Estimation of Relative Risk Under Variable Multiple Matching

When disease incidence is low, the odds ratio, which closely approximates relative risk, is estimated optimally in a closed form using a variable matching ratio in a retrospective design. The model also enables one to assess the homogeneity of the odds ratio from the same one matched sample. Analogous procedures are shown to hold for the prospective design.     

Tests of Special Structures on the Dispersion Matrix Associated with a Two-Way Mixed Effects Model

Exact and approximate methods are available in the literature to compare the fixed effect levels in an unbalanced two-way mixed model under the conventional distributional assumptions for random effects. However, as suggested by SHEFFÉ (1959) the conventional assumptions may not be justified in practice. Recently, KHATRI and PATEL (1992) have studied a model with an unstructured dispersion matrix associated with the random effects of which the conventional model is a special model. In this note we give likelihood ratio tests for testing some special structures on the dispersion matrix.     

Ten Years of the Relative Risk Model and Regional Scale Ecological Risk Assessment

It has been 10 years since the publication of the relative risk model (RRM) for regional scale ecological risk assessment. The approach has since been used successfully for a variety of freshwater, marine, and terrestrial environments in North America, South America, and Australia. During this period the types of stressors have been expanded to include more than contaminants. Invasive species, habitat loss, stream alteration and blockage, temperature, change in land use, and climate have been incorporated into the assessments. Major developments in the RRM have included the extensive use of geographical information systems, uncertainty analysis using Monte Carlo techniques, and its application to retrospective assessments to determine causation. The future uses of the RRM include assessments for forestry and conservation management, an increasing use in invasive species evaluation, and in sustainability. Developments in risk communication, the use of Bayesian approaches, and in uncertainty analyses are on the horizon.     

A Regional Multiple Stressor Risk Assessment of the Codorus Creek Watershed Applying the Relative Risk Model

The relative risk model (RRM) used in Port Valdez, AK, and in Oregon's Willamette/McKenzie Watershed was applied to the Codorus Creek Watershed in south central Pennsylvania. The assessment evaluated the relative risk model for its applicability for ranking ecological risks within the Codorus Creek Watershed. The Codorus Creek Watershed approach included ranking stressors and habitats for regions within the watershed. Geographical Information Systems were vital in compiling and comparing stressor and habitat spatial data from regions in the watershed. The risk of ecological impacts to degrade assessment endpoints were calculated and ranked by quantitatively determining the interactions of the stressors and habitats as defined in the conceptual site model. Uncertainty assessment was conducted and the impact upon the relative ranks and risk conclusions evaluated. To determine regional risks, risk management information was gathered identifying areas to be protected, areas of high stress, and areas where additional information is needed. The results supported the applicability of the RRM and suggested areas and stressors for restoration efforts in the Codorus Creek Watershed. Two critical sets of conclusions were drawn from the assessment. First, in the Codorus Creek Watershed, the most significant stressor is agriculture land use, the most significantly impacted endpoint is water quality, and the most vulnerable habitats are those for macroinvertebrates and warm-water fish. Second, this risk assessment demonstrates the feasibility of using the RRM for assessing risk from multiple stressors on habitats with multiple assessment endpoints in an eastern watershed.     

A Comparison of the Three Conditional Exact Tests in Two‐way Contingency Tables Using the Unconditional Exact Power

The conditional exact tests of homogeneity of two binomial proportions are often used in small samples, because the exact tests guarantee to keep the size under the nominal level. The Fisher's exact test, the exact chi‐squared test and the exact likelihood ratio test are popular and can be implemented in software StatXact. In this paper we investigate which test is the best in small samples in terms of the unconditional exact power. In equal sample cases it is proved that the three tests produce the same unconditional exact power. A symmetry of the unconditional exact power is also found. In unequal sample cases the unconditional exact powers of the three tests are computed and compared. In most cases the Fisher's exact test turns out to be best, but we characterize some cases in which the exact likelihood ratio test has the highest unconditional exact power. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Combining Estimates of Relative Risk Using the Negative Binomial Mode

The negative binomial distribution (N.B.) was previously proposed (BENNETT, 1981) in the estimation of and tests of significance for the relative risk (ψ) in prospective studies in epidemiology. This paper discusses the application of the N.B. model in combining estimates of ψ from a series of prospective studies and in statistical tests of the equality of these estimates.     

