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We introduce a statistical protocol for analyzing spatially varying data, including putative explanatory variables. The procedures comprise preliminary spatial autocorrelation analysis (from an earlier study), path analysis, clustering of the resulting set of path diagrams, ordination of these diagrams, and confirmatory tests against extrinsic information. To illustrate the application of these methods, we present incidence and mortality rates of 31 organ- and sex-specific cancers in Europe; these rates vary markedly with geography and type of cancer. Additionally, we investigated three factors (ethnohistory, genetics, and geography) putatively affecting these rates. The five variables were correlated separately for the 31 cancers over European reporting stations. We analyzed the correlations by path analysis, k-means clustering, and nonmetric multidimensional scaling; coefficients of the 31 path diagrams modeling the correlations vary substantially. To simplify interpretation, we grouped the diagrams into five clusters, for which we describe the differential effects of the three putative causes on incidence and mortality. When scaled, the path coefficients intergrade without marked gaps between clusters. Ethnic differences make for differences in cancer rates, even when the populations tested are ancient and complex mixtures. Path analysis usefully decomposes a structural model involving effects and putative causes, and estimates the magnitude of the model's components. Smooth intergradation of the path coefficients suggests the putative causes are the results of multiple forces. Despite this continuity of the path diagrams of the 31 cancers, clustering offers a useful segmentation of the continuum. Etiological and other extrinsic information on the cancers map significantly into the five clusters, demonstrating their epidemiological relevance., (Copyright 2003 Wiley-Liss, Inc.)

The Supplemental Therapeutic Oxygen for Prethreshold Retinopathy of Prematurity trial used the group-sequential alpha-spending approach with asymmetrical tails to investigate whether supplemental oxygen therapy would reduce the proportion of infants progressing from prethreshold retinopathy of prematurity (ROP) to threshold ROP from 30% to 20%. Three years of enrollment were predicted. After 4 years, the data and safety monitoring committee (DSMC), faced with a projected delay of 2-3 more years, opted to terminate the trial after 1 further year of enrollment despite a continually borderline test statistic. We discuss factors relating to the DSMC decision and its effect upon the conclusions that may be drawn from the trial.

We have previously shown that geographic differences in cancer mortalities in Europe are related to (in order of importance): geographic distances (reflecting environmental differences), ethnohistoric distances (encompassing cultural and genetic attributes), and genetic distances of the populations in the areas studied. In this study, we analyzed the relations of the same three factors to European incidences of 45 male and 47 female cancers. Differences in cancer incidences are correlated moderately, first with geographic distances, and then with genetic distances, but not at all with ethnohistoric distances. Comparing these findings to the earlier ones for cancer mortalities, we note the reversal in the importance of ethnohistory and genetics, and the generally lower correlations of incidence differences with the three putatively causal distance matrices. A path diagram combining both studies demonstrates the lack of cultural carcinogenic effects, but suggests cultural influences on procedures such as the registration of deaths in different political entities. Additionally, the relatively large correlation between ethnohistoric distances and mortality differences is caused by common factors behind the correlation of ethnohistoric and geographic distances. Geographic proximity results in similar ethnohistories. The direct effects of genetic distances are negligible and only their common effects with geographic distances play a role, accounting for the weak to negligible influence of genetics on incidence and mortality differences. Apparently, the genetic systems available to us do not substantially affect cancer incidence or mortality. We present indirect evidence that international differences in the quality of cancer rate data are greater in mortalities than in incidences.

Synthetic maps of human gene frequencies, which are maps of principal component scores based on correlation of interpolated surfaces, have been popularized widely by L. Cavalli-Sforza, P. Menozzi, and A. Piazza. Such maps are used to make ethnohistorical inferences or to support various demographic or historical hypotheses. We show from first principles and by analyses of real and simulated data that synthetic maps are subject to large errors and that apparent geographic trends may be detected in spatially random data. We conclude that results featured as synthetic maps should be approached with considerable caution.

