Statistical Methods in Medical Research

Objective: Presentation of effect sizes that can be interpreted in terms of clinical or practical significance is currently urged whenever statistical significance (a ‘p-value’) is reported in research journals. However, which effect size and how to interpret it are not yet clearly delineated. The present focus is on effect sizes indicating strength of correlation, that is, effect sizes that describe the strength of monotonic association between two random variables X and Y in a population.

Methods: A logical structure of measures of association is traced, showing the interrelationships among the many measures of association. Advantages and disadvantages of each are discussed.

Conclusions: Suggestions are made for the future use of measures of association in research to facilitate considerations of clinical significance, emphasizing distribution-free effect sizes such as the Spearman correlation coefficient and Kendall’s coefficient of concordance for ordinal versus ordinal associations, weighted and intraclass kappa for binary versus binary associations and risk difference (RD) for binary versus ordinal association.

The age-adjusted cancer rates are defined as the weighted average of the age-specific cancer rates, where the weights are positive, known, and normalized so that their sum is 1. Fay and Feuer developed a confidence interval for a single age-adjusted rate based on the gamma approximation. Fay used the gamma approximations to construct an F interval for the ratio of two age-adjusted rates. Modifications of the gamma and F intervals are proposed and a simulation study is carried out to show that these modified gamma and modified F intervals are more efficient than the gamma and F intervals, respectively, in the sense that the proposed intervals have empirical coverage probabilities less than or equal to their counterparts, and that they also retain the nominal level. The normal and beta confidence intervals for a single age-adjusted rate are also provided, but they are shown to be slightly liberal. Finally, for comparing two correlated age-adjusted rates, the confidence intervals for the difference and for the ratio of the two age-adjusted rates are derived incorporating the correlation between the two rates. The proposed gamma and F intervals and the normal intervals for the correlated age-adjusted rates are recommended to be implemented in the Surveillance, Epidemiology and End Results Program of the National Cancer Institute.

In a few cases, such as early pregnancy tests, the test results are dichotomous; many diagnostic tests, however, give results which are not binary. In the diagnosis of prostate cancer, prostate-specific antigen test result is on a continuous scale; or, in radiology, assessment of mammograms is on an ordinal scale. In such cases, the accuracy of the marker or test is often first summarized in a receiver operating characteristic (ROC) curve and then as the area under that curve. The area under the ROC curve, however, only shows the ‘potential’ of a marker; sooner or later, for practical uses, we still need to dichotomize the test result so that we can classify subjects as ‘diseased’ or ‘healthy’. Finding an ‘optimal’ cutpoint to dichotomize a continuous marker is desirable and is a very basic problem but, in all or most cases, cutpoints used in practice are arbitrary. The difficulty lies in our failure to define and justify a criterion for optimality. In this paper, we will propose a solution by maximizing a well-known parameter -the Youden’s Index -within the framework of the ROC curve.

The aim of this article is to discuss the distribution function of the number of subsequent users of a new treatment. A Bayesian approach is applied. Using the fact that the number of subsequent users of the new treatment will not be high, unless it is, in the statistical and also in the clinical sense, significantly better than the existing one, we obtain the distribution function of the number of subsequent users of a new treatment for which we assume the data have come from a normal distribution.

This paper presents an extension of a general parametric class of transitional models of order p. In these models, the conditional distribution of the current observation, given the present and past history, is a mixture of conditional distributions, each of them corresponding to the current observation, given each one of the p-lagged observations. Such conditional distributions are constructed using bivariate copula models which allow for a rich range of dependence suitable to model non-Gaussian time series. Fixed and time varying covariates can be included in the models. These models have the advantage of straightforward construction and estimation for the analysis of time series and more general longitudinal data. A poliomyelitis incidence data set is used to illustrate the proposed methods, contrary to other researches’ conclusions whose methods are mainly based on linear models, we find significant evidence of a decreasing trend in polio infection after accounting for seasonality.

In a comprehensive review, Benichou recently discussed adjusted estimators of the attributable risk (AR). Among these are model-based estimates, where adjustment for confounding factors is based on a regression model. Different model-based approaches have been developed for case-control and cohort studies. The purpose of this article is to provide a detailed review and illustration of model-based methods for both types of sampling. For case-control studies, we show that two previously proposed approaches for the common case of a logistic regression model are in fact identical. This allows a unified approach to the estimation of the adjusted AR, which also accommodates stratified sampling. For cohort studies, a loglinear model is proposed for the case where cross-sectional sampling allows estimation of the prevalence of exposure; the approach can also be used for stratified sampling when the prevalence is known or can be estimated. For both designs, the standard error of the adjusted AR is estimated using the delta method. Estimation of the generalized AR is also discussed for both types of sampling. Examples show that for even fairly complex models, the computations are practical using standard statistical software. The bootstrap provides an easily implemented alternative to the delta method for the computation of standard errors.