Unconditional Non-Asymptotic One-Sided Tests for Independent Binomial Proportions When the Interest Lies in Showing Non-Inferiority and/or Superiority

For two independent binomial proportions Barnard (1947) has introduced a method to construct a non-asymptotic unconditional test by maximisation of the probabilities over the ‘classical’ null hypothesis H₀= {(θ₁, θ₂) ∈ [0, 1]²: θ₁ = θ₂}. It is shown that this method is also useful when studying test problems for different null hypotheses such as, for example, shifted null hypotheses of the form H₀ = {(θ₁, θ₂) ∈ [0, 1]²: θ₂ ≤ θ₁ ± Δ } for non-inferiority and 1-sided superiority problems (including the classical null hypothesis with a 1-sided alternative hypothesis). We will derive some results for the more general ‘shifted’ null hypotheses of the form H₀ = {(θ₁, θ₂) ∈ [0, 1]²: θ₂ ≤ g(θ₁ )} where g is a non decreasing curvilinear function of θ₁. Two examples for such null hypotheses in the regulatory setting are given. It is shown that the usual asymptotic approximations by the normal distribution may be quite unreliable. Non-asymptotic unconditional tests (and the corresponding p-values) may, therefore, be an alternative, particularly because the effort to compute non-asymptotic unconditional p-values for such more complex situations does not increase as compared to the classical situation. For ‘classical’ null hypotheses it is known that the number of possible p-values derived by the unconditional method is very large, albeit finite, and the same is true for the null hypotheses studied in this paper. In most of the situations investigated it becomes obvious that Barnard's CSM test (1947) when adapted to the respective null space is again a very powerful test. A theorem is provided which in addition to allowing fast algorithms to compute unconditional non-asymptotical p-values fills a methodological gap in the calculation of exact unconditional p-values as it is implemented, for example, in Stat Xact 3 for Windows (1995).     

Ecological Risk Assessment of China's Freshwater Ecosystems Applying the Relative Risk Model: Toward an Ecosystem-Based Water Management in China

The relative risk model (RRM) was applied to evaluate the ecological risk characterization of the freshwater ecosystems in China, from both overall and region-specific levels. Ten large-scale river basins (further broken into 15 risk regions) in China were chosen as the study objects; 10 sources, two habitats, and seven endpoints were identified as risk components. The results reveal the status of ecosystem conditions, key ecological risk issues, and the spatial heterogeneity of the freshwater ecosystems in China. The policy implications for the ecosystem-based water management contained in the results are discussed. The results obtained in this article provide a deeper understanding of the ecological risk characterization of the freshwater ecosystems in China, and aid in promoting the applications of the RRM as the tool for ecosystem-based water management.     

Nonparametric Tests for Slope in Linear Regression Problems

In this paper some new, exactly distribution-free tests are offered for the hypothesis about the slope parameter in one-sample, two-sample, and several-sample simple linear regression problems. Asymptotic relative efficiencies of these test procedures are also studied.     

Tests of Bivariate Symmetry with a One-sided Alternative in the Analysis of Variance

We consider a two-factor experiment in which the factors have the same number of levels with a natural ordering among levels. We test the hypothesis that the effects of the two treatments are symmetric against a one-sided alternative using the likelihood ratio criteria. Test of the one-sided alternative as a null hypothesis against no restriction has also been studied. Exact distribution theory under the null hypothesis is derived and is shown to be a weighted mixture of chi-square distributions. An example is used to illustrate the procedure.     

Development of a Relative Ranking Risk Index for Risk Assessment in the Transportation of Liquefied Petroleum Gas in Mexico City's Metropolitan Area

The development of a relative ranking methodology created specifically for the assessment of the risk due transportation of Liquefied Petroleum Gas (LPG) in Mexico City is reported. Mexico City has a number of conditions that present specific challenges: Large population, varied geography, large consumption of LPG, and all sorts of vehicles, including those for LPG. Given Mexico's status as “emerging economy,” it is reasonable to assume that the main causes that promote accidents during transportation of LPG are quite different from those in developed countries. This issue was corroborated through information from official sources and from news media. Due to the lack of official data, a systematic collection of information on the media was performed. A relative ranking methodology was developed based on a systematic study to elucidate the main causes of accidents in Mexico and on the results derived from the integrated database from official data and the media. The weighting that made up the Risk Index for Transportation of LPG is based on the same database. A classification guide was created in order to harmonize criteria in the assessment of the parameters of the proposed risk index.     

A Model for Censored Survival Data When There is an Intervening Event

A model is discussed for incorporating information from a time-dependent covariable (an intervening event) and covariables independent of time into the analysis of survival data. In the model, it is assumed that individuals are potentially subject to two paths to failure, one including the intervening event and the other not. Additional assumptions are that failure times associated with the two paths are independent and that the time to failure subsequent to the intervening event is dependent on the intervening event time. Allowing the underlying hazard rates for the model to follow a WEIBULL form, use of the model and methods for fitting and hypothesis testing are illustrated by application to a follow-up study involving industrial workers where disability retirement was the intervening event. Extensions of the model to accommodate grouped survival data are presented.     

Point Estimation on Relative Risk under Inverse Sampling

When the underlying disease is rare, to control the coefficient of variation for the sample proportion of cases, we may wish to apply inverse sampling. In this paper, we derive the uniformly minimum variance unbiased estimator (UMVUE) of relative risk and its variance in closed form under inverse sampling. On the basis of a Monte Carlo simulation, we demonstrate that using the UMVUE of relative risk can substantially reduce the mean-squared-error of using the maximum likelihood estimator, especially when the number of index cases in both comparison samples is small. For a given fixed total cost, we include a program that can be used to find the optimal allocation for the number of index cases to minimize the variance of the UMVUE as well.