Mathematical description and use in forecasting of the caries curve

Caries curves drawn from empirical prevalences (DMFT counts) of US and Hungarian males as well as females, and British male-female combined samples were satisfactorily described by the transformed truncated Cauchy function: y = 1 + c [-1/2 + 1/pi arc tan (a x + b)]. The parameters a, b, and c, respectively, were determined by a computer with the least squares' method. Of these descriptive models, prevalences at specified ages (covered in the original reports) were read, and additionally the half-life values and maximum yearly relative increments of decay (with the age of their occurrence). The mean deviation of all individual readings in the five models from the observed prevalences was 3.6% only. In each sample, thereafter, relying upon empirical DMF counts in only five juvenile cohorts, analogous models, referred to as predictory, were constructed by the computer, and their extrapolated right tails were compared both with the empirical DMF counts and with the descriptive models. Slight deviations were experienced, the mean deviation of all readings from the empirical counts being 4.5%. Accordingly, predictions of future caries prevalence (in later adolescence in the US samples, and adulthood in all five ones) were feasible relying on DMFT counts. By the predictory models a trend to improving dental health was demonstrated in the American samples (based on the 1971-74 survey) whereas for the other three populations a further rise of caries prevalence was forecast in adults. Merits and limitations of such predictions as well as an improved new procedure used in the comparisons ("penalty points method"), taking into account clinical requirements, were discussed.