John D. Emerson

Use of Statistical Analysis in The New England Journal of Medicine

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.

A note on the Wilcoxon-Mann-Whitney test for 2 x k ordered tables

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.

Combining estimates of the odds ratio: the state of the art

Medical research commonly relies on the combination of 2 x 2 tables of counted data for making inferences about treatment effects or about the causes of disease. This article reviews point estimation and interval estimation for a common odds ratio. Traditional methods for providing these estimates face special challenges, and sometimes break down, when the data are sparse. Recent research provides practical alternatives to the traditional methods, and uses new computer algorithms to make them readily available in microcomputer software packages. This article illustrates and compares the various methods and offers recommendations for using the newer methods when analysing data sets of moderate size.

Leverage in Least Squares Additive-Plus-Multiplicative Fits for Two-Way Tables

Abstract An additive-plus-multiplicative model can describe both main effects and row x column interactions in two-way tables of data. When each cell contains exactly one observation, a least squares fit for this nonlinear model calculates the main effects, using means of rows and columns, and then fits a multiplicative term to the additive residuals, using the singular value decomposition. A natural extension of the hat matrix for a linear model yields a definition of leverage that provides insights about the impact of erroneous data values on the fit. Theoretical and numerical investigations reveal the complex nature of leverage for this nonlinear model.

Exploratory Methods for Choosing Power Transformations

Abstract Power transformations can often simplify the task of describing behavior in data that consist of positive measurements or counts. Tukeys diagnostic techniques based on two-dimensional plots are useful in searching for a suitable transformation in two types of data structures: multiple batches at different levels, and two-way tables. To these, we add plots for finding transformations in two other structures: a single batch, and y versus x. The basis for plots that indicate transformations for symmetrizing and for straightening is explored using second-order series approximations. For all four techniques, when the plot is roughly linear with slope 1 — p, the power of a transformation indicated by the plot is p. Each plot indicates whether any power transformation can be effective in achieving a desired objective.

Another Look at the Sign Test When Ties are Present: The Problem of Confidence Intervals

Abstract This article discusses several methods by which ties are treated in the usual sign test. The process of inverting a test to obtain a confidence interval shows that the different methods may lead to unusual intervals.

Effects of censoring on the robustness of exponential-based confidence intervals for median lifetime

Statistical procedures for constructing confidence intervals for median lifetime often rest on a distributional assumption for failure times.This paper explores the interplay between censoring levels and robustness for two construction procedures based on exponential lifetime, subject to general right-censoring. Data are simulated from nearby Weibull distributions. As expected, the simulations indicate that when the exponential assumption is not satisfied, observed coverage by the confidence intervals may differ substantially from the specified coverage level. The marked improvement in the robustness properties of the intervals as the level of censoring increases suggests questions for future research.