We applied the techniques of spatial autocorrelation (SA) analysis to 40 cancer mortality distributions in Western Europe. One of the aims of these methods is to describe the scale over which spatial patterns of mortalities occur, which may provide suggestions concerning the agents bringing about the patterns. We analyzed 355 registration areas, applying one- and two-dimensional SA as well as local SA techniques. We find that cancer mortalities are unusually strongly spatially structured, implying similar spatial structuring of the responsible agents. The small number of spatial patterns (4 or 5) in the 40 cancer mortalities suggests there are fewer spatially patterned agents than the number of cancers studied. SA present in variables will bias the results of conventional statistical tests applied to them. After correcting for such bias, some pairwise correlations of cancer mortality distributions remain significant, suggesting inherent, epidemiologically meaningful correlations. Local SA is a useful technique for exploring epidemiological maps. It found homogeneous high overall cancer mortalities in Denmark and homogeneous low mortalities in southern Italy, as well as a very heterogeneous pattern for ovarian cancer in Ireland.

We developed a Dry Eye Screening Questionnaire for the Dry Eye Epidemiology Projects (DEEP), a proposed large epidemiologic study. All persons who screen positive and a small sample of those who screen negative are to be invited for a diagnostic examination. Containing 19 questions, of which only 14 were used in the analysis, the questionnaire takes only a few minutes to administer on the telephone. To construct a discriminator function and thus a ROC curve, we used stepwise multiple regression on screening responses from a clinic series of 77 cases and 79 controls. Stepwise regression may incorporate into the predictor equation variables whose relation to the predicted is only accidental. Further, misclassification rates are underestimated by the resubstitution method, in which the proportion misclassified is obtained from the same dataset in which the discriminator function was fitted. To counter these problems, we randomly divided the data in half. We chose as predictors only those variables (Dry and Irritated) selected by stepwise regression in both data halves. We estimated unbiased misclassification rates using the unbiased test set method, in which the discriminator is fitted in one data half, and misclassification rates are calculated in the other half. Comparison of ROC curves arising from resubstitution and test set estimates indicates that resubstitution bias in misclassification rate estimation is negligible in our data. A resubstitution estimate made on the entire data is thus preferred. The resulting sensitivity/specificity values are reasonably high (e.g., 60%/94%), suggesting that the questionnaire will be a useful screening tool in the DEEP study. A second discriminator using the sum of all 14 responses is similar in its misclassification characteristics to the first discriminator. A second potentially significant error, arising from applying results from a clinical series to a general population, will be investigated as survey results in DEEP become available.

Geographic variation in cancer rates is thought to be the result of two major factors: environmental agents varying spatially and the attributes, genetic or cultural, of the populations inhabiting the areas studied. These attributes in turn result from the history of the populations in question. We had previously constructed an ethnohistorical database for Europe since 2200 B.C., permitting estimates of the ethnic composition of modern European populations. We were able to show that these estimates correlate with genetic distances. In this study, we wanted to see whether they also correlate with cancer rates. We employed two data sets of cancer mortalities from 42 types of cancer for the European Economic Community and for Central Europe. We subjected spatial differences in cancer mortalities, genetic, ethnohistorical, and geographic distances to matrix permutation tests to determine the magnitude and significance of their association. Our findings are that distances in cancer mortalities are correlated more with ethnohistorical distances than with genetic distances. Possibly the cancer rates may be affected by loci other than the genetic systems available to us, and/or by cultural factors mediated by the ethnohistorical differences. We find it remarkable that patterns of frequently ancient ethnic admixture are still reflected in modern cancer mortalities. Partial correlations with geography suggest that local environmental factors affect the mortalities as well.

