Nathan Mantel

Bio: Nathan Mantel is an academic researcher from George Washington University. The author has contributed to research in topics: Population & Contingency table. The author has an hindex of 50, co-authored 190 publications receiving 42274 citations. Previous affiliations of Nathan Mantel include National Institutes of Health & Harvard University.

Statistical Aspects of the Analysis of Data From Retrospective Studies of Disease

Abstract: The role and limitations of retrospective investigations of factors possibly associated with the occurrence of a disease are discussed and their relationship to forward-type studies emphasized. Examples of situations in which misleading associations could arise through the use of inappropriate control groups are presented. The possibility of misleading associations may be minimized by controlling or matching on factors which could produce such associations; the statistical analysis will then be modified. Statistical methodology is presented for analyzing retrospective study data, including chi-square measures of statistical significance of the observed association between the disease and the factor under study, and measures for interpreting the association in terms of an increased relative risk of disease. An extension of the chi-square test to the situation where data are subclassified by factors controlled in the analysis is given. A summary relative risk formula, R, is presented and discussed in connection with the problem of weighting the individual subcategory relative risks according to their importance or their precision. Alternative relative-risk formulas, R I , R2, Ra, and R4/ which require the calculation of subcategory-adjusted proportions ot the study factor among diseased persons and controls for the computation of relative risks, are discussed. While these latter formulas may be useful in many instances, they may be biased or inconsistent and are not, in fact, overages of the relative risks observed in the separate subcategories. Only the relative-risk formula, R, of those presented, can be viewed as such an average. The relationship of the matched-sample method to the subclassification approach is indicated. The statistical methodolo~y presented is illustrated with examples from a study of women with epidermoid and undifferentiated pulmonary ccrclnomc.e-J. Nat. Cancer Inst, 22: 719748, 1959.

The Detection of Disease Clustering and a Generalized Regression Approach

Abstract: The problem of identifying subtle time-space clustering of disease, as may be occurring in leukemia, is described and reviewed. Published approaches, generally associated with studies of leukemia, not dependent on knowledge of the underlying population for their validity, are directed towards identifying clustering by establishing a relationship between the temporal and the spatial separations for the n ( n - 1)/2 possible pairs which can be formed from the n observed cases of disease. Here it is proposed that statistical power can be improved by applying a reciprocal transform to these separations. While a permutational approach can give valid probability levels for any observed association, for reasons of practicability, it is suggested that the observed association be tested relative to its permutational variance. Formulas and computational procedures for doing so are given. While the distance measures between points represent symmetric relationships subject to mathematical and geometric regularities, the variance formula developed is appropriate for arbitrary relationships. Simplified procedures are given for the case of symmetric and skew-symmetric relationships. The general procedure is indicated as being potentially useful in other situations as, for example, the study of interpersonal relationships. Viewing the procedure as a regression approach, the possibility for extending it to nonlinear and multivariate situations is suggested. Other aspects of the problem and of the procedure developed are discussed. Similarly, pure temporal clustering can be identified by a study of incidence rates in periods of widespread epidemics. In point of fact, many epidemics of communicable diseases are somewhat local in nature and so these do actually constitute temporal-spatial clusters. For leukemia and similar diseases in which cases seem to arise substantially at random rather than as clear-cut epidemics, it is necessary to devise sensitive and efficient procedures for detecting any nonrandom component of disease occurrence. Various ingenious procedures which statisticians have developed for the detection of disease clustering are reviewed here. These procedures can be generalized so as to increase their statistical validity and efficiency. The technic to be given below for imparting statistical validity to the procedures already in vogue can be viewed as a generalized form of regression with possible useful application to problems arising in quite different contexts.

Chi-Square Tests with One Degree of Freedom; Extensions of the Mantel-Haenszel Procedure

Abstract: A published method for analyzing multiple 2×2 contingency tables arising in retrospective studies of disease is extended in application and form. Extensions of application include comparisons of age-adjusted death rates, life-table analyses, comparisons of two sets of quantal dosage-response data, and miscellaneous laboratory applications as appropriate. Extensions in form involve considering multiple contingency tables with arbitrarily many rows and/or columns, where rows and columns are orderable, and may even be on a continuous scale. The assignment of some score for each row or column is essential to use of the method. With scores assigned, a deviation of the sum of cross products from expectation, and its variance conditioned on all marginal totals, are computed for each table and a chi square is determined corresponding to the grand total of the deviations. For various specific instances and for various scoring procedures, the procedure extends or is equivalent to the asymptotic form of man...

Evaluation of Response-Time Data Involving Transient States: An Illustration Using Heart-Transplant Data

Abstract: The problem considered is how to compare time-to-response data for different groups when the group membership of an individual can be arbitrarily varied during a study. Modified life tables can be constructed which reflect such changes in an individual's status, and associated measures of relative risk and statistical significance calculated. This is illustrated with survival data for heart-transplant patients, for which a patient can transfer from the nontransplanted to the transplanted group. Alternative procedures are given in which distinctive groups are defined for each transplant day.

Regression Models and Life-Tables

Abstract: The analysis of censored failure times is considered. It is assumed that on each individual arc available values of one or more explanatory variables. The hazard function (age-specific failure rate) is taken to be a function of the explanatory variables and unknown regression coefficients multiplied by an arbitrary and unknown function of time. A conditional likelihood is obtained, leading to inferences about the unknown regression coefficients. Some generalizations are outlined.

Cochrane Handbook for Systematic Reviews of Interventions

Abstract: The Cochrane Handbook for Systematic Reviews of Interventions is the official document that describes in detail the process of preparing and maintaining Cochrane systematic reviews on the effects of healthcare interventions.

Statistical Aspects of the Analysis of Data From Retrospective Studies of Disease

Abstract: The role and limitations of retrospective investigations of factors possibly associated with the occurrence of a disease are discussed and their relationship to forward-type studies emphasized. Examples of situations in which misleading associations could arise through the use of inappropriate control groups are presented. The possibility of misleading associations may be minimized by controlling or matching on factors which could produce such associations; the statistical analysis will then be modified. Statistical methodology is presented for analyzing retrospective study data, including chi-square measures of statistical significance of the observed association between the disease and the factor under study, and measures for interpreting the association in terms of an increased relative risk of disease. An extension of the chi-square test to the situation where data are subclassified by factors controlled in the analysis is given. A summary relative risk formula, R, is presented and discussed in connection with the problem of weighting the individual subcategory relative risks according to their importance or their precision. Alternative relative-risk formulas, R I , R2, Ra, and R4/ which require the calculation of subcategory-adjusted proportions ot the study factor among diseased persons and controls for the computation of relative risks, are discussed. While these latter formulas may be useful in many instances, they may be biased or inconsistent and are not, in fact, overages of the relative risks observed in the separate subcategories. Only the relative-risk formula, R, of those presented, can be viewed as such an average. The relationship of the matched-sample method to the subclassification approach is indicated. The statistical methodolo~y presented is illustrated with examples from a study of women with epidermoid and undifferentiated pulmonary ccrclnomc.e-J. Nat. Cancer Inst, 22: 719748, 1959.