scatter increased with geographic distance within a specific subregion. Specifically, the authors applied the Mantel test to the residual matrix following linear regression of FST values and the calculated geography distance matrix. They found that differences in regional collard lizard history with respect to duration of occupancy as well as the extent and duration of forestation resulted in very different regional population structures in four distinct geographical regions studied. The Hutchinson and Templeton article is a well-regarded and highly cited article in population genetics. It has been cited nearly 900 times since 1999 and applied to a variety of fields including the biogeography of microorganisms.The Mantel test has also been applied to questions pertaining to the origin and dispersal of modern humans. Two primary theories of human origin exist: the single origin model and the multiregional continuity model. To test each of these theories, Waddle applied the Mantel test to evaluate the correlation between a morphologic distance matrix derived from 83 cranial fossils divided into 12 operational taxonomic units and a distance matrix representing either the single origin model or the multiregional continuity model (10). Her analysis found that the single origin model produced a stronger and more significant positive correlation to the cranial variation observed in the fossil evidence than the multiregional continuity model. While the study clearly provided evidence in support of the single origin theory, it was not able to definitively distinguish a site origin from the fossil evidence analyzed and this is an area of active investigation still.Dr. Nathan Mantel had an illustrious career at the NIH, where he interacted broadly with researchers in basic science and epidemiology, a science that he helped modernize. His colleagues at the NCI remember him as a creative, congenial, and energetic collaborator who fostered at the NIH the current style of multidisciplinary research in biology. His article is an example of the balance between clarity and detail. It is accessible both to those interested in the mathematical details as well as to those who want to understand the general usefulness of the method. It stands as a major paradigm and indeed anticipates by several decades the current discipline of mathematical oncology that is also the newest thematic section of Cancer Research. The work of Nathan Mantel helped us understand many phenomena in science and medicine and we are proud that a major contribution represented by the 1967 Cancer Research article remains so relevant and useful today—a worthy standard to emulate.No potential conflicts of interest were disclosed.Conception and design: S.D. MerajverDevelopment of methodology: M. WynnWriting, review, and/or revision of the manuscript: M. Wynn, K.M. Kidwell, S.D. MerajverAdministrative, technical, or material support (i.e., reporting or organizing data, constructing databases): S.D. MerajverOther (historical perspective): S.D. MerajverThis work was supported in part by the Breast Cancer Research Foundation (S.D. Merajver, M.Wynn) and the Breast Oncology Program (K.M. Kidwell) of the University of Michigan Comprehensive Cancer Center. Cancer Center Support Grant: 5 P30 CA46592.