This paper examines competing theories for cases in which both the data and the hypotheses can be represented as distance matrices. A test due to Dow & Cheverud has been used for such comparisons in anthropology, but when data are spatially, temporally, or phylogenetically autocorrelated, this test may be far too liberal. We examine a classification procedure based on ratios of probabilities obtained from Mantel tests of the competing hypotheses and find that design matrices describing only lag-one connections and those eliminating common connections of competing hypotheses are the most informative. We apply this method to simulated gene-frequency data in a 7 x 7 chessboard representing a stepping-stone model and discriminate between alternative theories with a 7% misclassification rate. We also apply these techniques to the current controversy concerning the origin of anatomically modern humans by testing design matrices representing regional continuity and single African origins. The outcome for lag-one matrices and those showing only unique lag-one differences indicate that the single African origin of anatomically modern humans fits the distance matrix based on 165 characters of 83 fossil crania better than the competing theory. However, we also tested a design matrix describing single origin out of southwest Asia. This design matrix was clearly most similar to the data in all tested cases. These results make the regional-continuity theory a less likely explanation for the observed cranial differences than the two single-origin theories. Of these, single southwest Asian origins seems the more likely interpretation of the data.

Population movements of 891 ethnic units in Europe over the past 4,200 years, and the correlations of these movements with modern genetic distances were investigated on a one-degree-square grid of the continent. There is significant spatial pattern in movements from sources, to targets, and overall. Patterns change significantly over time. Patterns of sources and targets differ significantly. Modern movements are more numerous than ancient movements. Movements on the periphery of Europe are few in number and are concentrated in direction, while Central European movements are numerous and unconcentrated in direction. Modern genetic distance is negatively correlated with the amount of population exchange between localities. Regional genetic variance is positively correlated with number of movements into, but not out of, areas. The findings are interpreted in the context of European ethnohistory and population biology. Am. J. Hum. Biol. 9:391-404, 1997. © 1997 Wiley-Liss, Inc., (Copyright © 1997 Wiley-Liss, Inc.)

We have newly constructed an ethnohistorical database consisting of 3460 records of ethnic locations and movements in Europe since 2200 B.C. Using this database, we computed vectors of proportions that peoples speaking various language families contributed to the gene pools of 2216 1 degree x 1 degree land-based quadrats of Europe. From these vectors we computed ethnohistorical distances as arc distances between all pairs of quadrats. We used these distances as predictors of genetic distances, which we calculated independently from 26 genetic systems. We find significant partial correlations between ethnohistorical and genetic distances when geographic distance, a common causative factor, is held constant. Ethnohistorical distances explain a significant amount of the genetic variation observed in modern populations. These results are highly robust to simulated errors in and omissions from the ethnohistorical database. Randomization tests show that the historical sequence of the movements does not affect estimates of the ethnohistory-genetics correlation, but the geographic locations of movements do. We track the development of the ethnohistory-genetics correlation through time and show it to be gradual and cumulative over the past 4200 years.

Allele frequency distributions were generated by computer simulation of five models of microevolution in European populations. Genetic distances calculated from these distributions were compared with observed genetic distances among Indo-European speakers. The simulated models differ in complexity, but all incorporate random genetic drift and short-range gene flow (isolation by distance). The best correlations between observed and simulated data were obtained for two models where dispersal of Neolithic farmers from the Near East depends only on population growth. More complex models, where the timing of the farmers' expansion is constrained by archaeological time data, fail to account for a larger fraction of the observed genetic variation; this is also the case for a model including late Neolithic migrations from the Pontic steppes. The genetic structure of current populations speaking Indo-European languages seems therefore to largely reflect a Neolithic expansion. This is consistent with the hypothesis of a parallel spread of farming technologies and a proto-Indo-European language in the Neolithic. Allele-frequency gradients among Indo-European speakers may be due either to incomplete admixture between dispersing farmers, who presumably spoke proto-Indo-European, and pre-existing hunters and gatherers (as in the traditional demic diffusion hypothesis), or to founder effects during the farmers' dispersal. By contrast, successive migrational waves from the East, if any, do not seem to have had genetic consequences detectable by the present comparison of observed and simulated allele frequencies.

