Chronolab: An Interactive Software Package for Chronobiologic Time Series Analysis Written for the Macintosh Computer

Abstract

Methods based on periodic regression have been designed for the detection of periodic components in short, noisy, and nonequidistant time series (as they are usually present in medicine and biology). The procedure consists of fitting a set of (cosine) curves to the data, with the analyst choosing the domain of trial periods to be analyzed and the distance between consecutive trial periods. We here describe an interactive program for least-squares rhythmometry written in C language for the Macintosh computer. For any given number of time series to be analyzed at once, the program is able to perform two different kinds of analyses: (a) linear in time, for the sequential fit of trial periods; and (b) linear in frequency, for the sequential fit of harmonic components from an initial fundamental period. For each series and for each trial period fitted to the data, the program gives the following information: fitted period; percent rhythm; p value from testing the assumption of zero amplitude; rhythm-adjusted mean or mesor, amplitude, and acrophase, each with corresponding standard errors and 95% confidence intervals when the component is statistically significant; and (when required by the analyst) p values from tests of sinusoidality, normality of residuals, and homogeneity of variance. Additionally, the program provides a summary report for each time series analyzed, including descriptive statistics such as the number of data analyzed for that series, minimum, maximum, arithmetic mean, standard deviation, standard error, 90% range, and 50% range. The analyst is also able to transform the data before doing any rhythmometric analysis. Transformations already integrated in the program include square root, logarithm, inverse, data as percentage of mean, data as percentage of mesor, and elimination of values outside ±3 SD from the mean. When several periods are suspected to be statistically significant, a multiple-component analysis can be also used by the concomitant least-squares fit of several harmonics. The program allows the simultaneous analysis of several periods in several variables from several individuals, with limitations depending solely on internal memory availability and speed requirements from the user. When series from different subjects or different variables in the same subject are available for analysis, a parameter test also included in the program can be used for comparison of rhythm characteristics at any given period. All information required in a single analysis is given by the analyst in the form of self-explanatory commands grouped in different “menus.” This program is an expandable tool designed for general use in chronobiologic applications, including modeling and simulation of biologic time series, chronobiologic signal processing, and rhythmo-metric parameter testing. Key Words: Rhythmometry–Macintosh computer– Interactive program–Multiple-component analysis–Parameter test–Linear least squares–Nonlinear least squares.