A graphical analysis of the interrelationships among waterborne asbestos, digestive system cancer and population density.

Abstract

Five statistical procedures were used to partial the correlation between waterborne asbestos and digestive site cancer for the putative effects of population density. These include: analysis based on a data subset with roughly homogeneous population density; standard residual analysis (partial correlation); conditional probability integral transformation; analysis based upon ranked data, and use of logarithmic transformation.Nonparametric regression graphical techniques are applied to examine the nature or shape of the asbestos-cancer dose-response curve. Evidence is presented that suggests that there is considerable difference between analyses involving nonhigh-density tracts and non-San Francisco tracts. Evidence is also presented that the modal-type nonparametric regression curve forks or bifurcates when adjustment is made for population density.

Model‐free data screening and cleaning

“…These, and many order statistic‐based (OSB) approaches, can help study data sets when n ≤ 200 4–6. When 0.01 ≤ p < 0.1, a bump hunting approach such as that described in Refs 7–9 can be applied, while, for larger values of p , mixture decomposition and cluster analysis techniques often help screen data 10–28…”

“…The N (0,0,1,1,0.25) distributed points shown exclusively would have been spaced most densely within the elliptical edge that encloses the points marked by X 's. (The estimator upon which Figure 2 was based, made use of findings described in Refs 6, 14, 17, 23–25, 27, 33–54. Alternate approaches that can be used include those described in Refs 45, 52, 54–73, 103, 104.…”

“…Other than the solid straight line, each of the curves shown in Figure 3 was associated, respectively, with the estimated mean, median, or mode of the same fifty estimates of the densities; f ( y | x j ), j = 1, 2, …, 50, conditioned on an equally spaced sequence of values; x j , j = 1, 2, … , 50; between the smallest and the largest observed x ‐coordinate 25. Here, as is typical of this data screening application, the mode‐based configuration cuts through the fog effectively while, due to its intrinsic stiffness combined with its sensitivity to outlying values, the ordinary least‐square‐based curve differs from the mode‐based curve substantially.…”

Modular Nonparametric Subsurvival Estimation

“…The study reported a dose-response relationship between exposure to asbestos in water and cancer incidence. Acting on a suggestion made at public hearings, Tarter, Cooper, and Freeman (1983) showed that when dose-response curves were calculated separately for San Francisco and non-San Francisco tracts, the relationship between water-borne asbestos and digestive cancer disappeared.…”