A variable is measured at two locations separated by a given distance. Are the values more similar to each other if the locations are oriented in one direction than another? This question has application to studies of human genetics, epidemics, and acid rain. One obvious analytic approach, regression on latitude and longitude, fails when data are non-directional (isotropic) but spatially autocorrelated. Moreover, although non-zero slope implies similarity between neighbours, the converse is not true. IDIFF, a statistic derived from Moran's coefficient of spatial autocorrelation, is developed to detect general directional effects that apply to the collection of data points. Simulations suggest that, when data have isotropic spatial autocorrelation but are incorrectly assumed to be independent, IDIFF will at worst reject too little. IDIFF has good power to distinguish epidemics that spread non-directionally from those that spread in a favoured direction.

From 420 records of ethnic locations and movements since 2000 B.C., we computed vectors describing the proportions which peoples of the various European language families contributed to the gene pools within 85 land-based 5 x 5-degree quadrats in Europe. Using these language family vectors, we computed ethnohistorical affinities as arc distances between all pairs of the 85 quadrats. These affinities are significantly correlated with genetic distances based on 26 genetic systems, even when geographic distances, a common causative factor, are held constant. Thus, the ethnohistorical distances explain a significant amount of the genetic variation observed in modern populations. Randomizations of the records by chronology result in loss of significance for the observed partial correlation between genetics and ethnohistory, when geography is held constant. However, a randomization of records by location only results in reduced significance. Thus, while the historical sequence of the movements does not seem to matter in Europe, their geographic locations do. We discuss the implications of these findings.

Two theories of the origins of the Indo-Europeans currently compete. M. Gimbutas believes that early Indo-Europeans entered southeastern Europe from the Pontic Steppes starting ca. 4500 B.C. and spread from there. C. Renfrew equates early Indo-Europeans with early farmers who entered southeastern Europe from Asia Minor ca. 7000 BC and spread through the continent. We tested genetic distance matrices for each of 25 systems in numerous Indo-European-speaking samples from Europe. To match each of these matrices, we created other distance matrices representing geography, language, time since origin of agriculture, Gimbutas' model, and Renfrew's model. The correlation between genetics and language is significant. Geography, when held constant, produces a markedly lower, yet still highly significant partial correlation between genetics and language, showing that more remains to be explained. However, none of the remaining three distances--time since origin of agriculture, Gimbutas' model, or Renfrew's model--reduces the partial correlation further. Thus, neither of the two theories appears able to explain the origin of the Indo-Europeans as gauged by the genetics-language correlation.

A common error in statistical analysis of ophthalmic data is the lack of accounting for the positive correlation generally present between observations made in fellow eyes. The alternative of data analysis from only one eye in each patient may lead to loss of power and unrealistically large confidence intervals. This paper discusses a method to estimate kappa, a measure of agreement between two graders, when both graders rate the same set of pairs of eyes. The method assumes that the true left-eye and right-eye kappa values are equal and makes use of the correlated binocular data to estimate confidence intervals for the common kappa. Simulations show that the new estimators are better than the estimator based on only one eye; new confidence intervals had the correct coverage probability, but were usually only about 70 per cent as wide as single-eye intervals. The general methodology described here applies to analysis of grader agreement in rating other paired body structures.

European agriculture originated in the Near East about 9,000 years ago. The Neolithic reached almost all areas suitable for agriculture by 5,000 yr BP (before present). The routes and times of the spread of agriculture through Europe are relatively well established, but not its manner of spreading. This could have been by cultural diffusion with few genetic consequences. By contrast, Ammerman and Cavalli-Sforza proposed that the spread of farming increased local population densities, causing demic expansion into new territory and diffusive gene flow between the neolithic farmers and mesolithic groups. We have now tested observed genetic patterns against expectations derived from the demic expansion hypothesis. We found significant partial correlations of genetic distances with a distance matrix especially designed to represent the spread of agriculture on that continent, when geographic distances are held constant. These findings support the hypothesis of Ammerman and Cavalli-Sforza and invite further investigation into Renfrew's hypothesis on the origin of the Indo-European languages.

