Infradian variation in the incidence of giardiasis assessed by linear-nonlinear rhythmometry

The analysis of biological time series necessarily involves mathematical and physiologic techniques for purposes of data collection and interpretation, respectively. To assess a biologic rhythm in a given time series, one can first fit a cosine curve with a fixed period to the data by LLS. When the period is unknown or when there is more than one significant period, with no integral relation among them, LLS have to be replaced by NLLS. In applying the NLLS method, initial values for all the parameters in the model are first estimated by LLS. These are usually the overall M and the periods, As and 0s corresponding to each component found to be statistically significant by LLS. This combined approach was used in the search for infradian variability in the incidence of GD, the most common gastrointestinal parasitic disease in the USA at the present time. Monthly totals in ten consecutive years (1977 to 1986) of cases of GD detected in Minnesota (USA) were first fitted by LLS. The linear harmonic analysis shows the anticipated 1-year synchronized circannual rhythm with a period of 8766 hours (P less than .001) and other prominent components with periods of 7 (P = .038), 6 (P = .003), 5 (P = .001) and 3 (P less than .001) years, which were not anticipated. The rhythm parameters thus obtained are then used as initial values for the nonlinear method. Components of 5, 3. and 1 years are then detected by the NLLS approach, that also gives estimates and 95% confidence intervals for the period, the M, the A, and the 0 of each significant component. Of very great interest are infradian changes also seen time-macroscopically in other data on numbers of waterborne cases and outbreaks of GD. Awareness of the thus detected predictable variability in the incidence of GD with frequencies lower than a year may be important in the diagnosis and treatment of this infectious disorder.