Lawrence H. Cox

Suppression Methodology and Statistical Disclosure Control

Abstract This article discusses theory and method of complementary cell suppression and related topics in statistical disclosure control. Emphasis is placed on the development of methods that are theoretically broad but also practical to implement. The approach draws from areas of discrete mathematics and linear optimization theory.

A review of statistical methods for the meteorological adjustment of tropospheric ozone

Abstract A variety of statistical methods for meteorological adjustment of ozone have been proposed in the literature over the last decade for purposes of forecasting, estimating ozone time trends, or investigating underlying mechanisms from an empirical perspective. The methods can be broadly classified into regression, extreme value, and space–time methods. We present a critical review of these methods, beginning with a summary of what meteorological and ozone monitoring data have been considered and how they have been used for statistical analysis. We give particular attention to the question of trend estimation, and compare selected methods in an application to ozone time series from the Chicago area. We conclude that a number of approaches make useful contributions to the field, but that no one method is most appropriate for all purposes and all meteorological scenarios. Methodological issues such as the need for regional-scale analysis, the nonlinear dependence of ozone on meteorology, and extreme value analysis for trends are addressed. A comprehensive and reliable methodology for space–time extreme value analysis is attractive but lacking.

A Constructive Procedure for Unbiased Controlled Rounding

Abstract It is often necessary to round values in a two-way statistical table, that is, replace each value by an adjacent integer multiple of an appropriately chosen integer rounding base. Such is the case when statistical data are to be presented in increments, such as personal income presented in multiples of

Network Models for Complementary Cell Suppression

1,000 or retail sales in units of

Applications of Transportation Theory to Statistical Problems

1 million, or when counts must be adjusted prior to release to reduce the risk of statistical disclosure (Cox, McDonald, and Nelson 1986). It is desirable that the rounded array also be additive along rows and columns and to the grand total. A table satisfying these conditions is called a controlled rounding of the original table. If, as is often the case, entries that are already integer multiples of the base must remain unchanged, the controlled rounding is said to be zero-restricted. Controlled rounding is an important adjunct to statistical methods for adjusting contingency tables such as iterative proportional fitting (Ireland and Kullback 1968), because suc...

On properties of multi-dimensional statistical tables

Abstract Complementary cell suppression is a method for protecting data pertaining to individual respondents from statistical disclosure when the data are presented in tabular form. Several mathematical methods for complementary suppression have been proposed in the statistical literature; some have been implemented in large-scale data processing environments by national statistical agencies. Each method has either theoretical or computational limitations. This article presents solutions to the complementary cell suppression problem based on linear optimization over a mathematical network. These methods are shown to be optimal for certain problems and to offer theoretical and practical advantages, including comprehensiveness, comprehensibleness, and computational efficiency.

Estimation of regional trends in sulfur dioxide over the eastern United States

Abstract The two-dimensional controlled selection problem and the problem of maximizing the overlap of old and new primary sampling units after restratification and change of selection probabilities have been studied for several decades but have never been completely solved until now. Using transportation theory, complete solutions are obtained here for these and other problems. The solution to the controlled selection problem is based on a specific transportation model that was originally developed, in a previous paper by Cox and Ernst (1982), to solve completely the controlled rounding problem, namely the problem of optimally rounding real-valued entries in a two-way tabular array to adjacent integer values in a manner that preserves the tabular (additive) structure of the array. This model is also applied to other statistical problems, such as raking and statistical disclosure for frequency count tabulations and microdata.

PROTECTING CONFIDENTIALITY IN SMALL POPULATION HEALTH AND ENVIRONMENTAL STATISTICS

Abstract Statistical data often can be conveniently organized in tabular form for display and analysis. Counts are nonnegative integers, and often magnitude data take nonnegative integer values. Two-dimensional tables enjoy mathematical properties on which important statistical methods depend, e.g., for stratified sampling, imputation, disclosure limitation, and sampling and fitting log-linear models to contingency tables. We demonstrate that many desirable mathematical properties, and consequently their associated statistical methods, are not extendible in all cases to three or higher dimensions. We demonstrate that ill-behaved examples are ubiquitous, abundant and consequently not mathematical anomalies. To address these shortcomings, we provide necessary and sufficient conditions and an empirical test for the existence of an n-dimensional table with prescribed (n−1)-dimensional marginal totals (feasibility) and a characterization of n-dimensional tables with prescribed (n−1)-dimensional marginals for which continuous bounds on integer-valued entries exist and are integer (integrality).

Linear sensitivity measures in statistical disclosure control

Emission reductions were mandated in the Clean Air Act Amendments of 1990 with the expectation of concomitant reductions in ambient concentrations of atmospherically-transported pollutants. To evaluate the effectiveness of the legislated emission reductions using monitoring data, this paper proposed a two-stage approach for the estimation of regional trends and their standard errors. In the first stage, a generalized model (GAM) is fitted to airborne sulfur dioxide (SO2) data at each of 35 sites in the eastern United States to estimate the form and magnitude of the site-specific trend (defined as percent total change) from 1989 to 1995. This analysis is designed to adjust the SO2 data for the influences of meteorology and season. In the second stage, the estimated trends are treated as samples with site-dependent measurement error from a Gaussian random field with a stationary covariance function. Kriging methodology is adapted to construct spatially-smoothed estimates of the true trend for three large regions in the eastern U.S. Finally, a Bayesian analysis with Markov Chain Monte Carlo (MCMC) methods is used to obtain regional trend estimates and their standard errors, which take account of the estimation of the unknown covariance parameters as well as the stochastic variation of the random fields. Both spatial estimation techniques produced similar results in terms of regional trend and standard error. Copyright

Balancing Quality and Confidentiality for Multivariate Tabular Data

Public policy decisions are fuelled by information. Often, this information is in the form of statistical data. Questions stemming from public health and environmental concerns often arise or are studied within small subgroups of a population. Continuing improvements in the performance and availability of computing resources, including geographic information systems, and the need to better understand environmental exposures and consequent health effects create increasing demand for small population health and environmental data. These demands are at odds with the need to preserve the privacy and data confidentiality of persons, groups or organizations covered by the data. Although confidentiality issues for demographic and economic data are well-studied and are gaining maturity for health data, these issues are only beginning to emerge for environmental data and combined environmental-health data. The aim of this paper is to provide a framework for that examination. Herein we examine confidentiality problems posed by small population health and environmental data, summarize available statistical methods, and propose avenues for the solution of new problems.