By means of three different methods we investigated whether 59 allele frequencies and ten cranial variables show increased change at 29 language-family boundaries in Europe. The quadrat-variance method compares variances of map quadrats crossed by language-family boundaries to variances of quadrats that are not crossed. The rate-of-change method examines the directional derivative of surfaces of the variables perpendicular to a language-family boundary and compares these derivatives to the same quantities obtained by randomly placing the language boundaries on the map of Europe. The difference method tests whether these variables differ more across language-family boundaries than across randomly placed boundaries. These special data-analytic techniques had to be developed to avoid the problem of spatial autocorrelation of both language and biological data. All three methods indicate increased genetic change at language-family boundaries. Clearer and more pronounced results are obtained by the first two methods than by the difference method. Thirteen language-family boundaries show significant gene frequency change by at least one of the methods. Changes are more marked in gene frequencies than in cranial variables. Different allele frequencies mark the increased change at different language boundaries. A model, based on the known history of each language-family boundary, was constructed to predict whether given boundaries should exhibit increased genetic change. The model is in good agreement with the observed results.

We investigated whether 59 allele frequencies and 10 cranial variables differed among speakers of the 12 modern language families in Europe. Although this is a classical analysis of variance design, special techniques had to be developed for the analysis because of spatial autocorrelation of both biological and language data. The method examines pooled sums of squares within language families. These are compared with the same quantities obtained by randomly partitioning the available data points in Europe into internally cohesive subsets representing the same sample sizes for each language family as in the originally observed data. Our results suggest that for numerous genetic systems, population samples differ more among language families than they do within families. These findings are considered in relation to two contrasting models: a model of random spatial differentiation of gene frequencies unrelated to language and a model of aboriginal genetic differences among speakers of different language groups. Our observed findings suggest partial validity of both models.

The aims of this study of spatial patterns of human gene frequencies in Europe are twofold. One is to present new methodology developed for the analysis of such data. The other is to report on the diversity of spatial patterns observed in Europe and their interpretation as evidence of population processes. Spatial variation in 59 allele and haplotype frequencies (26 genetic systems) for polymorphisms in blood antigens, enzymes, and proteins is analyzed for an aggregate of 3,384 localities, using homogeneity tests, one-dimensional and directional spatial correlograms, and SYMAP interpolated surfaces. The data matrices are reduced to reveal the principal patterns by clustering techniques. The findings of this study can be summarized as follows: 1) There is significant heterogeneity in allele frequencies among the localities for all but one genetic system. 2) There are significant spatial patterns for most allele frequencies. 3) There is a substantial minority of clinal patterns in these populations. Clinal trends are found more frequently in HLA alleles than for other variables. North-south and northwest-southwest gradients predominate. 4) There is a strong decline in overall genetic similarity with geographic distance for most variables. 5) There are few, if any, appreciable correlations in pairs of allele frequencies over the continent, and there is little interesting correlation structure in the resulting correlation matrix. 6) Few spatial correlograms are markedly similar to each other, yet they form well-defined clusters. Spatial variation patterns, therefore, differ among allele frequencies. Patterns of human gene frequencies in modern Europe are diverse and complex. No single model suffices for interpretation of the observed genetic structure. Some clinal patterns reported here support the Neolithic demic-expansion hypothesis, others suggest latitudinal selection. Most of the clinal patterns are in HLA alleles, but there is also evidence from ABO for east-west migration diffusion. The majority of patterns are patchy, consistent with hypotheses of isolation by distance or of settlement of genetically differing, subsequently expanding ethnic groups. While undoubtedly there has been an ongoing stochastic process of differentiation consistent with the isolation-by-distance model, this has not obscured the directional patterns caused by migration (demic diffusion), and has perhaps only reinforced the contribution from settlement of ethnic units to patterns of genetic variation. However, the impact of the latter is most difficult to discern and requires further methodological developments.