Evaluation of the accuracy of multilevel analysis parameter estimates for intra-cluster correlation in correlated binary data

Many studies in biostatistics deal with binary data. Some of these studies involve correlated observations, which can complicate the analysis of the resulting data. Studies of this kind typically arise when a high degree of commonality exists between test subjects. If there exists a natural hierarchy in the data, multilevel analysis is an appropriate tool for the analysis. Two examples are the measurements on identical twins, or the study of symmetrical organs or appendages such as in the case of ophthalmic studies. Although this type of matching appears ideal for the purposes of comparison, analysis of the resulting data while ignoring the effect of intra-cluster correlation has been shown to produce biased results.^ This paper will explore the use of multilevel modeling of simulated binary data with predetermined levels of correlation. Data will be generated using the Beta-Binomial method with varying degrees of correlation between the lower level observations. The data will be analyzed using the multilevel software package MlwiN (Woodhouse, et al, 1995). Comparisons between the specified intra-cluster correlation of these data and the estimated correlations, using multilevel analysis, will be used to examine the accuracy of this technique in analyzing this type of data. ^

RUNOFF FROM COAL PILES: EFFECTS ON THE ENVIRONMENT AND THE PUBLIC'S HEALTH

The use of coal for fuel in place of oil and natural gas has been increasing in the United States. Typically, users store their reserves of coal outdoors in large piles and rainfall on the coal creates runoffs which may contain materials hazardous to the environment and the public's health. To study this hazard, rainfall on model coal piles was simulated, using deionized water and four coals of varying sulfur content. The simulated surface runoffs were collected during 9 rainfall simulations spaced 15 days apart. The runoffs were analyzed for 13 standard water quality parameters, extracted with organic solvents and then analyzed with capillary column GC/MS, and the extracts were tested for mutagenicity with the Ames Salmonella microsomal assay and for clastogenicity with Chinese hamster ovary cells.^ The runoffs from the high-sulfur coals and the lignite exhibited extremes of pH (acidity), specific conductance, chemical oxygen demand, and total suspended solids; the low-sulfur coal runoffs did not exhibit these extremes. Without treatment, effluents from these high-sulfur coals and lignite would not comply with federal water quality guidelines.^ Most extracts of the simulated surface runoffs contained at least 10 organic compounds including polycyclic aromatic hydrocarbons, their methyl and ethyl homologs, olefins, paraffins, and some terpenes. The concentrations of these compounds were generally less than 50 (mu)g/l in most extracts.^ Some of the extracts were weakly mutagenic and affected both a DNA-repair proficient and deficient Salmonella strain. The addition of S9 decreased the effect significantly. Extracts of runoffs from the low-sulfur coal were not mutagenic.^ All extracts were clastogenic. Extracts of runoffs from the high-sulfur coals were both clastogenic and cytotoxic; those from the low-sulfur coal and the lignite were less clastogenic and not cytotoxic. Clastogenicity occurred with and without S9 activation. Chromosomal lesions included gaps, breaks and exchanges. These data suggest a relationship between the sulfur content of a coal, its mutagenicity and also its clastogenicity.^ The runoffs from actual coal piles should be investigated for possible genotoxic effects in view of the data presented in this study.^