Analysis of pediatric blood lead levels in New York City for 1970-1976.

A study was completed of more than 170,000 records of pediatric venous blood levels and supporting demographic information collected in New York City during 1970-1976. The geometric mean (GM) blood lead level shows a consistent cyclical variation superimposed on an overall decreasing trend with time for all ages and ethnic groups studied. The GM blood lead levels for blacks are significantly greater than those for either Hispanics or whites. Regression analysis indicates a significant statistical association between GM blood lead level and ambient air lead level, after appropriate adjustments are made for age and ethnic group. These highly significant statistical relationships provide extremely strong incentives and directions for research into casual factors related to blood lead levels in children.

Relation of pediatric blood lead levels to lead in gasoline.

Analysis of a large data set of pediatric blood lead levels collected in New York City (1970-1976) shows a highly significant association between geometric mean blood lead levels and the amount of lead present in gasoline sold during the same period. This association was observed for all age and ethnic groups studied, and it suggests that possible exposure pathways other than ambient air should be considered. Even without detailed knowledge of the exact exposure pathways, sufficient information now exists for policy analysis and decisions relevant to controls and standards related to lead in gasoline and its effect on subsets of the population.

Sensitivity of trends in geometric mean blood levels to random measurement errors.

A statistical model is investigated that expresses observations, such as blood lead levels, as an additive function of true levels and random measurement errors. Both empirical results (obtained from a series of computer simulation experiments) and theoretical results indicate how certain summary statistics for the observations vary in response to random measurement errors. Such results are applied to a very large data base of pediatric blood lead levels collected in New York City during 1970-1976, and they indicate that the observed trends in geometric mean blood lead levels are not significantly altered by the possible presence of measurement errors.

Norm Approximation Problems and Norm Statistics.

This paper explores a relation between various approximation problems (arising from fitting linear models to data) and corresponding statistical measures (norm statistics). It is established that for any optimal solution to an approximation problem defined with respect to a norm, the resulting residuals have zero as their norm statistic. This result holds whenever the underlying design matrix has a column of ones. An extension to the case of arbitrary design matrices is also considered.

Player Aggregation in Noncooperative Games.

A condition is given, under which subsets of the players of a noncooperative game can be combined into "aggregate players" without changing the set of equilibrium-point solutions of the game. The condition is that an individual player's payoff does not depend on the strategy choices of the other players forming the same aggregate player. "Approximate" versions of this result are also formulated and proven.

Optimal locations for a class of nonlinear, single-facility location problems on a network.

This paper investigates a class of single-facility location problems on an arbitrary network. Necessary and sufficient conditions are obtained for characterizing locally optimal locations with respect to a certain nonlinear objective function. This approach produces a number of new results for locating a facility on an arbitrary network, and in addition it unifies several known results for the special case of tree networks. It also suggests algorithmic procedures for obtaining such optimal locations.