Mathematical model of mean age, mean arsenic dietary dose and age-specific prevalence rate from endemic chronic arsenic poisoning: a human toxicology study.

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.