Zaldívar R, Ghai G L
Zentralbl Bakteriol B Hyg Krankenhaushyg Betriebshyg Prav Med. 1980;170(5-6):402-8.
The aim of this investigation was to develop a mathematical model of mean age, mean arsenic dietary dose, and age-specific prevalence rate for endemic chronic arsenic poisoning. Data on mean age (years), mean arsenic dietary dose (mg/kg body weight/day), and age-specific prevalence rate per 100,000 population for endemic chronic arsenic poisoning in Antofagasta Commune, northern Chile, for the 1968-1971 period, were collected. Endemic chronic arsenic poisoning means here chronic arsenical dermatosis associated with marked or sever symptoms (or signs) of chronic arsenic poisoning (chronic diarrhoea, hepatic cirrohsis, chronic bronchitis, bronchiectasis, recurrent broncho-pneumonia, cardiomegaly, systemic occlusive arterial disease, cerebral thrombosis, etc.) There was a strong positive correlation between age-specific prevalence rate per 100,000 population and mean arsenic dose (r = + 0.9593) and a negative correlation between prevalence rate and mean age (r = 0.8789). These findings show that the prevalence rate declines with the advancing age and increases with the increase of arsenic dose. A multiple linear regression model E(y) = alpha + beta X1 + gamma X2, where y represents the age-specific prevalence rate per 100,000 population, X1 the mean arsenic dose, and X2 the mean age, was fitted to the data. The estimates of the parameters (alpha, beta, and gamma) were obtained by minimizing the residual sum of squares sigma(y - alpha - beta X1 - gamma X2)2. The following multiple linear regression equation was obtained: Y = 202.161 + 8452.455 X1 - 2.394 X2. Of the total variability in the prevalence rate, 96.22 per cent was accounted for by the multiple regression.
本研究的目的是建立一个关于地方性慢性砷中毒的平均年龄、平均膳食砷摄入量和年龄别患病率的数学模型。收集了智利北部安托法加斯塔公社1968 - 1971年期间地方性慢性砷中毒的平均年龄（岁）、平均膳食砷摄入量（毫克/千克体重/天）以及每10万人口的年龄别患病率数据。这里的地方性慢性砷中毒是指与慢性砷中毒的明显或严重症状（或体征）（慢性腹泻、肝硬化、慢性支气管炎、支气管扩张、复发性支气管肺炎、心脏肥大、系统性闭塞性动脉疾病、脑血栓等）相关的慢性砷性皮炎。每10万人口的年龄别患病率与平均砷剂量之间存在强正相关（r = + 0.9593），患病率与平均年龄之间存在负相关（r = - 0.8789）。这些发现表明，患病率随着年龄的增长而下降，随着砷剂量的增加而上升。将多元线性回归模型E(y) = alpha + beta X1 + gamma X2应用于这些数据，其中y表示每10万人口的年龄别患病率，X1表示平均砷剂量，X2表示平均年龄。通过最小化残差平方和sigma(y - alpha - beta X1 - gamma X2)2来获得参数（alpha、beta和gamma）的估计值。得到了以下多元线性回归方程：Y = 202.161 + 8452.455 X1 - 2.394 X2。在患病率的总变异性中，96.22%可由多元回归解释。
