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A two-stage approach has recently been proposed to assess confounding by copollutants or other variables in time-series epidemiology studies for airborne particulate matter (PM), using independent series from different cities. In the first stage of the proposed method, two regression models are fitted for each city in the analysis. The first relates the health effect to the putative causal variable such as PM without including any copollutant or confounder. The other first-stage model relates a putative confounding variable to PM. In the second stage of the analysis, the estimated city-specific regression slopes for the health-effect-versus-PM model are regressed against the estimated city-specific regression slopes for the confounder-versus-PM model. Under the proposed method, a nonzero intercept estimate in the second-stage regression would be interpreted as indicating a direct pathway from PM to the health effect, and a nonzero slope estimate would be interpreted as indicating at least partial confounding of PM with the putative confounder. A simple counterexample using an additional copollutant variable shows that inferences based on this method could be misleading.

The integrated exposure uptake biokinetic model for lead in children was developed to provide plausible blood lead distributions corresponding to particular combinations of multimedia lead exposure. The model is based on a set of equations that convert lead exposure (expressed as micrograms per day) to blood lead concentration (expressed as micrograms per deciliter) by quantitatively mimicking the physiologic processes that determine blood lead concentration. The exposures from air, food, water, soil, and dust are modeled independently by several routes. Amounts of lead absorbed are modeled independently for air, food, water, and soil/dust, then combined as a single input to the blood plasma reservoir of the body. Lead in the blood plasma reservoir, which includes extracellular fluids, is mathematically allocated to all tissues of the body using age-specific biokinetic parameters. The model calculation provides the estimate for blood lead concentration for that age. This value is treated as the geometric mean of possible values for a single child, or the geometric mean of expected values for a population of children exposed to the same lead concentrations. The distribution of blood lead concentrations about this geometric mean is estimated using a geometric standard deviation, typically 1.6, derived from the analysis of well-conducted community blood studies.

Although formal hypothesis tests provide a convenient framework for displaying the statistical results of empirical comparisons, standard tests should not be used without consideration of underlying measurement error structure. As part of the validation process, predictions of individual blood lead concentrations from models with site-specific input parameters are often compared with blood lead concentrations measured in field studies that also report lead concentrations in environmental media (soil, dust, water, paint) as surrogates for exposure. Measurements of these environmental media are subject to several sources of variability, including temporal and spatial sampling, sample preparation and chemical analysis, and data entry or recording. Adjustments for measurement error must be made before statistical tests can be used to empirically compare environmental data with model predictions. This report illustrates the effect of measurement error correction using a real dataset of child blood lead concentrations for an undisclosed midwestern community. We illustrate both the apparent failure of some standard regression tests and the success of adjustment of such tests for measurement error using the SIMEX (simulation-extrapolation) procedure. This procedure adds simulated measurement error to model predictions and then subtracts the total measurement error, analogous to the method of standard additions used by analytical chemists.

Clustering of mutant pollen grains in a population of normal pollen due to premeiotic mutational events complicates translating mutation frequencies into rates. Embryo ontogeny in barley will be described and used to illustrate the formation of such mutant clusters. The nature of the statistics for mutation frequency will be described from a study of the reversion frequencies of various waxy mutants in barley. Computer analysis by a "jackknife" method of the reversion frequencies of a waxy mutant treated with the mutagen sodium azide showed a significantly higher reversion frequency than untreated material. Problems of the computer analysis suggest a better experimental design for pollen mutation experiments. Preliminary work on computer modeling for pollen development and mutation will be described.