Donald C. Olivier

Covariance Analysis of Censored Survival Data Using Log-Linear Analysis Techniques

Abstract This paper unites two different fields, survival and contingency table analysis, in a single analytical framework based on the log-linear model. We demonstrate that many currently popular approaches to modeling survival data, including the approaches of Glasser (1967), Cox (1972), Breslow (1972, 1974), and Holford (1976), can be handled by using existing computer packages developed for the log-linear analysis of contingency table data. More important, we demonstrate that the log-linear modeling system used to characterize counted data structures directly characterizes survival data as well. Counted data methodologies for testing and estimation are also applicable here. Much of the theoretical basis for this work has been independently derived by Holford (1980) and Aitkin and Clayton (1980). The emphasis in this paper is not to develop new methodologies, but rather to present new uses and interpretations for already familiar methodologies.

The structure of the color space in naming and memory for two languages

Abstract Ss from two cultures with markedly different color terminologies were tested on two color-judgment tasks. One was a nonverbal task of color matching from memory, while the other was a verbal task of color-naming. Both tasks were performed by 41 American Ss and 40 New Guinea Dani (who have a basically two-term color language). Multidimensional scaling based upon the four resulting sets of data yielded structures that were more similar under the memory condition than under the naming condition. For neither culture were equally distant colors confused in memory more within than across name boundaries. Retention of color images in short-term memory appears to be unaffected by wide cultural differences in the semantic reference of color words.

Metrics on spaces of finite trees

Abstract With the increasing popularity of hierarchical clustering methods in behavioral science, there is a need for ways of quantitatively comparing different tree structures on the same set of items. We employ lattice-theoretic methods to construct a variety of metrics on spaces of trees and to analyze their properties. Certain of these metrics are applied to data from Fillenbaum and Rapoport (1971) on the semantic structure of common English kin terms. This application shows that tree metrics can be used to select a componential analysis which is maximally consistent with an empirically derived set of trees.

Incidence of depression and anxiety: the Stirling County Study.

Prevalence studies in psychiatric epidemiology out-number incidence investigations by a wide margin. This report gives descriptive information about the incidence of depression and anxiety disorders in a general population. Using data gathered in a 16-year follow-up of an adult sample selected as part of the Stirling County Study (Canada), the incidence of these types of disorders was found to be approximately nine cases per 1,000 persons per year. The data suggest that for every man who became ill for the first time with one of these disorders, three women became ill. Incidence tended to be higher among relatively young persons. These incidence rates are consistent with prevalence rates of approximately 10 per cent to 15 per cent for depression and anxiety disorders aggregated together, given an estimated average duration of illness of about 10 years. It is concluded that these incidence rates are fairly realistic in view of evidence that disorders of these types tend to be chronic.

Computer diagnosis of depression and anxiety: the Stirling County Study.

A computer programme (DPAX) was constructed for a longitudinal study of psychiatric epidemiology in Stirling County (Canada). It identifies disorders involving the syndromes of depression and anxiety based on responses given in structured questionnaire interviews. The programme follows a diagnostic algorithm that uses criteria for: (1) essential features; (2) number, frequency, and pattern of associated symptoms; (3) impairment; and (4) duration. The programme reproduces case evaluations provided by psychiatrists, as conveyed by a sensitivity of 92% and a specificity of 98%.

Mortality risk and psychiatric disorders: results of a general physician survey

SummaryAs part of the Stirling County Study (Canada), general physicians were interviewed to identify the psychiatric disorders experienced by a sample of adults selected in 1952. Based on information about vital status gathered 16 years later, we found that those with a psychiatric disorder at the beginning of the study experienced 1.6 times the expected number of deaths. The effect in regard to premature mortality and accidental deaths was particularly strong. Four of six categories of psychiatric diagnoses were significantly associated with mortality. In terms of standardized mortality ratios, depression had the highest and anxiety the lowest risk in this general population. The findings are discussed as providing historical background from the 1950s and 1960s for studying trends.

Methods for Exact Goodness-of-Fit Tests

Abstract Numerous goodness-of-fit tests with asymptotic chi-squared distributions have been proposed for discrete multivariate data, and there has been much discussion about using asymptotic results for computing critical values when there are small expected cell values. Although exact methods would be preferred in these situations, it generally is believed that such methods are computationally intractable. We propose methods for calculating exact distributions and significance levels for goodness-of-fit statistics that are computationally feasible over a wide range of models. In particular, the distribution for a simple multinomial model can be evaluated in polynomial time. For composite null hypotheses, we calculate the distribution conditional on the sufficient statistics for the nuisance parameters. We calculate the characteristic function of a distribution and invert the characteristic function using the fast Fourier transform (FFT). Our approach emphasizes the relationship between exact methods and ...

Methods for the Analysis of Contingency Tables with Large and Small Cell Counts

Abstract The traditional practice has been to analyze contingency tables using asymptotic χ2 approximations for the tail probability of certain test statistics even when the approximation is known to be poor. For two-dimensional tables Pearsons X 2 statistic is most commonly used, whereas for multidimensional tables the likelihood ratio test is preferred because it makes it easy to test series of nested hypotheses. When asymptotic approximations are not adequate, exact tests are preferred. Recent advances in algorithms have broadened the range of two-dimensional tables for which satisfactory answers can be obtained (Baglivo, Olivier, and Pagano 1985; Mehta and Patel 1983, 1986; Pagano and Taylor-Halvorsen 1981). In this article we propose algorithms that use a mixture of exact and asymptotic techniques to calculate tail probabilities. Our methods can be used with several different test statistics for two-dimensional and multidimensional contingency-table models and hence further broaden the set of tables...

Analysis of discrete data: rerandomization methods and complexity

Analysis of discrete data, and especially contingency table data, plays a central role in biostatistics. Traditional methods rely on approximations based on asymptotic results which are very powerful but not always appropriate. In this article we show that efficient rerandomization methods may be developed for many commonly used models and tests: multinomial testing, specifically goodness-of-fit and max tests; and goodness-of-fit of log-linear models for contingency tables. The feasibility (complexity) of these algorithms is a function of the sufficient statistics for the models. By contrast, algorithms which require the explicit enumeration of all outcomes in the sample space are exponential in the degrees of freedom, and are usually not feasible except when sample sizes are unrealistically small. The algorithms we present are different from recently proposed methods since we show how to calculate permutation distributions of commonly used statistics rather than calculating p-values for exact tests, and we emphasize underlying probability formulas rather than implementation details.