No abstract

Clinical investigations often involve data in the form of ordered categories--e.g., "worse," "unchanged," "improved," "much improved." Comparison of two groups when the data are of this kind should not be done by the chi-square test, which wastes information and is insensitive in this context. The Wilcoxon-Mann-Whitney test provides a proper analysis. Alternatively, scores may be assigned to the categories in order, and the t-test applied. We demonstrate both approaches here. Sometimes data in ordered categories are reduced to a two-by-two table by the collapsing of the high categories into one category and the low categories into another. This practice is inefficient; moreover, it entails avoidable subjectivity in the choice of the cutting point that defines the two super-categories. The Wilcoxon-Mann-Whitney procedure (or the t-test with use of ordered scores) is preferable. A survey of research articles in Volume 306 of the New England Journal of Medicine shows many instances of ordered-category data (about 20 per cent of the articles had such data) and no instance of analysis by the preferred methods presented here. We suggest that investigators who are unfamiliar with these methods should seek the assistance of a professional statistician when they must deal with such data.

Biological and medical investigations often use ordered categorical data. When two groups are to be compared and the data for the groups fall in three or more ordered categories, the Wilcoxon-Mann-Whitney (WMW) test uses information in the ordering to give a test that is usually powerful against shift alternatives. However, such applications of WMW often involve distributions for which extensive ties play an important role. Newly available computer programs for performing exact tests give deeper insights into the characteristics of the exact WMW distributions and the suitability of normal approximations. We offer practical advice, based on experience with published biomedical data sets and on numerical studies of hypothetical ordered tables, for the use of WMW and its normal approximations.

Meta-analyses often use a random-effects model to incorporate unexplained heterogeneity of study results. Trimmed versions of meta-analytic estimators for the risk difference, adapted from procedures designed for a random-effects analysis, can resist the impact of a few anomalous studies. A simulation study compared untrimmed and trimmed versions of four meta-analytic procedures that give weighted averages of risk differences. An adaptation of Winsorized estimates of components of variance gains some resistance to anomalous studies when estimating variability. The simulations found that a modified version of the DerSimonian-Laird estimator is attractive when risk differences reveal the added variability described by a random-effects model, and that a 20 per cent trimmed, weighted version of this procedure offers resistance against the impact of highly anomalous results. Among four trimmed procedures considered, the trimmed version of the modified DerSimonian-Laird estimator offers the best performance over a wide range of simulation designs and sample sizes. None of the methods, whether trimmed or untrimmed, is uniformly preferable. A published meta-analysis of a vaccination against TB provides data that serve to illustrate differences among the eight procedures.

A sorting of the statistical methods used by authors of the 760 research and review articles in Volumes 298 to 301 of The New England Journal of Medicine indicates that a reader who is conversant with descriptive statistics (percentages, means, and standard deviations) has statistical access to 58 per cent of the articles. Understanding t-tests increases this access to 67 per cent. The addition of contingency tables gives statistical access to 73 per cent of the articles. Familiarity with each additional statistical method gradually increases the percentage of accessible articles. Original Articles use statistical techniques more extensively than other articles in the Journal. Research studies based on a longitudinal design make heavier use of statistics than do those using a cross-sectional design. The tabulations in this study should aid clinicians and medical investigators who are planning their continuing education in statistical methods, and faculty who design or teach courses in quantitative methods for medical and health professionals.